# Adami, Sheikh-Jabbari, Taghiloo ## Gravitational Stress Tensor and Current at Null Infinity in Three Dimensions \[Links: [arXiv](https://arxiv.org/abs/2405.00149), [PDF](https://arxiv.org/pdf/2405.00149.pdf)\] \[Abstract: We develop the framework that reveals the intrinsic conserved stress tensor and current associated with the null infinity of a three-dimensional (3d) asymptotically flat spacetime. These are, respectively, canonical conjugates of degenerate metric and Ehresmann connection of the boundary [[0419 Carrollian CFT|Carrollian]] geometry. Their conservation reproduces the Bondi-mass and angular momentum conservation equations if the asymptotic boundary is endowed with a torsional affine connection that we specify. Our analysis and results shed further light on the 3d [[0491 Flat holography|flat holography]]; the stress tensor and current give rise to an asymptotically flat [[0228 Fluid-gravity correspondence|fluid/gravity correspondence]]. The requirement of a well-defined 3d action principle yields Schwarzian action at null infinity governing the dynamics induced by reparametrizations over the [[0022 Celestial sphere|celestial circle]], in accord with the codimension 2 holography of 3d flat spacetimes.\] # Adamo, Bu, Tourkine, Zhu ## Eikonal amplitudes on the celestial sphere \[Links: [arXiv](https://arxiv.org/abs/2405.15594), [PDF](https://arxiv.org/pdf/2405.15594)\] \[Abstract: [[0516 Celestial correlators|Celestial scattering amplitudes]] for massless particles are [[0079 Mellin transform|Mellin transforms]] of momentum-space scattering amplitudes with respect to the energies of the external particles, and behave as conformal correlators on the celestial sphere. However, there are few explicit cases of well-defined celestial amplitudes, particularly for gravitational theories: the mixing between low- and high-energy scales induced by the Mellin transform generically yields divergent integrals. In this paper, we argue that the most natural object to consider is the gravitational amplitude dressed by an oscillating phase arising from semi-classical effects known as eikonal exponentiation. This leads to gravitational celestial amplitudes which are analytic, apart from a set of poles at integer negative conformal dimensions, whose degree and residues we characterize. We also study the large conformal dimension limits, and provide an asymptotic series representation for these celestial eikonal amplitudes. Our investigation covers two different frameworks, related by eikonal exponentiation: $2\to2$ scattering of scalars in flat spacetime and $1\to1$ scattering of a probe scalar particle in a curved, stationary spacetime. These provide data which any putative celestial dual for Minkowski, [[0117 Shockwave|shockwave]] or black hole spacetimes must reproduce. We also derive dispersion and monodromy relations for these celestial amplitudes and discuss Carrollian eikonal-probe amplitudes in curved spacetimes.\] # Afxonidis, Karch, Murdia ## The boundary entropy function for interface conformal field theories \[Links: [arXiv](https://arxiv.org/abs/2412.05381), [PDF](https://arxiv.org/pdf/2412.05381)\] \[Abstract: In 1+1 dimensional [[0548 Boundary CFT|conformal field theory with a boundary]] the boundary contribution to the [[0301 Entanglement entropy|entanglement entropy]] is determined by a single number $g$ effectively counting the boundary degrees of freedom. In contrast, in 1+1 dimensional [[0065 Defect CFT|interface CFTs]] the corresponding quantity is a non-trivial *function* depending on the position of the interval relative to the interface, giving access to much more detailed information about the defect. In this work we determined this $g$-function in several examples using holography and derive some of its basic properties from holography and [[0218 Strong subadditivity|strong subadditivity]].\] # Akers, Sorce ## Relative state-counting for semiclassical black holes \[Links: [arXiv](https://arxiv.org/abs/2404.16098), [PDF](https://arxiv.org/pdf/2404.16098.pdf)\] \[Abstract: It has been shown that entropy differences between certain states of perturbative quantum gravity can be computed without specifying an ultraviolet completion. This is analogous to the situation in classical statistical mechanics, where entropy differences are defined but absolute entropy is not. Unlike in classical statistical mechanics, however, the entropy differences computed in perturbative quantum gravity do not have a clear physical interpretation. Here we construct a family of perturbative black hole states for which the entropy difference can be interpreted as a relative [[0248 Black hole microstates|counting of states]]. Conceptually, this paper begins with the algebra of mass fluctuations around a fixed black hole background, and points out that while this is a type I [[0415 Von Neumann algebra|algebra]], it is not a factor and therefore has no canonical definition of entropy. As in previous work, coupling the mass fluctuations to quantum matter embeds the mass algebra within a type II factor, in which entropy differences (but not absolute entropies) are well defined. It is then shown that for microcanonical wavefunctions of mass fluctuation, the type II entropy difference equals the logarithm of the dimension of the extra Hilbert space that is needed to map one microcanonical window to another using gauge-invariant unitaries. The paper closes with comments on type II entropy difference in a more general class of states, where the [[0301 Entanglement entropy|von Neumann entropy]] difference does not have a physical interpretation, but "one-shot" entropy differences do.\] # Akers, Wei ## Background independent tensor networks \[Links: [arXiv](https://arxiv.org/abs/2402.05910), [PDF](https://arxiv.org/pdf/2402.05910.pdf)\] \[Abstract: Conventional holographic [[0054 Tensor network|tensor networks]] can be described as toy holographic maps constructed from many small linear maps acting in a spatially local way, all connected together with ''background entanglement'', i.e. links of a fixed state, often the maximally entangled state. However, these constructions fall short of modeling real holographic maps. One reason is that their ''areas'' are trivial, taking the same value for all states, unlike in gravity where the geometry is dynamical. Recently, new constructions have ameliorated this issue by adding degrees of freedom that ''live on the links''. This makes areas non-trivial, equal to the background entanglement piece plus a new positive piece that depends on the state of the link degrees of freedom. Nevertheless, this still has the downside that there is background entanglement, and hence it only models relatively limited code subspaces in which every area has a definite minimum value given by the background entanglement. In this note, we simply point out that a version of these constructions goes one step further: they can be background independent, with no background entanglement in the holographic map. This is advantageous because it allows tensor networks to model holographic maps for larger code subspaces. In addition to pointing this out, we address some subtleties involved in making it work and point out a nice connection it offers to recent discussions of random CFT data.\] # Ahmad, Klinger, Lin ## Semifinite von Neumann algebras in gauge theory and gravity \[Links: [arXiv](https://arxiv.org/abs/2407.01695), [PDF](https://arxiv.org/pdf/2407.01695)\] \[Abstract: [[0415 Von Neumann algebra|von Neumann algebras]] have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through the commutation theorem, rendering it a useful tool for constructing gauge invariant algebras. The crossed product of a Type III algebra with its modular automorphism group is semifinite, which means that the crossed product regulates divergences in local quantum field theories. In this letter, we find a sufficient condition for the semifiniteness of the crossed product of a type III algebra with any locally compact group containing the modular automorphism group. Our condition surprisingly implies the centrality of the [[0416 Modular Hamiltonian|modular flow]] in the symmetry group, and we provide evidence for the necessity of this condition. Under these conditions, we construct an associated trace which computes physical expectation values. We comment on the importance of this result and and its implications for subregion physics in gauge theory and gravity.\] # Ahmed, Lowenstein ## Perturbative Unorientable JT Gravity and Matrix Models \[Links: [arXiv](https://arxiv.org/abs/2403.13968), [PDF](https://arxiv.org/pdf/2403.13968)\] \[Abstract: We consider an orthogonal polynomial formulation of the double scaling limit of multicritical [[0197 Matrix model|matrix models]] in the $\beta=1$ Dyson-Wigner class. They capture the physics of 2D quantum gravity coupled to minimal matter on [[0624 Unorientable manifold|unorientable]] surfaces, otherwise called unoriented minimal strings. We derive a formula for the density of states valid to all orders in perturbation theory. We show how to define an interpolation between the multicritical models and that a certain interpolation among an infinite number of them provides an alternative definition of unoriented [[0050 JT gravity|JT gravity]]. We discuss the strengths and weaknesses of our formulation.\] # Albertini, Platt, Wiseman ## Towards a uniqueness theorem for static black holes in Kaluza-Klein theory with small circle size \[Links: [arXiv](https://arxiv.org/abs/2410.20967), [PDF](https://arxiv.org/pdf/2410.20967)\] \[Abstract: [[0169 Kaluza-Klein|Kaluza-Klein]] theory, by which we mean vacuum gravity in 5-dimensions, with asymptotics that are a product of a circle with Minkowski spacetime, has a variety of different static black hole solutions; localized black holes and the homogeneous and inhomogeneous black strings. There is currently no [[0455 Black hole uniqueness theorems|uniqueness theorem]] for the solutions, and for fixed circle size multiple solutions with the same mass co-exist. Intuitively for small circle sizes we might expect the theory truncates to become 4-dimensional, and correspondingly the only black holes are the homogeneous black strings. Thus we conjecture that for fixed mass and sufficiently small circle size, the only black holes are homogeneous ones. Here we give evidence that this is indeed the case. Firstly we introduce a toy scalar field model with a potential that allows tachyonic behaviour. Putting this theory on a product of Minkowski with a circle gives an analogous set of static homogeneous and inhomogeneous solutions to that of the black holes. We prove that solutions must be homogeneous for small circle sizes, the analog of our conjecture for this toy model. A weaker statement that is straightforward to derive is a bound on how inhomogeneous a solution can be - putting this scalar theory in a large but finite cavity, a norm of the wavefunction of the Kaluza-Klein modes can be shown to vanish in the small circle limit. Turning to the full gravitational theory, we employ a metric ansatz that imposes static axisymmetry, encompasses the homogeneous and inhomogeneous black strings (but not the localized solutions) and allows us to measure inhomogeneity of a solution. Employing a finite cavity and imposing boundary conditions that are compatible with homogeneity we show a similar result; the norm of certain Kaluza-Klein modes is bounded by the circle size, providing evidence that our conjecture is true.\] # Alday, Nocchi, Ruzziconi, Srikant ## Carrollian Amplitudes from Holographic Correlators \[Links: [arXiv](https://arxiv.org/abs/2406.19343), [PDF](https://arxiv.org/pdf/2406.19343)\] \[Abstract: Carrollian amplitudes are flat space amplitudes written in position space at null infinity which can be re-interpreted as correlators in a putative dual [[0419 Carrollian CFT|Carrollian CFT]]. We argue that these amplitudes are the natural objects obtained in the [[0454 Flat holography from AdS-CFT|flat space limit]] of AdS Lorentzian boundary correlators. The flat limit is taken entirely in position space by introducing Bondi coordinates in the bulk. From the bulk perspective, this procedure makes it manifest that the flat limit of any Witten diagram is the corresponding flat space Feynman diagram. It also makes explicit the fact that the flat limit in the bulk is implemented by a Carrollian limit at the boundary. We systematically analyse tree-level two, three and four-point correlators. Familiar features such as the distributional nature of Carrollian amplitudes and the presence of a bulk point singularity arise naturally as a consequence of requiring a finite and non-trivial Carrollian limit.\] # Ali, Suneeta ## A local Generalized second law in crossed product constructions \[Links: [arXiv](https://arxiv.org/abs/2404.00718), [PDF](https://arxiv.org/pdf/2404.00718)\] \[Abstract: In this paper, we show a local [[0082 Generalised second law|generalized second law]] (the generalized entropy is nondecreasing) in crossed product constructions for maximally extended static and Kerr black holes using modular theory. The new ingredient is the use of results from a recent paper discussing the entropy of the algebra of operators in subregions of arbitrary spacetimes. These results rely on an assumption which we show is true in our setting. However, we do assume as in that paper, that the gravitational constraints are implemented on each partial Cauchy slice. In this version, we have also added a discussion on inclusion of an observer in the calculation. In the last part of the paper, we look at [[0416 Modular Hamiltonian|modular Hamiltonians]] of deformed half-spaces in a class of static spacetimes, including the Schwarzschild spacetime. These are computed using path integrals, and we primarily compute them to investigate whether these non-local modular Hamiltonians can be made local by subtracting off pieces from the algebra and its commutant, as has been surmised in the literature. Along the way, the [[0417 Averaged null energy condition|averaged null energy condition]] (ANEC) also follows in this class of spacetimes.\] # Alessio, Arzano ## A new pairwise boost quantum number from celestial states \[Links: [arXiv](https://arxiv.org/abs/2403.03760), [PDF](https://arxiv.org/pdf/2403.03760.pdf)\] \[Abstract: Infrared effects in the scattering of particles in gravity and electrodynamics entail an exchange of relativistic angular momentum between pairs of particles and the gauge field. Due to this exchange particles can carry an asymptotically non-vanishing "pairwise" boost-like angular momentum proportional to the product of their couplings to the field. At the quantum level this asymptotic angular momentum suggests the existence of a new quantum number carried by multi-particle states. We argue that such quantum number is related to a modification of the action of the generators of Lorentz transformations on multi-particle states. We derive such a modification using a group-theoretic argument based on the little group of the [[0148 Conformal basis|conformal primary basis]] for asymptotic states. The corresponding representation is an extension of the ordinary multi-particle Fock representation of the Poincaré group. The new multi-particle states belonging to such representation no longer factorize into tensor products of one-particle states. Viewed from a gravitational point of view, our results provide evidence for a universal breakdown of the description of multi-particle sates in terms of Fock space due to infrared back-reaction.\] # Almheiri, Goel, Hu ## Quantum gravity of the Heisenberg algebra \[Links: [arXiv](https://arxiv.org/abs/2403.18333), [PDF](https://arxiv.org/pdf/2403.18333)\] \[Abstract: We consider a simplified model of [[0503 Double-scaled SYK|double scaled SYK]] (DSSYK) in which the Hamiltonian is the position operator of the Harmonic oscillator. This model captures the high temperature limit of DSSYK but could also be defined as a quantum theory in its own right. We study properties of the emergent geometry including its dynamics in response to inserting matter particles. In particular, we find that the model displays de Sitter-like properties such as that infalling matter reduces the rate of growth of geodesic slices between the two boundaries. The simplicity of the model allows us to compute the full generating functional for correlation functions of the length mode or any number of matter operators. We provide evidence that the effective action of the geodesic length between boundary points is non-local. Furthermore, we use the on-shell solution for the geodesic lengths between any two boundary points to reconstruct an effective bulk metric and reverse engineer the dilaton gravity theory that generates this metric as a solution.\] # Almheiri, Popov ## Holography on the Quantum Disk \[Links: [arXiv](https://arxiv.org/abs/2401.05575), [PDF](https://arxiv.org/pdf/2401.05575.pdf)\] \[Abstract: Motivated by recent study of [[0503 Double-scaled SYK|DSSYK]] and the non-commutative nature of its bulk dual, we review and analyze an example of a non-commutative spacetime known as the quantum disk proposed by L. Vaksman. The quantum disk is defined as the space whose isometries are generated by the quantum algebra $U_q(\mathfrak{su}_{1,1})$. We review how this algebra is defined and its associated group $SU_q(1,1)$ that it generates, highlighting its non-trivial coproduct that sources bulk non-commutativity. We analyze the structure of holography on the quantum disk and study the imprint of non-commutativity on the putative boundary dual.\] # Alonso-Monsalve, Harlow, Jefferson ## Phase space of Jackiw-Teitelboim gravity with positive cosmological constant \[Links: [arXiv](https://arxiv.org/abs/2409.12943), [PDF](https://arxiv.org/pdf/2409.12943)\] \[Abstract: In this paper we construct the classical phase space of [[0050 JT gravity|Jackiw-Teitelboim gravity]] with positive cosmological constant on spatial slices with circle topology. This turns out to be somewhat more intricate than in the case of negative cosmological constant; this phase space has many singular points and is not even Hausdorff. Nonetheless, it admits a group-theoretic description which is quite amenable to quantization.\] # Altland, Kim, Micklitz, Rezaei, Sonner, Verbaarschot ## Quantum Chaos on Edge \[Links: [arXiv](https://arxiv.org/abs/2403.13516), [PDF](https://arxiv.org/pdf/2403.13516)\] \[Abstract: In recent years, the physics of many-body [[0008 Quantum chaos|quantum chaotic]] systems close to their ground states has come under intensified scrutiny. Such studies are motivated by the emergence of model systems exhibiting chaotic fluctuations throughout the entire spectrum (the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] (SYK) model being a renowned representative) as well as by the physics of holographic principles, which likewise unfold close to ground states. Interpreting the edge of the spectrum as a quantum critical point, here we combine a wide range of analytical and numerical methods to the identification and comprehensive description of two different universality classes: the near edge physics of ''sparse'' and the near edge of ''dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension, which is exponentially small or algebraically small in the sparse and dense case, respectively. Notable representatives of the two classes are generic chaotic many-body models (sparse) and single particle systems, invariant random matrix ensembles, or chaotic gravitational systems (dense). While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different. Considering the SYK model as a representative of the sparse class, we apply a combination of field theory and exact diagonalization to a detailed discussion of its edge spectrum. Conversely, [[0050 JT gravity|Jackiw-Teitelboim gravity]] is our reference model for the dense class, where an analysis of the [[0555 Gravitational path integral|gravitational path integral]] and [[0579 Random matrix theory|random matrix theory]] reveal universal differences to the sparse class, whose implications for the construction of holographic principles we discuss.\] # Anastasiou, Araya, Avila, Guijosa, Patino-Lopez ## Extrinsic Holographic Renormalization for a Scalar Field \[Links: [arXiv](https://arxiv.org/abs/2405.15186), [PDF](https://arxiv.org/pdf/2405.15186)\] \[Abstract: In the context of the holographic correspondence, we introduce a purely extrinsic [[0209 Holographic renormalisation|renormalization]] prescription, exemplified with the case of a minimally-coupled scalar field in AdS space. The counterterms depend only on the field and its radial derivatives. Consistency with the Dirichlet variational principle is achieved considering that the asymptotic structure of asymptotically locally AdS spacetimes relates the tangential and radial derivatives of the field. Crucially, as seen from a path integral definition of the bulk partition function involved in the standard GKPW formula, this relation is valid beyond the saddle. We find that the extrinsic renormalization prescription is maximally efficient when the scalar field is massless, which is suggestive of a connection with the Kounterterm method for renormalization of pure gravity.\] # Anegawa, Tamaoka ## Black Hole Singularity and Timelike Entanglement \[Links: [arXiv](https://arxiv.org/abs/2406.10968), [PDF](https://arxiv.org/pdf/2406.10968)\] \[Abstract: We study [[0606 Timelike entanglement|timelike]] and conventional [[0301 Entanglement entropy|entanglement entropy]] as potential probes of black hole singularities via the[[0001 AdS-CFT|AdS/CFT]] correspondence. Using an analytically tractable example, we find characteristic behavior of holographic timelike entanglement entropy when the geometry involves a curvature singularity. We also observe interesting phenomena that, in some particular setups, holographic timelike and conventional entanglement entropy are determined from multiple [[0335 Complex metrics|complex saddle]] points, which fall outside the assumptions of the [[2013#Lewkowycz, Maldacena|Lewkowycz-Maldacena]] type argument.\] # Antonini, Rath (Essay) ## Do holographic CFT states have unique semiclassical bulk duals? \[Links: [arXiv](https://arxiv.org/abs/2408.02720), [PDF](https://arxiv.org/pdf/2408.02720)\] \[Abstract: We discuss a situation where a holographic CFT state has multiple semiclassical bulk duals. In our example, a given holographic state has two simple, semiclassical descriptions, one with a closed universe, constructed using the [[0555 Gravitational path integral|gravitational path integral]], and one without a closed universe, constructed using the [[0590 Extrapolate dictionary|extrapolate dictionary]]. This highlights an ambiguity in the [[0001 AdS-CFT|AdS/CFT]] dictionary. We propose various options for resolving this tension although none are perfectly satisfactory. We also discuss what this implies for the black hole interior and the gravitational path integral.\] # Aoki, Balog, Shimada ## Derivation of the GKP-Witten relation by symmetry without Lagrangian \[Links: [arXiv](https://arxiv.org/abs/2411.16269), [PDF](https://arxiv.org/pdf/2411.16269)\] \[Abstract: We derive the [[0001 AdS-CFT|GKP-Witten relation]] in terms of correlation functions by symmetry without referring to a Lagrangian or the large $N$ expansion. By constructing bulk operators from boundary operators in conformal field theory (CFT) by the conformal smearing, we first determine bulk-boundary 2-pt functions for an arbitrary spin using both conformal and bulk symmetries, then evaluate their small $z$ behaviors, where $z$ is the ($d+1$)-th coordinate in the bulk. Next, we explicitly determine small $z$ behaviors of bulk-boundary-boundary 3-pt functions also by the symmetries, while small $z$ behaviors of correlation functions among one bulk and $n$ boundary operators with $n\ge 3$ are fixed by the [[0030 Operator product expansion|operator product expansion]] (OPE). Combining all results, we construct the GKP-Witten relation in terms of these correlation functions at all orders in an external source $J$. We compare our non-Lagrangian approach with the standard approach employing the bulk action. Our results indicate that the GKP-Witten relation holds not only for holographic CFTs but also for generic CFTs as long as certain conditions are satisfied.\] # Apolo, Belin, Bintanja ## Searching for strongly coupled AdS matter with multi-trace deformations \[Links: [arXiv](https://arxiv.org/abs/2401.15141), [PDF](https://arxiv.org/pdf/2401.15141.pdf)\] \[Abstract: [[0122 Holographic CFT|Holographic CFTs]] admit a dual emergent description in terms of semiclassical [[0554 Einstein gravity|general relativity]] minimally coupled to matter fields. While the gravitational interactions are required to be suppressed by the Planck scale, the matter sector is allowed to interact strongly at the AdS scale. From the perspective of the dual CFT, this requires breaking large-$N$ factorization in certain sectors of the theory. Exactly marginal multi-trace deformations are capable of achieving this while still preserving a consistent large-$N$ limit. We probe the effect of these deformations on the bulk theory by computing the relevant four-point functions in conformal perturbation theory. We find a simple answer in terms of a finite sum of conformal blocks, indicating that the correlators display no bulk-point singularities. This implies that the matter of the bulk theory is made strongly coupled by boundary terms rather than local bulk interactions. Our results suggest that holographic CFTs that describe strongly coupled AdS matter cannot be continuously connected to conventional holographic CFTs where all correlators factorize in the large-$N$ limit.\] # Arenas-Henriquez, Diaz, Rivera-Betancour ## Generalized Fefferman-Graham gauge and boundary Weyl structures \[Links: [arXiv](https://arxiv.org/abs/2411.12513), [PDF](https://arxiv.org/pdf/2411.12513)\] \[Abstract: In the framework of AdS/CFT correspondence, the [[0011 Fefferman-Graham expansion|Fefferman-Graham]] (FG) gauge offers a useful way to express asymptotically anti-de Sitter spaces, allowing a clear identification of their boundary structure. A known feature of this approach is that choosing a particular conformal representative for the boundary metric breaks explicitly the boundary scaling symmetry. Recent developments have shown that it is possible to generalize the FG gauge to restore boundary Weyl invariance by adopting the Weyl-Fefferman-Graham gauge. In this paper, we focus on [[0002 3D gravity|three-dimensional gravity]] and study the emergence of a boundary Weyl structure when considering the most general AdS boundary conditions introduced by Grumiller and Riegler. We extend the [[0209 Holographic renormalisation|holographic renormalization]] scheme to incorporate Weyl covariant quantities, identifying new subleading divergences appearing at the boundary. To address these, we introduce a new codimension-two counterterm, or corner term, that ensures the finiteness of the gravitational action. From here, we construct the quantum-generating functional, the holographic stress tensor, and compute the corresponding Weyl anomaly, showing that the latter is now expressed in a full Weyl covariant way. Finally, we discuss explicit applications to holographic integrable models and accelerating black holes. For the latter, we show that the new corner term plays a crucial role in the computation of the Euclidean on-shell action.\] # Arora, Headrick, Lawrence, Sasieta, Wolfe ## Geometric Surprises in the Python's Lunch Conjecture \[Links: [arXiv](https://arxiv.org/abs/2401.06678), [PDF](https://arxiv.org/pdf/2401.06678.pdf)\] \[Abstract: A bulge surface, on a time reflection-symmetric Cauchy slice of a holographic spacetime, is a non-minimal extremal surface that occurs between two locally minimal surfaces homologous to a given boundary region. According to the [[0196 Python's lunch|python's lunch]] conjecture of Brown et al., the bulge's area controls the complexity of bulk reconstruction, in the sense of the amount of post-selection that needs to be overcome for the reconstruction of the entanglement wedge beyond the outermost extremal surface. We study the geometry of bulges in a variety of classical spacetimes, and discover a number of surprising features that distinguish them from more familiar extremal surfaces such as [[0007 RT surface|Ryu-Takayanagi surfaces]]: they spontaneously break spatial isometries, both continuous and discrete; they are sensitive to the choice of boundary infrared regulator; they can self-intersect; they probe entanglement shadows and orbifold singularities; and they probe the compact space in AdS$_p\times S^q$. These features imply, according to the python's lunch conjecture, novel qualitative differences between complexity and entanglement in the holographic context. We also find, surprisingly, that extended black brane interiors have a non-extensive complexity; similarly, for multi-boundary wormhole states, the complexity pleateaus after a certain number of boundaries have been included.\] # Arrechea, Neri, Liberati ## Inner horizon instability via the trace anomaly effective action \[Links: [arXiv](https://arxiv.org/abs/2411.14964), [PDF](https://arxiv.org/pdf/2411.14964)\] \[Abstract: In quantum field theory applied to black hole spacetimes, substantial evidence suggests that the Unruh and Hartle-Hawking vacuum states become singular at Cauchy horizons. This raises essential questions regarding the impact of quantum field backreaction on the stability of Cauchy horizons in static scenarios and inner horizons in evolving spacetimes. To approach this problem, we employ analytic approximations to the renormalized stress-energy tensor (RSET) of quantum fields in four dimensions. Specifically, we utilize the anomaly-induced effective action, which generates four-dimensional approximate RSETs through a pair of auxiliary scalar fields that satisfy higher-order equations of motion. The boundary conditions imposed on these auxiliary fields yield RSETs with leading-order terms that mimic the behaviour of different vacuum states. This study presents the first application of the anomaly-induced effective action method to Reissner-Nordström black hole interiors, evaluating its accuracy, applicability, and connections with prior RSET approximations. Among the range of possible states accessible through this method, we found none that remain regular at both the event and Cauchy horizons, aligning with theoretical expectations. The method shows strong agreement with exact four-dimensional RSET results for the Hartle-Hawking state but does not fully capture the unique characteristics of the Unruh state in Reissner-Nordström spacetimes. We conclude by suggesting possible extensions to address these limitations.\] # Astaneh ## Holographic Action Principle for $T\bar{T}$-deformation \[Links: [arXiv](https://arxiv.org/abs/2407.16391), [PDF](https://arxiv.org/pdf/2407.16391)\] \[Abstract: We explore the action principle for the holographic $T\bar{T}$-[[0170 TTbar|deformation]]. We develop a scheme in which one can holographically reproduce the action of the [[0562 Liouville theory|Liouville theory]] deformed by $T\bar{T}$-insertion. This scheme necessitates considering the bending energy of the finite cut-off surface. Following our proposal, one observes a perfect match between the actions of deformed theory on the field theory and gravity sides.\] # Bagchi, Dhivakar, Dutta ## 3D Stress Tensor for Gravity in 4D Flat Spacetime \[Links: [arXiv](https://arxiv.org/abs/2408.05494), [PDF](https://arxiv.org/pdf/2408.05494)\] \[Abstract: Three dimensional (3d) [[0419 Carrollian CFT|Carrollian CFTs]] are potential co-dimension one holographic duals of 4d asymptotically flat spacetimes that live on the whole of the null boundary. In this paper, we show that the local stress tensor of the 3d Carrollian conformal theory (without any additional sources) constructed in terms of the geometric structure at asymptotic null infinity naturally encodes both the leading and subleading [[0009 Soft theorems|soft graviton theorems]]. We relate the 3d Carroll stress tensor to the 2d Celestial one and show how the 3d version naturally localises the non-local 2d [[0010 Celestial holography|Celestial]] stress tensor. We also comment on the relation with stress tensors in relativistic 3d CFTs and connections to the [[0454 Flat holography from AdS-CFT|flat limit]] of [[0001 AdS-CFT|AdS/CFT]].\] # Balasubramanian, Craps, Hernandez, Khramtsov, Knysh (Oct) ## Factorization of the Hilbert space of eternal black holes in general relativity \[Links: [arXiv](https://arxiv.org/abs/2410.00091), [PDF](https://arxiv.org/pdf/2410.00091)\] \[Abstract: We generalize recent results in two-dimensional Jackiw-Teitelboim gravity to study [[0514 Lorentzian factorisation problem|factorization of the Hilbert space]] of eternal black holes in quantum gravity with a negative cosmological constant in any dimension. We approach the problem by computing the trace of two-sided observables as a sum over a recently constructed family of semiclassically well-controlled black hole microstates. These microstates, which contain heavy matter shells behind the horizon and form an overcomplete basis of the Hilbert space, exist in any theory of gravity with general relativity as its low energy limit. Using this representation of the microstates, we show that the trace of operators dual to functions of the Hamiltonians of the left and right holographic CFTs factorizes into a product over left and right factors to leading order in the semiclassical limit. Under certain conditions this implies factorization of the Hilbert space.\] # Balasubramanian, Craps, Hernandez, Khramtsov, Knysh (Dec) ## Counting microstates of out-of-equilibrium black hole fluctuations \[Links: [arXiv](https://arxiv.org/abs/2412.06884), [PDF](https://arxiv.org/pdf/2412.06884)\] \[Abstract: We construct and count the [[0248 Black hole microstates|microstates]] of out-of-equilibrium eternal AdS black holes in which a shell carrying an order one fraction of the black hole mass is emitted from the past horizon and re-absorbed at the future horizon. Our microstates have semiclassical interpretations in terms of matter propagating behind the horizon. We show that they span a Hilbert space with a dimension equal to the exponential of the horizon area of the intermediate black hole. This is consistent with the idea that, in a non-equilibrium setting, entropy is the logarithm of the number of microscopic configurations consistent with the dynamical macroscopic state. In our case, therefore, the entropy should measure the number of microstates consistent with a large and atypical macroscopic black hole fluctuation due to which part of the early time state becomes fully known to an external observer.\] # Balasubramanian, Kang, Murdia, Ross ## Signals of multiparty entanglement and holography \[Links: [arXiv](https://arxiv.org/abs/2411.03422), [PDF](https://arxiv.org/pdf/2411.03422)\] \[Abstract: We study [[0264 Multi-partite entanglement|multiparty entanglement]] signals, which are functions of a quantum state that are non-zero only when the state has multiparty entanglement. We consider known signals of three- and four-party entanglement, and propose new signals for four- and higher-party entanglement. We make some remarks on their general properties, but mainly focus on using holographic states in AdS$_3$/CFT$_2$ as a test case to explore their properties. For both the AdS vacuum and multiboundary wormhole states, we find that the multiparty entanglement signals are generically non-zero and of order one in units of the [[0033 Central charge|central charge]] of the dual CFT, revealing substantial multiparty entanglement. In the large-horizon limit of multiboundary wormhole states, however, the signals for three or more parties become small indicating the short-range nature of entanglement.\] # Balasubramanian, Magan, Nandi, Wu ## Spread complexity and the saturation of wormhole size \[Links: [arXiv](https://arxiv.org/abs/2412.02038), [PDF](https://arxiv.org/pdf/2412.02038)\] \[Abstract: Recent proposals equate the size of Einstein-Rosen bridges in [[0050 JT gravity|JT gravity]] to spread complexity of a dual, [[0503 Double-scaled SYK|double-scaled SYK]] theory (DSSYK). We show that the auxiliary ''chord basis'' of these proposals is an extrapolation from a sub-exponential part of the finite-dimensional physical Krylov basis of a spreading [[0574 Thermofield double|thermofield double state]]. The physical tridiagonal Hamiltonian coincides with the DSSYK approximation on the initial Krylov basis, but deviates markedly over an exponentially large part of the state space. We non-perturbatively extend the identification of ER bridge size and spread complexity to the complete Hilbert space, and show that it saturates at late times. We use methods for tridiagonalizing random Hamiltonians to study all universality classes to which large $N$ SYK theories and JT gravities can belong. The saturation dynamics depends on the universality class, and displays ''white hole'' physics at late times where the ER bridge shrinks from maximum size to a plateau. We describe extensions of our results to higher dimensions.\] # Ball ## Currents in Celestial CFT \[Links: [arXiv](https://arxiv.org/abs/2407.13558), [PDF](https://arxiv.org/pdf/2407.13558)\] \[Abstract: In this review we discuss currents in [[0010 Celestial holography|celestial CFT]] and the consistency of their naive symmetry algebras. In particular we study in detail the Jacobi identity and the double residue condition for soft insertions, hard momentum space insertions, and hard celestial insertions. In the latter case we introduce the notion of a "hard current" in CFT and work through examples in the 2D critical Ising model. The current algebra of hard insertions in pure Einstein gravity is a slight conceptual generalization of the familiar $w_{1+\infty}$-wedge current algebra. We also review branch cut terms in the [[0114 Celestial OPE|celestial OPE]], which indicate new primary content and were previously missed until recently. We work through an explicit toy example illustrating the mechanism by which such branch cut terms can arise. These branch cut terms prevent a symmetry interpretation but are fully compatible with a consistent OPE.\] # Ball, Law, Wong ## Dynamical Edge Modes and Entanglement in Maxwell Theory \[Links: [arXiv](https://arxiv.org/abs/2403.14542), [PDF](https://arxiv.org/pdf/2403.14542)\] \[Abstract: Previous work on black hole partition functions and entanglement entropy suggests the existence of "[[0556 Edge mode|edge]]" degrees of freedom living on the (stretched) horizon. We identify a local and "shrinkable" boundary condition on the stretched horizon that gives rise to such degrees of freedom. They can be interpreted as the Goldstone bosons of gauge transformations supported on the boundary, with the electric field component normal to the boundary as their symplectic conjugate. Applying the covariant phase space formalism for manifolds with boundary, we show that both the symplectic form and Hamiltonian exhibit a bulk-edge split. We then show that the thermal edge partition function is that of a codimension-two ghost compact scalar living on the horizon. In the context of a de Sitter static patch, this agrees with the edge partition functions found by Anninos et al. in arbitrary dimensions. It also yields a 4D [[0301 Entanglement entropy|entanglement entropy]] consistent with the conformal anomaly. Generalizing to Proca theory, we find that the prescription of Donnelly and Wall reproduces existing results for its edge partition function, while its classical phase space does not exhibit a bulk-edge split.\] # Banados, Bianchi, Munoz, Skenderis ## AdS amplitudes as CFT correlators \[Links: [arXiv](https://arxiv.org/abs/2412.09503), [PDF](https://arxiv.org/pdf/2412.09503)\] \[Abstract: We show that [[0105 AdS amplitudes|AdS amplitudes]] are CFT correlators to all orders in the loop expansion by showing that they obey the conformal [[0106 Ward identity|Ward identities]]. In particular, we provide explicit formulas for the constants and functions of cross-ratios that determine the CFT correlators in terms of bulk data.\] # Banerjee ## Boundary operators in asymptotically flat space-time \[Links: [arXiv](https://arxiv.org/abs/2406.06690), [PDF](https://arxiv.org/pdf/2406.06690)\] \[Abstract: In [[2023#Jain, Kundu, Minwalla, Parrikar, Prabhu, Shrivastava]] the authors have proposed an interesting framework for studying holography in flat space-time. In this note we explore the relationship between their proposal and the [[0010 Celestial holography|Celestial Holography]]. In particular, we find that in both the massive and in the massless cases the asymptotic boundary limit of the bulk time-ordered Green's function $G$ is related to the Celestial amplitudes by an integral transformation. In the massless case the integral transformation reduces to the well known [[0039 Shadow transform|shadow transformation]] of the celestial amplitude. Now the relation between the asymptotic limit of $G$ and the celestial amplitudes suggests that in asymptotically flat space-time if the scattering states are described by the conformal primary basis (and it's analytic continuation in dimension $\Delta$) then the boundary operators holographically dual to the (massless) bulk fields are given by the shadow transformation of the [[0148 Conformal basis|conformal primary]] operators living on the [[0022 Celestial sphere|celestial sphere]]. In other words, conformal primary operators themselves are not boundary operators but their shadows are. This is consistent with the fact that in celestial holography the boundary stress tensor is given by the shadow transformation of the subleading soft graviton.\] # Banerjee, Basu, Bhatkar ## Light transformation: A Celestial and Carrollian perspective \[Links: [arXiv](https://arxiv.org/abs/2407.08379), [PDF](https://arxiv.org/pdf/2407.08379)\] \[Abstract: In this paper, we first study the consequence of spacetime translations and Lorentz transformations on [[0114 Celestial OPE|Celestial CFT OPEs]]. Working with the [[0412 Light transform|light transforms]] of the operators belonging to the modified Mellin basis, we found that the leading order singularity in the OPE of such operators could be fixed purely using Poincaré symmetries owing to the non-trivial action of the translations on these operators. The OPE coefficient is then fixed using the soft limit of the correlation functions. We check that this singular structure obtained from symmetries is consistent with the OPE limit of three-point functions. This approach could potentially be useful for studying Celestial CFT without adverting to bulk physics. As another goal, we explore the significance of light transformation in [[0419 Carrollian CFT|Carrollian CFTs]]. In the special cases we considered, we show that light transformation equips us with a map between two branches of Carroll CFT in $d=3$ dimension at the level of correlation functions in the near coincident limit.\] # Banerjee, Erdmenger, Karl ## Non-Locality induces Isometry and Factorisation in Holography \[Links: [arXiv](https://arxiv.org/abs/2411.09616), [PDF](https://arxiv.org/pdf/2411.09616)\] \[Abstract: In holography, two manifestations of the black hole [[0131 Information paradox|information paradox]] are given by the non-isometric nature of the bulk-boundary map and by the factorisation puzzle. By considering time-shifted microstates of the eternal black hole, we demonstrate that both these puzzles may be simultaneously resolved by taking into account non-local quantum corrections that correspond to wormholes arising from state averaging. This is achieved by showing, using a resolvent technique, that the resulting Hilbert space for an eternal black hole in Anti-de Sitter space is finite-dimensional with a discrete energy spectrum. The latter gives rise to a transition to a type I [[0415 Von Neumann algebra|von Neumann algebra]].\] # Banihashemi, Jacobson ## On the lapse contour \[Links: [arXiv](https://arxiv.org/abs/2405.10307), [PDF](https://arxiv.org/pdf/2405.10307)\] \[Abstract: The [[0555 Gravitational path integral|gravitational path integral]] is usually implemented with a covariant action by analogy with other gauge field theories, but the gravitational case is different in important ways. A key difference is that the integrand has an essential singularity, which occurs at zero lapse where the spacetime metric degenerates. The lapse integration contour required to impose the local time reparametrization constraints must run from $-\infty$ to $+\infty$, yet must not pass through zero. This raises the question: what is the correct integration contour, and why? We study that question by starting with the reduced phase space path integral, which involves no essential singularity. We observe that if the momenta are to be integrated before the lapse, to obtain a configuration space path integral, the lapse contour should pass below the origin in the complex lapse plane. This contour is also consistent with the requirement that quantum field fluctuation amplitudes have the usual short distance vacuum form, and with obtaining the Bekenstein-Hawking horizon entropy from a Lorentzian path integral. We close with a discussion of related issues, including potential obstacles to deriving a nonperturbative covariant gravitational path integral.\] # Bao, Furuya, Naskar ## Towards a complete classification of holographic entropy inequalities \[Links: [arXiv](https://arxiv.org/abs/2409.17317), [PDF](https://arxiv.org/pdf/2409.17317)\] \[Abstract: We propose a deterministic method to find all [[0259 Holographic entropy cone|holographic entropy inequalities]] and prove the completeness of our method. We use a triality between holographic entropy inequalities, contraction maps and partial cubes. More specifically, the validity of a holographic entropy inequality is implied by the existence of a contraction map, which we prove to be equivalent to finding an isometric embedding of a contracted graph. Thus, by virtue of the completeness of the contraction map proof method, the problem of finding all holographic entropy inequalities is equivalent to the problem of finding all contraction maps, which we translate to a problem of finding all image graph partial cubes. We give an algorithmic solution to this problem and characterize the complexity of our method. We also demonstrate interesting by-products, most notably, a procedure to generate candidate quantum entropy inequalities.\] # Bao, Hung, Jiang, Liu ## QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow \[Links: [arXiv](https://arxiv.org/abs/2412.12045), [PDF](https://arxiv.org/pdf/2412.12045)\] \[Abstract: By analyzing the non-perturbative RG flows that explicitly preserve given symmetries, we demonstrate that they can be expressed as quantum path integrals of the [[0661 SymTFT|SymTFT]] in one higher dimension. When the symmetries involved include Virasoro defect lines, such as in the case of $T\bar{T}$ deformations, the RG flow corresponds to the 3D quantum gravitational path integral. For each 2D CFT, we identify a corresponding ground state of the SymTFT, from which the [[0345 Wheeler-DeWitt (WdW) equation|Wheeler-DeWitt equation]] naturally emerges as a non-perturbative constraint. These observations are summarized in the slogan: **SymQRG = QG**. The recently proposed exact discrete formulation of [[0562 Liouville theory|Liouville theory]] in [1] allows us to identify a universal SymQRG kernel, constructed from quantum $6j$ symbols associated with $U_q(SL(2,\mathbb{R}))$. This kernel is directly related to the quantum path integral of the [[0596 Virasoro TQFT|Virasoro TQFT]], and manifests itself as an exact and analytical 3D background-independent MERA-type holographic [[0054 Tensor network|tensor network]]. Many aspects of the AdS/CFT correspondence, including the [[0249 Factorisation problem|factorization puzzle]], admit a natural interpretation within this framework. This provides the first evidence suggesting that there is a universal holographic principle encompassing AdS/CFT and topological holography. We propose that the non-perturbative AdS/CFT correspondence is a *maximal* form of topological holography.\] # Bao, Jiang, Naskar ## Subregion duality, wedge classification and no global symmetries in AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/2408.04016), [PDF](https://arxiv.org/pdf/2408.04016)\] \[Abstract: We study various notions of '[[0219 Entanglement wedge reconstruction|subregion duality]]' in the context of [[0001 AdS-CFT|AdS/CFT]]. We highlight the differences between the 'background wedge' and the 'operator reconstruction wedges,' providing a resolution to the paradox raised in [1]. Additionally, we elucidate the distinctions between four different 'operator reconstruction wedges' and demonstrate how to enhance the proof for the [[0187 Global symmetries in QG|absence of global symmetries]] in geometrical states in AdS/CFT [2,3] as an example of these distinctions.\] # Bao, Naskar ## Properties of the contraction map for holographic entanglement entropy inequalities \[Links: [arXiv](https://arxiv.org/abs/2403.13283), [PDF](https://arxiv.org/pdf/2403.13283)\] \[Abstract: We present a deterministic way of finding contraction maps for candidate [[0259 Holographic entropy cone|holographic entanglement entropy inequalities]] modulo choices due to actual degeneracy. We characterize its complexity and give an argument for the completeness of the contraction map proof method as a necessary and sufficient condition for the validity of an entropy inequality for [[0007 RT surface|holographic entanglement]].\] # Basak, Malvimat, Yoon ## A New Genuine Multipartite Entanglement Measure: from Qubits to Multiboundary Wormholes \[Links: [arXiv](https://arxiv.org/abs/2411.11961), [PDF](https://arxiv.org/pdf/2411.11961)\] \[Abstract: We introduce the Latent Entropy (L-entropy) as a novel measure to characterize the genuine [[0264 Multi-partite entanglement|multipartite entanglement]] in quantum systems. Our measure leverages the upper bound of reflected entropy, achieving maximal values for $n$-party 2-uniform states ($n\ge4$) and GHZ state for 3-party quantum systems. We demonstrate that the measure functions as a multipartite pure state entanglement monotone and briefly address its extension to mixed multipartite states. We then analyze its interesting characteristics in spin chain models and the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] (SYK) model. Subsequently, we explore its implications to holography by deriving a Page-like curve for the L-entropy in the CFT dual to a multi-boundary wormhole model. Furthermore, we examine the behavior of L-entropy in Haar random states, deriving analytical expressions and validating them against numerical results. In particular, we show that for $n\ge5$, random states approximate 2-uniform states with maximal multipartite entanglement. Furthermore, we propose a potential connection between random states and multi-boundary wormhole geometries. Extending to finite-temperature systems, we introduce the Multipartite Thermal Pure Quantum (MTPQ) state, a multipartite generalization of the thermal pure quantum state, and explore its entanglement properties. By incorporating state dependent construction of MTPQ state, we resolve the factorization issue in the random average of the MTPQ state, ensuring consistency with the correlation functions in the holographic dual multiboundary wormhole. Finally, we apply this construction to the multi-copy SYK model and examine its multipartite entanglement structure.\] # Basteiro, Di Giulio, Erdmenger, Xian ## Entanglement in interacting Majorana chains and transitions of von Neumann algebras \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum phase transition controlled by the hopping parameters and manifests itself in a discontinuous entanglement entropy, obtained by constraining the one-sided modular Hamiltonian. Inspired by recent work within the [[0001 AdS-CFT|AdS/CFT]] correspondence, we identify transitions between types of [[0415 Von Neumann algebra|von Neumann operator algebras]] throughout the phase diagram. We find transitions of the form $II_1\leftrightarrow\,III\,\,\leftrightarrow\,\,I_\infty$ that reduce to $II_1\leftrightarrow\,\,I_\infty$ in the strongly interacting limit, where they connect non-factorized and factorized ground states. Our results provide novel realizations of such transitions in a controlled many-body model.\] # Baulieu, Wetzstein ## BRST Covariant Phase Space and Holographic Ward Identities \[Links: [arXiv](https://arxiv.org/abs/2405.18898), [PDF](https://arxiv.org/pdf/2405.18898)\] \[Abstract: This paper develops an enlarged [[0331 BRST quantisation|BRST]] framework to treat the large gauge transformations of a given quantum field theory. It determines the associated infinitely many Noether charges stemming from a gauge fixed and BRST invariant Lagrangian, a result that cannot be obtained from Noether's second theorem. The geometrical significance of this result is highlighted by the construction of a trigraded BRST covariant phase space, allowing a BRST invariant gauge fixing procedure. This provides an appropriate framework for determining the conserved BRST Noether current of the global BRST symmetry and the associated global Noether charges. The latter are found to be equivalent with the usual classical corner charges of large gauge transformations. It allows one to prove the gauge independence of their physical effects at the perturbative quantum level. In particular, the underlying BRST fundamental canonical relation provides the same graded symplectic brackets as in the classical covariant phase space. A unified Lagrangian [[0106 Ward identity|Ward identity]] for small and large gauge transformations is built. It consistently decouples into a bulk part for small gauge transformations, which is the standard BRST--BV quantum master equation, and a boundary part for large gauge transformations. The boundary part provides a perturbation theory origin for the invariance of the Hamiltonian physical $\mathcal{S}$-matrix under [[0060 Asymptotic symmetry|asymptotic symmetries]]. [[0209 Holographic renormalisation|Holographic anomalies]] for the boundary Ward identity are studied and found to be solutions of a codimension one Wess--Zumino consistency condition. Such solutions are studied in the context of extended [[0064 BMS group|BMS]] symmetry. Their existence clarifies the status of the 1-loop correction to the subleading [[0009 Soft theorems|soft graviton theorem]].\] # Baumann, Mathys, Pimentel, Rost ## A New Twist on Spinning (A)dS Correlators \[Links: [arXiv](https://arxiv.org/abs/2408.02727), [PDF](https://arxiv.org/pdf/2408.02727)\] \[Abstract: Massless spinning correlators in cosmology are extremely complicated. In contrast, the scattering amplitudes of massless particles with spin are very simple. We propose that the reason for the unreasonable complexity of these correlators lies in the use of inconvenient kinematic variables. For example, in de Sitter space, consistency with unitarity and the background isometries imply that the correlators must be conformally covariant and also conserved. However, the commonly used kinematic variables for correlators do not make all of these properties manifest. In this paper, we introduce twistor space as a powerful way to satisfy all kinematic constraints. We show that conformal correlators of conserved currents can be written as twistor integrals, where the conservation condition translates into holomorphicity of the integrand. The functional form of the [[0330 Twistor theory|twistor]]-space correlators is very simple and easily bootstrapped. For the case of three-point functions, we verify explicitly that this reproduces known results in embedding space. We also perform a half-Fourier transform of the twistor-space correlators to obtain their counterparts in momentum space. We conclude that twistors provide a promising new avenue to study conformal correlation functions that exposes their hidden simplicity.\] # Benjamin, Collier, Maloney, Meruliya ## Resurgence in Liouville Theory \[Links: [arXiv](https://arxiv.org/abs/2408.14574), [PDF](https://arxiv.org/pdf/2408.14574)\] \[Abstract: [[0562 Liouville theory|Liouville conformal field theory]] is a prototypical example of an exactly solvable quantum field theory, in the sense that the correlation functions in an arbitrary background can be determined exactly using only the constraints of unitarity and crossing symmetry. For example, the three point correlation functions are given by the famous formula of Dorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ). Unlike many other exactly solvable theories, Liouville theory has a continuously tunable parameter -- essentially $\hbar$ -- which is related to the central charge of the theory. Here we investigate the nature of the perturbative expansion in powers of $\hbar$, which is the loop expansion around a semi-classical solution. We show that the perturbative coefficients grow factorially, as expected of a Feynman diagram expansion, and take the form of an asymptotic series. We identify the singularities in the Borel plane, and show that they are associated with complex instanton solutions of Liouville theory; they correspond precisely to the complex solutions described by Harlow, Maltz, and Witten. Both single- and multi-valued solutions of Liouville appear. We show that the perturbative loop expansions around these different saddle points mix in the way expected for a trans-series expansion. Thus Liouville theory provides a calculable example of a quantum field theory where perturbative and instanton contributions can be summed up and assembled into a finite answer.\] # Berkooz, Brukner, Jia, Mamroud (Short) ## From Chaos to Integrability in Double Scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2403.01950), [PDF](https://arxiv.org/pdf/2403.01950.pdf)\] \[Abstract: We study thermodynamic phase transitions between integrable and chaotic dynamics. We do so by analyzing models that interpolate between the chaotic [[0503 Double-scaled SYK|double scaled Sachdev-Ye-Kitaev]] (SYK) and the integrable $p$-spin systems, in a limit where they are described by chord diagrams. We develop a path integral formalism by coarse graining over the diagrams, which we use to argue that the system has two distinct phases: one is continuously connected to the chaotic system, and the other to the integrable. They are separated by a line of first order transition that ends at a critical point.\] # Berkooz, Brukner, Jia, Mamroud (Long) ## A Path Integral for Chord Diagrams and Chaotic-Integrable Transitions in Double Scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2403.05980), [PDF](https://arxiv.org/pdf/2403.05980.pdf)\] \[Abstract: We study transitions from [[0008 Quantum chaos|chaotic]] to integrable Hamiltonians in the [[0503 Double-scaled SYK|double scaled SYK]] and $p$-spin systems. The dynamics of our models is described by chord diagrams with two species. We begin by developing a path integral formalism of coarse graining chord diagrams with a single species of chords, which has the same equations of motion as the bi-local ($G\Sigma$) Liouville action, yet appears otherwise to be different and in particular well defined. We then develop a similar formalism for two types of chords, allowing us to study different types of deformations of double scaled SYK and in particular a deformation by an integrable Hamiltonian. The system has two distinct thermodynamic phases: one is continuously connected to the chaotic SYK Hamiltonian, the other is continuously connected to the integrable Hamiltonian, separated at low temperature by a first order phase transition. We also analyze the phase diagram for generic deformations, which in some cases includes a zero-temperature phase transition.\] # Berkooz, Frumkin, Mamroud, Seitz ## Twisted times, the Schwarzian and its deformations in DSSYK \[Links: [arXiv](https://arxiv.org/abs/2412.14238), [PDF](https://arxiv.org/pdf/2412.14238)\] \[Abstract: The IR dynamics of [[0201 Sachdev-Ye-Kitaev model|SYK]] is that of the Schwarzian theory, the effective theory of broken reparametrization invariance. In the [[0503 Double-scaled SYK|double scaling]] limit, SYK is completely solvable by chord diagrams, whose generating functional is a bilocal [[0562 Liouville theory|Liouville theory]]. At low temperatures a set of modes in this description becomes soft. We interpret them as reparametrization of some twisted time coordinates, and show explicitly that they lead to the nonlinear Schwarzian theory. We further consider deformations of the theory in the double scaling limit, giving rise to diagrams with multiple species of chords, and show that the generating functional is now a Liouville theory with multiple fields. These deformations can be tracked to the IR and we discuss how they affect the Schwarzian.\] # Berkooz, Mamroud (Review) ## A Cordial Introduction to Double Scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2407.09396), [PDF](https://arxiv.org/pdf/2407.09396)\] \[Abstract: We review recent progress regarding the [[0503 Double-scaled SYK|double scaled Sachdev-Ye-Kitaev]] model and other $p$-local quantum mechanical random Hamiltonians. These models exhibit an expansion using chord diagrams, which can be solved by combinatorial methods. We describe exact results in these models, including their spectrum, correlation functions, and [[0466 Lyapunov exponent|Lyapunov exponent]]. In a certain limit, these techniques manifest the relation to the Schwarzian quantum mechanics, a theory of quantum gravity in AdS$_2$. More generally, the theory is controlled by a rigid algebraic structure of a quantum group, suggesting a theory of quantum gravity on non-commutative q-deformed AdS$_2$. We conclude with discussion of related universality classes, and survey some of the current research directions.\] # Bernamonti, Galli, Ge ## Boundary-induced transitions in Möbius quenches of holographic BCFT \[Links: [arXiv](https://arxiv.org/abs/2402.16555), [PDF](https://arxiv.org/pdf/2402.16555.pdf)\] \[Abstract: Boundary effects play an interesting role in finite-size physical systems. In this work, we study the boundary-induced properties of 1+1-dimensional critical systems driven by inhomogeneous Möbius-like [[0558 Quantum quench|quenches]]. We focus on the [[0301 Entanglement entropy|entanglement entropy]] in [[0548 Boundary CFT|BCFTs]] with a large [[0033 Central charge|central charge]] and a sparse spectrum of low-dimensional operators. We find that the choice of boundary conditions leads to different scenarios of dynamical phase transitions. We also derive these results in a holographic description in terms of intersecting branes in AdS$_3$, and find a precise match.\] # Bernamonti, Galli, Myers, Reyes ## Rényi second laws for black holes \[Links: [arXiv](https://arxiv.org/abs/2407.01753), [PDF](https://arxiv.org/pdf/2407.01753)\] \[Abstract: Hawking's [[0005 Black hole second law|black hole area theorem]] provides a geometric realization of the second law of thermodynamics and constrains gravitational processes. In this work we explore a one-parameter extension of this constraint formulated in terms of the monotonicity properties of [[0293 Renyi entropy|Rényi entropies]]. We focus on black hole mergers in asymptotically AdS space and determine new restrictions which these Rényi second laws impose on the final state. We evaluate the entropic inequalities starting from the thermodynamic ensembles description of black hole geometries, and find that for many situations they set more stringent bounds than those imposed by the area increase theorem.\] # Bhardwaj, Srikant ## Celestial soft currents at one-loop and their OPEs \[Links: [arXiv](https://arxiv.org/abs/2403.10443), [PDF](https://arxiv.org/pdf/2403.10443)\] \[Abstract: Conformally soft operators and their associated [[0009 Soft theorems|soft theorems]] on the celestial sphere encode the low energy behaviour of bulk scattering amplitudes. They lead to an infinite dimensional symmetry algebra of the celestial CFT at tree-level. In this paper, we introduce new operators in the [[0010 Celestial holography|celestial CFT]] in order to extend the definition of conformally soft currents to include one-loop effects. We then compute their [[0114 Celestial OPE|OPEs]] with other operators in the theory. We also examine new subtleties that arise in defining OPEs of two conformally soft operators. We elucidate the connection between the new operators and loop corrected soft theorems in the bulk. Finally, we conclude by demonstrating how these operators fit into the framework of a logarithmic CFT.\] # Bhattacharyya, Biswas, Kundu ## A classical Bousso bound for higher derivative corrections to general relativity \[Links: [arXiv](https://arxiv.org/abs/2403.16658), [PDF](https://arxiv.org/pdf/2403.16658)\] \[Abstract: We prove the classical version of the [[0171 Covariant entropy bound|covariant entropy bound]] (also known as the Bousso bound) in arbitrary diffeomorphism invariant gravitational theories. We focus on theories for which the [[0006 Higher-derivative gravity|higher derivative]] terms are considered as small corrections in the Lagrangian to Einstein's two-derivative theory of [[0554 Einstein gravity|general relativity]] (GR). Even if the higher derivative corrections are treated perturbatively, we provide instances of specific configurations for which they can potentially violate the Bousso bound. To tackle this obstruction, we propose a modification in the Bousso bound that incorporates the offending contributions from the higher derivative corrections. Our proposed modifications are equivalent to replacing the Bekenstein-Hawking area term by [[0559 Wald entropy|Wald]]'s definition (with dynamical corrections as suggested by Wall) for the black hole entropy. Hence, the modifications are physically well motivated by results from the laws of [[0127 Black hole thermodynamics|black hole mechanics]] in higher derivative theories.\] # Bhattacharyya, Ghosh, Nandi, Pal ## 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator \[Links: [arXiv](https://arxiv.org/abs/2408.01538), [PDF](https://arxiv.org/pdf/2408.01538)\] \[Abstract: In this paper, we compute the partition functions of $\mathcal{N}=1$ SUGRA for different boundary topologies, i.e. sphere and torus, using super-[[0596 Virasoro TQFT|Virasoro TQFT]]. We use fusion and modular kernels of the super-[[0562 Liouville theory|Liouville theory]] to compute the necklace-channel conformal block and showcase formalism by proving that the inner product holds for superconformal blocks, defined as states in the Hilbert space. Finally, we compute the [[0482 Out-of-time-order correlator|out-of-time-order correlator]] for the torus topology with superconformal primary insertions as matter using the tools of super-Virasoro TQFT and investigate its early-time behaviour.\] # Bianchi, Firrotta, Sonnenschein, Weissman ## From spectral to scattering form factor \[Links: [arXiv](https://arxiv.org/abs/2403.00713), [PDF](https://arxiv.org/pdf/2403.00713.pdf)\] \[Abstract: We propose a novel indicator for chaotic quantum scattering processes, the scattering form factor (ScFF). It is based on mapping the locations of peaks in the scattering amplitude to random matrix eigenvalues, and computing the analog of the [[0062 Spectral form factor|spectral form factor]] (SFF). We compute the spectral and scattering form factors of several non-chaotic systems. We determine the ScFF associated with the phase shifts of the leaky torus, closely related to the distribution of the zeros of Riemann zeta function. We compute the ScFF for the decay amplitude of a highly excited string states into two tachyons. We show that it displays the universal features expected from [[0579 Random matrix theory|random matrix theory]] - a decline, a ramp and a plateau - and is in general agreement with the Gaussian unitary ensemble. It also shows some new features, owning to the special structure of the string amplitude, including a "bump" before the ramp associated with gaps in the average eigenvalue density. The "bump" is removed for highly excited string states with an appropriate state dependent unfolding. We also discuss the SFF for the Gaussian β- ensemble, writing an interpolation between the known results of the Gaussian orthogonal, unitary, and symplectic ensembles.\] # Bissi, Donnay, Valsesia ## Logarithmic doublets in CCFT \[Links: [arXiv](https://arxiv.org/abs/2407.17123), [PDF](https://arxiv.org/pdf/2407.17123)\] \[Abstract: We investigate the presence of [[0563 Log CFT|logarithmic CFT]] doublets in the soft sector of [[0010 Celestial holography|celestial CFT]] related with supertranslations. We show that the quantum operator associated with a $\log u$ late-time behavior for the asymptotic gravitational shear forms a logarithmic CFT pair of conformal dimension $\Delta=1$ with an IR-regulated supertranslation Goldstone current. We discuss this result in connection with previous encounters of log CFT structures in the IR-finite part of [[0114 Celestial OPE|celestial OPEs]].\] # Bittleston, Bogna, Heuveline, Kmec, Mason, Skinner ## On AdS$_4$ deformations of celestial symmetries \[Links: [arXiv](https://arxiv.org/abs/2403.18011), [PDF](https://arxiv.org/pdf/2403.18011)\] \[Abstract: [[0010 Celestial holography|Celestial holography]] has led to the discovery of new symmetry algebras arising from the study of [[0078 Collinear limit|collinear limits]] of perturbative gravity amplitudes in flat space. We explain from the twistor perspective how a non-vanishing cosmological constant $\Lambda$ naturally modifies the [[0328 w(1+infinity)|celestial chiral algebra]]. The cosmological constant deforms the Poisson bracket on twistor space, so the corresponding deformed algebra of Hamiltonians under the new bracket is automatically consistent. This algebra is equivalent to that recently found by Taylor and Zhu. We find a number of variations of the deformed algebra. We give the Noether charges arising from the expression of this algebra as a symmetry of the twistor action for self-dual gravity with cosmological constant.\] # Blommaert, Colin-Ellerin ## Gravitons on the edge \[Links: [arXiv](https://arxiv.org/abs/2405.12276), [PDF](https://arxiv.org/pdf/2405.12276)\] \[Abstract: We study free graviton entanglement between Rindler wedges in the Minkowski vacuum state via the Euclidean path integral. We follow Kabat's method for computing the conical entropy, using the heat kernel on the cone with the tip removed, whose resulting [[0301 Entanglement entropy|von Neumann entropy]] for photons correctly predicted electromagnetic [[0556 Edge mode|edge modes]]. We find that, in addition to the bulk graviton contributions, the conical entropy has a contact term that can be attributed to a vector field anchored to the ($d-2$)-dimensional (Euclidean) Rindler horizon whose contribution equals $d-2$ times Kabat's contact term for photons. We suggest that graviton edge modes are hence the $d-2$ large diffeomorphisms which act internally within the Rindler horizon. Along the way, we address several known issues regarding graviton entanglement. We furthermore sketch how our results may be used to study edge modes in closed bosonic string theory.\] # Blommaert, Levine, Mertens, Papalini, Parmentier ## An entropic puzzle in periodic dilaton gravity and DSSYK \[Links: [arXiv](https://arxiv.org/abs/2411.16922), [PDF](https://arxiv.org/pdf/2411.16922)\] \[Abstract: We study 2d dilaton gravity theories with a periodic potential, with special emphasis on sine dilaton gravity, which is holographically dual to [[0503 Double-scaled SYK|double-scaled SYK]]. The periodicity of the potentials implies a symmetry under (discrete) shifts in the momentum conjugate to the length of geodesic slices. This results in divergences. The correct definition is to gauge this symmetry. This discretizes the geodesic lengths. Lengths below a certain threshold are null states. Because of these null states, the entropy deviates drastically from [[0004 Black hole entropy|Bekenstein-Hawking]] and the Hilbert space becomes finite dimensional. The spacetimes have a periodic radial coordinate. These are toy models of 2d quantum cosmology with a normalizable wavefunction. We study two limiting dualities: one between flat space quantum gravity and the Heisenberg algebra, and one between topological gravity and the Gaussian [[0197 Matrix model|matrix integral]]. We propose an exact density of states for certain classes of periodic dilaton gravity models.\] # Blommaert, Mertens, Papalini ## The dilaton gravity hologram of double-scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2404.03535), [PDF](https://arxiv.org/pdf/2404.03535)\] \[Abstract: We work out a precise holographic duality between sine dilaton gravity, and [[0503 Double-scaled SYK|DSSYK]]. More precisely, canonical quantization of sine dilaton gravity reproduces $q$-Schwarzian quantum mechanics, which is the auxiliary system that arises from the chord diagrams of DSSYK. The role of the chord number in DSSYK is played by the (Weyl rescaled) geodesic length in the bulk. The most puzzling aspect of reconciling DSSYK with a simple gravitational dual at the classical level is the distinction between temperature and "fake temperature". At the $q$-Schwarzian level, we clarify how this arises from the constraint that the chord number is positive. The on-shell $q$-Schwarzian action with the constraint reproduces the thermodynamics of DSSYK. Semi-classically, in sine dilaton gravity this translates to the insertion of a defect, from which we deduce that fake temperature is the Hawking temperature of a smooth Lorentzian black hole. We comment on several relations with dS space. One remarkable feature is that in sine dilaton gravity quantization discretizes spacetime, therefore the Hilbert space is discrete.\] # Blommaert, Chen, Nomura ## Firewalls at exponentially late times \[Links: [arXiv](https://arxiv.org/abs/2403.07049), [PDF](https://arxiv.org/pdf/2403.07049.pdf)\] \[Abstract: We consider a version of the typical state [[0195 Firewall|firewall]] setup recently reintroduced by [[2022#Stanford, Yang|Stanford and Yang]], who found that wormholes may create firewalls. We examine a late-time double scaling limit in [[0050 JT gravity|JT gravity]] in which one can resum the expansion in the number of wormholes, and we use this to study the exact distribution of interior slices at times exponential in the entropy. We consider a [[0574 Thermofield double|thermofield double]] with and without early perturbations on a boundary. These perturbations can appear on interior slices as dangerous high energy [[0117 Shockwave|shocks]]. For exponentially late times, wormholes tend to teleport the particles created by perturbations and render the interior more dangerous. In states with many perturbations separated by large times, the probability of a safe interior is exponentially small. Such states thus almost certainly have firewalls at the horizon, even though they would be safe without wormholes. With perturbation, even in the safest state we conceive, the odds of encountering a firewall are fifty-fifty. One interpretation of the phenomena found here is that wormholes can change time-ordered contours into effective out-of-time-ordered folds, making shockwaves appear in unexpected places.\] # Bogna, Heuveline ## Towards celestial chiral algebras of self-dual black holes \[Links: [arXiv](https://arxiv.org/abs/2408.14324), [PDF](https://arxiv.org/pdf/2408.14324)\] \[Abstract: In this note, we show that several self-dual spacetimes previously studied in the context of [[0010 Celestial holography|celestial]] and [[0130 Twisted holography|twisted holography]] arise as limits of a certain Taub-NUT AdS$_4$ metric, the Pedersen metric, in which their Mass, NUT charge and cosmological constant obey a self-duality relation. In particular, self-dual Taub-NUT, a singular double cover of Eguchi-Hanson space, Euclidean AdS$_4$, and non-compact $\mathbb{CP}^2$, which is conformally equivalent to Burns space, arise as special limits of the Pedersen metric. The Pedersen metric can be derived from a curved twistor space which we conjecture to arise from a backreaction of self-dual gravity in the presence of a cosmological constant when coupled to a defect operator wrapping a certain $\mathbb{CP}^1$ at infinity. The curved twistor space gives rise to a 2-parameter deformation of the [[0328 w(1+infinity)|celestial symmetry algebra]] $Lw_\wedge$ which reduces to previously studied algebras in various limits. A companion paper will discuss additional details and relations to previously studied self-dual black holes.\] # Boruch, Iliesiu, Lin, Yan ## How the Hilbert space of two-sided black holes factorises \[Links: [arXiv](https://arxiv.org/abs/2406.04396), [PDF](https://arxiv.org/pdf/2406.04396)\] \[Abstract: In AdS/CFT, two-sided black holes are described by states in the tensor product of two Hilbert spaces associated with the two asymptotic boundaries of the spacetime. Understanding how such a tensor product arises from the bulk perspective is an important open problem in holography, known as the [[0514 Lorentzian factorisation problem|factorisation puzzle]]. In this paper, we show how the Hilbert space of bulk states factorises due to non-perturbative contributions of spacetime wormholes: the trace over two-sided states with different particle excitations behind the horizon factorises into a product of traces of the left and right sides. This precisely occurs when such states form a complete basis for the bulk Hilbert space. We prove that the factorisation of the trace persists to all non-perturbative orders in $1/G_N$, consequently providing a possible resolution to the factorisation puzzle from the [[0555 Gravitational path integral|gravitational path integral]]. In the language of [[0415 Von Neumann algebra|von Neumann algebras]], our results provide strong evidence that the algebra of one-sided observables transitions from a Type II or Type III algebra, depending on whether or not perturbative gravity effects are included, to a Type I factor when including non-perturbative corrections in the bulk.\] # Bourne, Castro, Fliss ## Spinning up the spool: Massive spinning fields in 3d quantum gravity \[Links: [arXiv](https://arxiv.org/abs/2407.09608), [PDF](https://arxiv.org/pdf/2407.09608)\] \[Abstract: We show how to incorporate massive spinning fields into the Euclidean path integral of three-dimensional quantum gravity via its Chern-Simons formulation. The coupling of the spinning fields to gravity is captured by a [[0653 Wilson spool|Wilson spool]], a collection of Wilson loops winding around closed paths of the geometry, and generalizes the proposal of [1,2]. We present a robust derivation of the Wilson spool by providing a new group-theoretic perspective of the quasinormal mode method for one-loop determinants. We test our proposal on Euclidean BTZ and $S^3$ backgrounds. We also evaluate explicitly the quantum corrections to the path integral on $S^3$, and report on how $G_N$ and the mass are renormalized to leading order in perturbation theory.\] # Bousso, Kaya ## Geometric Quantum States Beyond AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/2404.11644), [PDF](https://arxiv.org/pdf/2404.11644)\] \[Abstract: We characterize the quantum states dual to entanglement wedges in arbitrary spacetimes, in settings where the matter entropy can be neglected compared to the geometric entropy. In [[0001 AdS-CFT|AdS/CFT]], such states obey special entropy inequalities known as the [[0259 Holographic entropy cone|holographic entropy cone]]. In particular, the mutual information of CFT subregions is monogamous (MMI). We extend this result to arbitrary spacetimes, using a recent proposal for the generalized entanglement wedge $e(a)$ of a gravitating region $a$. Given independent input regions $a$, $b$, and $c$, we prove MMI: Area$[e(a)]$+$Area$[e(b)]$+$Area$[e(c)]$-$Area$[e(ab)]$-$Area$[e(bc)]$-$Area$[e(ca)]$+$Area$[e(abc)] \leq 0$. We expect that the full holographic entropy cone can be extended to arbitrary spacetimes using similar methods.\] # Bousso, Tabor ## Discrete Max-Focusing \[Links: [arXiv](https://arxiv.org/abs/2410.18192), [PDF](https://arxiv.org/pdf/2410.18192)\] \[Abstract: The [[0243 Quantum focusing conjecture|Quantum Focusing Conjecture]] (QFC) lies at the foundation of holography and semiclassical gravity. The QFC implies the [[0171 Covariant entropy bound|Bousso bound]] and the [[0405 Quantum null energy condition|Quantum Null Energy Condition]] (QNEC). The QFC also ensures the consistency of the [[0212 Quantum extremal surface|quantum extremal surface]] prescription and [[0026 Bulk reconstruction|bulk reconstruction]] in [[0001 AdS-CFT|AdS/CFT]]. However, the central object in the QFC -- the expansion of lightrays -- is not defined at points where geodesics enter or leave a null congruence. Moreover, the expansion admits three inequivalent quantum extensions in terms of the conditional max, min, and von Neumann entropies. Here we formulate a discrete notion of nonexpansion that can be evaluated even at non-smooth points. Moreover, we show that a single conjecture, the discrete max-QFC, suffices for deriving the QNEC, the Bousso bound, and key properties of both max and min entanglement wedges. Continuous numerical values need not be assigned, nor are the von Neumann or min-versions of the quantum expansion needed. Both our new notion of nonexpansion, and also the properties of conditional max entropies, are inherently asymmetric and outward directed from the input wedge. Thus the framework we develop here reduces and clarifies the axiomatic structure of semiclassical gravity, eliminating redundancies and fixing ambiguities. We also derive a new result: the [[0218 Strong subadditivity|strong subadditivity]] of the generalized smooth conditional max and min entropies of entanglement wedges.\] # Brendle, Hung ## Systolic inequalities and the Horowitz-Myers conjecture \[Links: [arXiv](https://arxiv.org/abs/2406.04283), [PDF](https://arxiv.org/pdf/2406.04283)\] \[Abstract: Let $3 \leq n \leq 7$, and let $g$ be a Riemannian metric on $B^2 \times T^{n-2}$ with scalar curvature at least $-n(n-1)$. We establish an inequality relating the systole of the boundary to the infimum of the mean curvature on the boundary. As a consequence, we confirm a conjecture of [[0407 Horowitz-Myers conjecture|Horowitz and Myers]].\] # Britto, Duhr, Hannesdottir, Mizera ## Cutting-Edge Tools for Cutting Edges \[Links: [arXiv](https://arxiv.org/abs/2402.19415), [PDF](https://arxiv.org/pdf/2402.19415.pdf)\] \[Abstract: We review different notions of cuts appearing throughout the literature on scattering amplitudes. Despite similar names, such as unitarity cuts or generalized cuts, they often represent distinct computations and distinct physics. We consolidate this knowledge, summarize how cuts are used in various computational strategies, and explain their relations to other quantities including imaginary parts, discontinuities, and monodromies. Differences and nuances are illustrated on explicit examples.\] # Bucca, Mezei ## Nonlinear soft mode action for the large-$p$ SYK model \[Links: [arXiv](https://arxiv.org/abs/2412.14799), [PDF](https://arxiv.org/pdf/2412.14799)\] \[Abstract: The physics of the [[0201 Sachdev-Ye-Kitaev model|SYK]] model at low temperatures is dominated by a soft mode governed by the Schwarzian action. In [arXiv:1604.07818](https://arxiv.org/abs/1604.07818) the linearised action was derived from the soft mode contribution to the four-point function, and physical arguments were presented for its nonlinear completion to the Schwarzian. In this paper, we give two derivations of the full nonlinear effective action in the large $p$ limit, where $p$ is the number of fermions in the interaction terms of the Hamiltonian. The first derivation uses that the collective field action of the large-$p$ SYK model is [[0562 Liouville theory|Liouville theory]] with a non-conformal boundary condition that we study in conformal perturbation theory. This derivation can be viewed as an explicit version of the renormalisation group argument for the nonlinear soft mode action in [arXiv:1711.08467](https://arxiv.org/abs/1711.08467). The second derivation uses an Ansatz for how the soft mode embeds into the microscopic configuration space of the collective fields. We generalise our results for the large-$p$ SYK chain and obtain a "Schwarzian chain" effective action for it. These derivations showcase that the large-$p$ SYK model is a rare system, in which there is sufficient control over the microscopic dynamics, so that an effective description can be derived for it without the need for extra assumptions or matching (in the effective field theory sense).\] # Buchel ## Holographic Gauss-Bonnet transport \[Links: [arXiv](https://arxiv.org/abs/2402.16109), [PDF](https://arxiv.org/pdf/2402.16109.pdf)\] \[Abstract: We extend the computational framework of [[2023#Buchel, Cremonini, Early]] to analysis of [[0430 Holographic shear viscosity|shear and bulk viscosities]] in generic strongly coupled holographic Gauss-Bonnet gauge theories. The finite Gauss-Bonnet coupling constant encodes holographic plasma with non-equal central charges $c\ne a$ at the ultraviolet fixed point. In a simple model we discuss transport coefficients within the causality window $-\frac12\le \frac{c-a}{c}\le \frac 12$ of the theory.\] # Bueno, Cano, Hennigar ## Kasner Eons \[Links: [arXiv](https://arxiv.org/abs/2402.14912), [PDF](https://arxiv.org/pdf/2402.14912.pdf)\] \[Abstract: As shown in the classic work of Belinski, Khalatnikov and Lifshitz, the approach to a generic space-like singularity in general relativity consists of a sequence of eras and epochs in which the metric is locally [[0126 Kasner singularity|Kasner]], connected by brief transitions. When quantum gravity effects are included, we argue that a new type of transition arises, giving rise to Kasner eons: periods which are dominated by emergent physics at each energy scale. We comment on the different ways in which the Einsteinian eon may come to an end and show explicitly how additional Kasner eons arise in the interior of a black hole solution due to [[0006 Higher-derivative gravity|higher-derivative corrections]].\] # Caceres, Murcia, Patra, Pedraza ## Kasner eons with matter: holographic excursions to the black hole singularity \[Links: [arXiv](https://arxiv.org/abs/2408.14535), [PDF](https://arxiv.org/pdf/2408.14535)\] \[Abstract: Recent work has shown that introducing [[0006 Higher-derivative gravity|higher-curvature]] terms to the Einstein-Hilbert action causes the approach to a space-like singularity to unfold as a sequence of [[0126 Kasner singularity|Kasner]] eons. Each eon is dominated by emergent physics at an energy scale controlled by higher-curvature terms of a given order, transitioning to higher-order eons as the singularity is approached. The purpose of this paper is twofold. First, we demonstrate that the inclusion of matter dramatically modifies the physics of eons compared to the vacuum case. We illustrate this by considering a family of quasi-topological gravities of arbitrary order minimally coupled to a scalar field. Second, we investigate Kasner eons in the interior of black holes with field theory duals and analyze their imprints on holographic observables. We show that the behavior of the thermal a-function, two-point functions of heavy operators, and holographic complexity can capture distinct signatures of the eons, making them promising tools for diagnosing stringy effects near black hole singularities.\] # Cao, Faulkner ## Ramp from Replica Trick \[Links: [arXiv](https://arxiv.org/abs/2405.15873), [PDF](https://arxiv.org/pdf/2405.15873)\] \[Abstract: We compute the [[0062 Spectral form factor|spectral form factor]] of the [[0416 Modular Hamiltonian|modular Hamiltonian]] $K=-\ln\rho_A$ associated to the reduced density matrix of a Haar random state. A ramp is demonstrated and we find an analytic expression for its slope. Our method involves an application of the replica trick, where we first calculate the correlator lt;\text{tr}\rho_A^n\;\text{tr}\rho_A^m>$ at large bond dimension and then analytically continue the indices $n,m$ from integers to arbitrary complex numbers. We use steepest descent methods at large modular times to extract the ramp. The large bond dimension limit of the replicated partition function is dominated by a sum over *annular non-crossing permutations*. We explored the similarity between our results and calculations of the spectral form factor in low dimensional gravitational theories where the ramp is determined by the double trumpet geometry. We find there is an underlying resemblance in the two calculations, when we interpret the annular non-crossing permutations as representing a discretized version of the double trumpet. Similar results are found for an equilibrated pure state in place of the Haar random state.\] # Ceplak, Liu, Parnachev, Valach ## Black Hole Singularity from OPE \[Links: [arXiv](https://arxiv.org/abs/2404.17286), [PDF](https://arxiv.org/pdf/2404.17286.pdf)\] \[Abstract: Eternal asymptotically AdS black holes are dual to [[0574 Thermofield double|thermofield double states]] in the boundary CFT. It has long been known that black hole singularities have certain signatures in boundary thermal [[0103 Two-point functions|two-point functions]] related to null geodesics bouncing off the singularities (bouncing geodesics). In this paper we shed light on the manifestations of black hole singularities in the dual CFT. We decompose the boundary CFT correlator of scalar operators using the [[0030 Operator product expansion|Operator Product Expansion]] (OPE) and focus on the contributions from the identity, the stress tensor, and its products. We show that this part of the correlator develops singularities precisely at the points that are connected by bulk bouncing geodesics. Black hole singularities are thus encoded in the analytic behavior of the boundary correlators determined by multiple stress tensor exchanges. Furthermore, we show that in the limit where the conformal dimension of the operators is large, the sum of multi-stress-tensor contributions develops a branch point singularity as predicted by the geodesic analysis. We also argue that the appearance of complexified geodesics, which play an important role in computing the full correlator, is related to the contributions of the double-trace operators in the boundary CFT.\] # Chakraborty, Chakraborty (Review) ## A Revisit to Classical and Quantum aspects of Raychaudhuri equation and possible resolution of Singularity \[Links: [arXiv](https://arxiv.org/abs/2402.16956), [PDF](https://arxiv.org/pdf/2402.16956.pdf)\] \[Abstract: In this review, we provide a concrete overview of the [[0408 Raychaudhuri equation|Raychaudhuri equation]], Focusing theorem and Convergence conditions in a plethora of backgrounds and discuss the consequences. We also present various classical and quantum approaches suggested in the literature that could potentially mitigate the initial big-bang singularity and the black-hole singularity.\] # Chandra, Hartman, Meruliya ## Statistics of three-dimensional black holes from Liouville line defects \[Links: [arXiv](https://arxiv.org/abs/2404.15183), [PDF](https://arxiv.org/pdf/2404.15183.pdf)\] \[Abstract: Black holes and wormholes in the [[0555 Gravitational path integral|gravitational path integral]] can be used to calculate the statistics of heavy operators. An explicit example in higher dimensions is provided by thin shells of matter. We study these solutions in [[0002 3D gravity|3D gravity]], and reproduce the behavior of black holes and wormholes from the dual CFT using the large-$c$ [[0036 Conformal bootstrap|conformal bootstrap]]. The CFT operator that creates a thin shell black hole is a line defect, so we begin by using the bootstrap to study the statistics of line defects, both at finite $c$ and in the holographic large-$c$ limit. The crossing equation leads to a universal formula for the average high-energy matrix elements of the line defect in any compact, unitary 2d CFT with $c>1$. The asymptotics are controlled by a line defect in [[0562 Liouville theory|Liouville CFT]] at the same value of the [[0033 Central charge|central charge]]. At large $c$, three distinct quantities are related: The statistics of line defects in holographic CFTs, the individual matrix elements of a line defect in Liouville CFT, and the on-shell action of black holes and wormholes in 3D gravity. The three calculations match for black holes, and if the statistics of the line defects are assumed to be approximately Gaussian, then a class of wormholes is also reproduced by the dual CFT.\] # Chang, Chen, Sia, Yang ## Fortuity in SYK Models \[Links: [arXiv](https://arxiv.org/abs/2412.06902), [PDF](https://arxiv.org/pdf/2412.06902)\] \[Abstract: We study the fortuity phenomenon in supersymmetric [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] (SYK) models. For generic choices of couplings, all the BPS states in the $\mathcal{N}=2$ SUSY SYK model are [[0646 Fortuity|fortuitous]]. The SYK models reveal an intimate connection between fortuity and the Schwarzian description of supersymmetric black holes, reflected in a sharp feature of $R$-charge concentration - microscopically, all the fortuitous states are concentrated in particular charge sectors. We propose that both $R$-charge concentration and the random matrix behavior near the BPS states are key properties of a generic $q$-local supercharge and formulate these as a supercharge chaos conjecture. We expect supercharge chaos to hold universally for supercharges in holographic CFTs near their fortuitous states, potentially providing a microscopic interpretation for the charge constraints of supersymmetric black holes. We also construct SYK models that contain both fortuitous states and monotonous states and contrast their properties, providing further evidence that monotonous states are less chaotic than fortuitous states.\] # Chang, Lin ## Holographic covering and the fortuity of black holes \[Links: [arXiv](https://arxiv.org/abs/2402.10129), [PDF](https://arxiv.org/pdf/2402.10129.pdf)\] \[Abstract: We propose a classification of [[0178 BPS|BPS]] states into monotone versus fortuitous in holographic CFTs, based on their behaviors in the large $N$ limit. Intuitively, monotone BPS states form infinite sequences with increasing rank $N$, while fortuitous ones are isolated existences at individual ranks. A precise definition is formulated using supercharge cohomology. We conjecture that under the [[0001 AdS-CFT|AdS/CFT]] correspondence, monotone BPS states are dual to smooth horizonless geometries, while fortuitous ones are responsible for the typical black hole microstate and give the dominant contribution to the entropy. We present supporting evidence for our conjectures in ${\cal N}=4$ [[0155 N=4 SYM|SYM]] and symmetric product orbifolds.\] # Chapman, Demulder, Galante, Sheorey, Shoval ## Krylov complexity and chaos in deformed SYK models \[Links: [arXiv](https://arxiv.org/abs/2407.09604), [PDF](https://arxiv.org/pdf/2407.09604)\] \[Abstract: [[0564 Krylov complexity|Krylov complexity]] has recently been proposed as a quantum probe of chaos. The Krylov exponent characterising the exponential growth of Krylov complexity is conjectured to upper-bound the [[0466 Lyapunov exponent|Lyapunov exponent]]. We compute the Krylov and the Lyapunov exponents in the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] model and in some of its deformations. We do this analysis both at infinite and finite temperatures, in models where the number of fermionic interactions is both finite and infinite. We consider deformations that interpolate between two regions of near-maximal chaos and deformations that become nearly-integrable at low temperatures. In all cases, we find that the Krylov exponent upper-bounds the Lyapunov one. However, we find that while the Lyapunov exponent can have non-monotonic behaviour as a function of temperature, in all studied examples the Krylov exponent behaves monotonically. For instance, we find models where the Lyapunov exponent goes to zero at low temperatures, while the Krylov exponent saturates to its maximal bound. We speculate on the possibility that this monotonicity might be a generic feature of the Krylov exponent in quantum systems evolving under unitary evolution.\] # Charalambous ## Love numbers and Love symmetries for $p$-form and gravitational perturbations of higher-dimensional spherically symmetric black holes \[Links: [arXiv](https://arxiv.org/abs/2402.07574), [PDF](https://arxiv.org/pdf/2402.07574.pdf)\] \[Abstract: The static [[0581 Tidal Love numbers|Love numbers]] of four-dimensional asymptotically flat, isolated, general-relativistic black holes are known to be identically vanishing. The Love symmetry proposal suggests that such vanishings are addressed by selection rules following from the emergence of an enhanced $\text{SL}(2,\mathbb{R})$ (''Love'') symmetry in the near-zone region; more specifically, it is the fact that the black hole perturbations belong to a highest-weight representation of this near-zone $\text{SL}(2,\mathbb{R})$ symmetry, rather than the existence of the Love symmetry itself, that outputs the vanishings of the corresponding Love numbers. In higher spacetime dimensions, some towers of magic zeroes with regards to the black hole response problem have also been reported for scalar, electromagnetic and gravitational perturbations of the Schwarzschild-Tangherlini black hole. Here, we extend these results by supplementing with $p$-form perturbations of the Schwarzschild-Tangherlini black hole. We furthermore analytically extract the static Love numbers and the leading order dissipation numbers associated with spin-0 scalar and spin-2 tensor-type tidal perturbations of the higher-dimensional Reissner-Nordström black hole. We find that Love symmetries exist and that the vanishings of the static Love numbers are captured by representation theory arguments even for these higher spin perturbations of the higher-dimensional spherically symmetric black holes of [[0554 Einstein gravity|General Relativity]]. Interestingly, these near-zone $\text{SL}(2,\mathbb{R})$ structures acquire extensions to Witt algebras. Our setup allows to also study the $p$-form response problem of a static spherically symmetric black hole in a generic theory of gravity. We perform explicit computations for some black holes in the presence of string-theoretic corrections and investigate under what geometric conditions Love symmetries emerge in the near-zone.\] # Chatterjee, Witten (Review) ## Liouville Theory: An Introduction to Rigorous Approaches \[Links: [arXiv](https://arxiv.org/abs/2404.02001), [PDF](https://arxiv.org/pdf/2404.02001)\] \[Abstract: In recent years, a surprisingly direct and simple rigorous understanding of quantum [[0562 Liouville theory|Liouville theory]] has developed. We aim here to make this material more accessible to physicists working on quantum field theory.\] # Chen, Dymarsky, Tian, Wang (a) ## Subsystem entropy in 2d CFT and KdV ETH \[Links: [arXiv](https://arxiv.org/abs/2409.19046), [PDF](https://arxiv.org/pdf/2409.19046)\] \[Abstract: We study subsystem entropy in [[0003 2D CFT|2d CFTs]], for subsystems constituting a finite fraction of the full system. We focus on the extensive contribution, which scales linearly with the subsystem size in the thermodynamic limit. We employ the so-called diagonal approximation to evaluate subsystem entropy for the chaotic CFTs in thermal state (canonical ensemble), microcanonical ensemble, and in a primary state, matching previously known results. We then proceed to find analytic expressions for the subsystem entropy at leading order in $c$, when the global CFT state is the KdV generalized Gibbs ensemble or the KdV microcanonical ensemble. Previous studies of primary eigenstates have shown that, akin to fixed-area states in [[0001 AdS-CFT|AdS/CFT]], corresponding subsystem entanglement spectrum is flat. This behavior is seemingly in sharp contradiction with the one for the thermal (microcanonical) state, and thus in apparent contradiction with the subsystem [[0040 Eigenstate thermalisation hypothesis|Eigenstate Thermalization Hypothesis]] (ETH). In this work, we resolve this issue by comparing the primary state with the KdV (micro)canonical ensemble. We show that the results are consistent with the KdV-generalized version of the subsystem ETH, in which local properties of quantum eigenstates are governed by their values of conserved KdV charges. Our work solidifies evidence for the KdV-generalized ETH in 2d CFTs and emphasizes [[0293 Renyi entropy|Renyi entropy]] as a sensitive probe of the reduced-density matrix.\] # Chen, Dymarsky, Tian, Wang (b) ## Holographic Renyi entropy of 2d CFT in KdV generalized ensemble \[Links: [arXiv](https://arxiv.org/abs/2409.19271), [PDF](https://arxiv.org/pdf/2409.19271)\] \[Abstract: The [[0040 Eigenstate thermalisation hypothesis|eigenstate thermalization hypothesis]] (ETH) in chaotic two dimensional CFTs is subtle due to infinitely many conserved KdV charges. Previous works have demonstrated that primary CFT eigenstates have flat entanglement spectrum, which is very different from the microcanonical ensemble. This result is an apparent contradiction to conventional ETH, which does not take KdV charges into account. In a companion paper, we resolve this discrepancy by studying the subsystem entropy of a chaotic CFT in KdV-generalized Gibbs and microcanonical ensembles. In this paper, we carry out parallel computations in the context of AdS/CFT. We focus on the high density limit, which is equivalent to thermodynamic limit in conformal theories. In this limit holographic Renyi entropy can be computed using the so-called gluing construction. We explicitly study the KdV-generalized microcanonical ensemble with the densities of the first two KdV charges $\langle \mathcal{Q}_1\rangle = q_1,\langle \mathcal{Q}_3\rangle = q_3$ fixed and obeying $q_3-q_1^2 \ll q_1^2$. In this regime we found that the refined Renyi entropy $\tilde{S}_n$ is n-independent for $n>n_{cut}$, where $n_{cut}$ depends on $q_1,q_3$. By taking the primary state limit $q_3\to q_1^2$, we recover flat entanglement spectrum characteristic of fixed-area states, in agreement with the primary state behavior. This provides a consistency check of the KdV-generalized ETH in 2d CFTs.\] # Chen, Hikida, Taki, Uetoko ## The semi-classical saddles in three-dimensional gravity via holography and mini-superspace approach \[Links: [arXiv](https://arxiv.org/abs/2404.10277), [PDF](https://arxiv.org/pdf/2404.10277)\] \[Abstract: We determine the [[0335 Complex metrics|complex geometries]] dual to the semi-classical saddles in [[0002 3D gravity|three-dimensional gravity]] with positive or negative cosmological constant. We examine the semi-classical saddles in [[0562 Liouville theory|Liouville field theory]] and interpret them in terms of gravity theory. For this, we describe the gravity theory by [[0089 Chern-Simons theory|Chern Simons theory]] and classify the possible saddles based on homotopy group argument. We further realize the semi-classical saddles using the mini-superspace model of quantum gravity and explicitly determine the integral contour. In the case of positive cosmological constant, we recovered the geometry used for no-boundary proposal of [[0162 No-boundary wavefunction|Hartle and Hawking]]. In the case of negative cosmological constant, the geometry can be identified with Euclidean anti-de Sitter space attached with imaginary radius spheres. The geometry should be unphysical and several arguments on this issue are provided. Partial results were already presented in our earlier letter, and more detailed derivations and explanations on the results are given along with additional results. In particular, we reproduce the classical Liouville action from the Chern-Simons formulation of dual gravity theory.\] # Chen, Hung, Jiang, Lao ## Quantum 2D Liouville Path-Integral Is a Sum over Geometries in AdS$_3$ Einstein Gravity \[Links: [arXiv](https://arxiv.org/abs/2403.03179), [PDF](https://arxiv.org/pdf/2403.03179.pdf)\] \[Abstract: There is a renowned solution of the modular bootstrap that defines the UV complete quantum [[0562 Liouville theory|Liouville theory]]. We triangulate the path-integral of this Liouville CFT on any 2D surface $\mathcal{M}$, by proposing a shrinkable boundary condition for this special CFT that allows small holes to close, analogous to the proposal in rational CFTs [1-3]. This is essentially a tensor network that admits an interpretation of a state-sum of a 3D topological theory constructed with quantum [[0597 6j symbol|6j symbols]] of $\mathcal{U}_q(SL(2,\mathbb{R}))$ with non-trivial boundary conditions, and it reduces to a sum over 3D geometries weighted by the Einstein-Hilbert action to leading order in large $c$. The boundary conditions of quantum Liouville theory specifies a very special sum over bulk geometries to faithfully reproduce the CFT path-integral. The triangulation coincides with producing a network of geodesics in the AdS bulk, which can be changed making use of the pentagon identity and orthogonality condition satisfied by the 6j symbols, and arranged into a precise holographic tensor network.\] # Chen, Lin, Shenker ## BPS Chaos \[Links: [arXiv](https://arxiv.org/abs/2407.19387), [PDF](https://arxiv.org/pdf/2407.19387)\] \[Abstract: Black holes are [[0008 Quantum chaos|chaotic]] quantum systems that are expected to exhibit random matrix statistics in their finite energy spectrum. Lin, Maldacena, Rozenberg and Shan (LMRS) have proposed a related characterization of chaos for the ground states of [[0178 BPS|BPS]] black holes with finite area horizons. On a separate front, the "fuzzball program" has uncovered large families of horizon-free geometries that account for the entropy of holographic BPS systems, but only in situations with sufficient supersymmetry to exclude finite area horizons. The highly structured, non-random nature of these solutions seems in tension with strong chaos. We verify this intuition by performing analytic and numerical calculations of the LMRS diagnostic in the corresponding boundary quantum system. In particular we examine the 1/2 and 1/4-BPS sectors of \mathcal{N}=4 SYM, and the two charge sector of the D1-D5 CFT. We find evidence that these systems are only weakly chaotic, with a Thouless time determining the onset of chaos that grows as a power of N. In contrast, finite horizon area BPS black holes should be strongly chaotic, with a Thouless time of order one. In this case, finite energy chaotic states become BPS as N is decreased through the recently discovered "fortuity" mechanism. Hence they can plausibly retain their strongly chaotic character.\] # Chen, Murthy, Turiaci ## Gravitational index of the heterotic string \[Links: [arXiv](https://arxiv.org/abs/2402.03297), [PDF](https://arxiv.org/pdf/2402.03297.pdf)\] \[Abstract: The fundamental heterotic string has a tower of [[0178 BPS|BPS]] states whose [[0568 Supersymmetric index|supersymmetric index]] has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of [[0385 Supergravity corrections|higher-derivative]] terms in four-dimensional $\mathcal{N}=2$ supergravity resolves the singularity. In doing so, we extend the recently-developed "new attractor mechanism" to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble.\] # Choi, Laddha, Puhm (Mar) ## Asymptotic Symmetries for Logarithmic Soft Theorems in Gauge Theory and Gravity \[Links: [arXiv](https://arxiv.org/abs/2403.13053), [PDF](https://arxiv.org/pdf/2403.13053)\] \[Abstract: Gauge theories and perturbative gravity in four dimensions are governed by a tower of infinite-dimensional symmetries which arise from tree-level [[0009 Soft theorems|soft theorems]]. However, aside from the leading soft theorems which are all-loop exact, subleading ones receive loop corrections due to long-range infrared effects which result in new soft theorems with logarithmic dependence on the energy of the soft particle. The conjectured universality of these logarithmic soft theorems to all loop orders cries out for a symmetry interpretation. In this letter we initiate a program to compute long-range infrared corrections to the charges that generate the asymptotic symmetries in (scalar) QED and perturbative gravity. For late-time fall-offs of the electromagnetic and gravitational fields which give rise to infrared dressings for the matter fields, we derive finite charge conservation laws and show that in the quantum theory they correspond precisely to the first among the infinite tower of logarithmic soft theorems. This symmetry interpretation, by virtue of being universal and all-loop exact, is a key element for a holographic principle in spacetimes with flat asymptotics.\] # Choi, Laddha, Puhm (Dec) ## The Classical Super-Rotation Infrared Triangle \[Links: [arXiv](https://arxiv.org/abs/2412.16142), [PDF](https://arxiv.org/pdf/2412.16142)\] \[Abstract: The universality of gravitational scattering at low energies and large distances encoded in [[0009 Soft theorems|soft theorems]] and [[0287 Memory effect|memory effects]] can be understood from [[0060 Asymptotic symmetry|symmetries]]. In four-dimensional asymptotically flat spacetimes the infinite enhancement of translations, extending the Poincaré group to the BMS group, is the symmetry underlying Weinberg's soft graviton theorem and the gravitational displacement memory effect. Beyond this leading infrared triangle, loop corrections alter their nature by introducing logarithms in the soft expansion and late time tails to the memory, and this persists in the classical limit. In this work we give the first complete description of an 'infrared triangle' where the long-range nature of gravitational interactions is accounted for. Building on earlier results in [2403.13053](https://arxiv.org/abs/2403.13053) where we derived a novel conservation law associated to the infinite dimensional enhancement of Lorentz transformations to superrotations, we prove here its validity to all orders in the gravitational coupling and show that it implies the classical logarithmic soft graviton theorem of Saha-Sahoo-Sen in [1912.06413](https://arxiv.org/abs/1912.06413). We furthermore extend the formula for the displacement memory and its tail from particles to fields, thus completing the classical superrotation infrared triangle.\] # Choun, Kim, Kim ## Holographic dual effective field theory for an SYK model \[Links: [arXiv](https://arxiv.org/abs/2402.12097), [PDF](https://arxiv.org/pdf/2402.12097.pdf)\] \[Abstract: We derive an emergent holographic dual description for an [[0201 Sachdev-Ye-Kitaev model|SYK]] model, where the renormalization group (RG) flows of collective bi-local fields appear manifestly in the bulk effective action with an emergent extradimension. This holographic dual effective field theory reproduces $1/N$ quantum corrections given by the Schwarzian action when we take the UV limit in the bulk effective action. Going into the IR regime in the extradimension, we observe that the field theoretic $1/N$, $1/N^{2}$, ... quantum corrections are resummed in the all-loop order and reorganized to form a holographic dual effective field theory in a large $N$ fashion living on the one-higher dimensional spacetime. Taking the large $N$ limit in the holographic dual effective field theory, we obtain nonlinearly coupled second-order bulk differential equations of motion for the three bi-local order-parameter fields of fermion self-energy, Green's function, and polarization function. Here, both UV and IR boundary conditions are derived self-consistently from the boundary effective action. We solve these highly intertwined nonlinear differential equations based on the so called matching method. Our ansatz for the bi-local order-parameter fields coincide with the conformally invariant solution of the field theoretic large $N$ limit in the UV limit, but their overall coefficients RG-flow along the extradimensional space, respectively, reflecting effects of higher-order quantum corrections. As a result, we find an insulating behavior, where the self-energy diverges at IR. To confirm this insulating physics, we investigate thermodynamics. We obtain an effective free energy functional in terms of such bi-local dual order-parameter fields, which satisfy the [[0227 Hamilton-Jacobi|Hamilton-Jacobi]] equation of the holographic dual effective field theory. Based on the insulating solution, we find that the density of states vanishes at IR. This indicates that the RG flows of the collective dual order-parameter fields give rise to deviation from the [[0004 Black hole entropy|Bekenstein-Hawking entropy]] behavior of the field theoretic large $N$ limit.\] # Chowdhury, Chowdhury, Moga, Singh ## Loops, Recursions, and Soft Limits for Fermionic Correlators in (A)dS \[Links: [arXiv](https://arxiv.org/abs/2408.00074), [PDF](https://arxiv.org/pdf/2408.00074)\] \[Abstract: Study of correlation functions in [[0001 AdS-CFT|AdS/CFT]] and in-in correlators in de Sitter space often requires the computation of [[0109 Witten diagrams|Witten diagrams]]. Due to the complexity of evaluating radial integrals for these correlators, several indirect approaches have been developed to simplify computations. However, in momentum space, these methods have been limited to fields with integer spin. In this paper, we formulate tools for evaluating Witten diagrams with spin-$\frac{1}{2}$ fields in momentum space and discuss where they differ from the corresponding integer-spin analysis. We formulate our tools explicitly for massless fermions and present how appropriate Weight shifting operators with respect to the external kinematics can be used to obtain the generalization to fermions with integer mass. We apply these tools to loop Witten diagrams and also discuss their use for evaluating in-in correlators in dS. In cases where we can evaluate the loop integrals, we find their transcendentality is lower than the corresponding scalar field results. Further, we classify the nature of IR divergences encountered for interacting massive scalars and fermions. We also prove a novel Weinberg-like [[0009 Soft theorems|soft theorem]] for gauge fields coupled to matter in AdS and show that the universal terms in the leading soft factor are sensitive to the spin of the matter field. These generalize the recently discovered soft theorems for pure Yang-Mills to Yang-Mills with matter.\] # Chowdhury, Lipstein, Mei, Mo ## Soft Limits of Gluon and Graviton Correlators in Anti-de Sitter Space \[Links: [arXiv](https://arxiv.org/abs/2407.16052), [PDF](https://arxiv.org/pdf/2407.16052)\] \[Abstract: We derive formulae for the soft limit of tree-level gluon and graviton correlators in Anti-de Sitter space, which arise from Feynman diagrams encoding the Weinberg [[0009 Soft theorems|soft theorems]] in flat space. Other types of diagrams can also contribute to the soft limit at leading order in the soft momentum, but have a different pole structure. We derive these results at four points using explicit formulae recently obtained from the cosmological bootstrap and [[0067 Double copy|double copy]], and extend them to any multiplicity using bootstrap techniques in Mellin-momentum space.\] # Chu, Kharel ## Towards the Feynman rule for $n$-point gluon Mellin amplitudes in AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/2401.00038), [PDF](https://arxiv.org/pdf/2401.00038.pdf)\] \[Abstract: We investigate the embedding formalism in conjunction with the [[0079 Mellin transform|Mellin transform]] to determine tree-level gluon amplitudes in [[0001 AdS-CFT|AdS/CFT]]. Detailed computations of three to five-point correlators are conducted, ultimately distilling what were previously complex results for five-point correlators into a more succinct and comprehensible form. We then proceed to derive a recursion relation applicable to a specific class of n-point gluon amplitudes. This relation is instrumental in systematically constructing amplitudes for a range of topologies. We illustrate its efficacy by specifically computing six to eight-point functions. Despite the complexity encountered in the intermediate steps of the recursion, the higher-point correlator is succinctly expressed as a polynomial in boundary coordinates, upon which a specific differential operator acts. Remarkably, we observe that these amplitudes strikingly mirror their counterparts in flat space, traditionally computed using standard Feynman rules. This intriguing similarity has led us to propose a novel dictionary: comprehensive rules that bridge [[0105 AdS amplitudes|AdS Mellin amplitudes]] with flat-space gluon amplitudes.\] # Climent, Emparan, Magan, Sasieta, Lopez ## Universal Construction of Black Hole Microstates \[Links: [arXiv](https://arxiv.org/abs/2401.08775), [PDF](https://arxiv.org/pdf/2401.08775.pdf)\] \[Abstract: We refine and extend a recent construction of sets of [[0248 Black hole microstates|black hole microstates]] with semiclassical interiors that span a Hilbert space of dimension $e^S$, where $S$ is the [[0004 Black hole entropy|black hole entropy]]. We elaborate on the definition and properties of microstates in statistical and black hole mechanics. The gravitational description of microstates employs matter shells in the interior of the black hole, and we argue that in the limit where the shells are very heavy, the construction acquires universal validity. To this end, we show it for very wide classes of black holes: we first extend the construction to rotating and charged black holes, including extremal and near-extremal solutions, with or without supersymmetry, and we sketch how the construction of microstates can be embedded in String Theory. We then describe how the approach can include general quantum corrections, near or far from extremality. For supersymmetric black holes, the microstates we construct differ from other recent constructions in that the interior excitations are not confined within the near-extremal throat.\] # Colin-Ellerin, Lin ## Generalized entropy of photons in AdS \[Links: [arXiv](https://arxiv.org/abs/2406.12851), [PDF](https://arxiv.org/pdf/2406.12851)\] \[Abstract: This work analyzes the quantum corrections to [[0007 RT surface|holographic entanglement entropy]] at first subleading order in $G_{N}$ due to photon excited states in AdS. We compute the vacuum-subtracted von Neumann entropy of a $U(1)$ current excited state for a polar cap region on the cylinder in any large-$N$, strongly-coupled CFT$_{d}$ holographically dual to weakly-coupled [[0554 Einstein gravity|Einstein gravity]] for any dimension $d>2$. We then quantize a Maxwell field in AdS$_{d+1}$ dual to the $U(1)$ current and consider a photon excited state whose vacuum-subtracted generalized entropy for the entanglement wedge is calculated. In order to factorise the Maxwell Hilbert space in AdS, we construct an extended Hilbert space and the corresponding electromagnetic edge modes. We find exact agreement between the CFT entanglement entropy and AdS [[0212 Quantum extremal surface|generalized entropy]] without the inclusion of entropy of the [[0556 Edge mode|edge modes]]. Finally, we show via explicit calculation that the contribution to the vacuum-subtracted [[0301 Entanglement entropy|von Neumann entropy]] from electromagnetic edge modes indeed vanishes, which is crucial for consistency with known holographic entropy formulas.\] # Collier, Eberhardt, Muhlmann, Rodriguez (Sep, a) ## The complex Liouville string \[Links: [arXiv](https://arxiv.org/abs/2409.17246), [PDF](https://arxiv.org/pdf/2409.17246)\] \[Abstract: We introduce the [[0650 Complex Liouville string|complex Liouville string]], a solvable string theory defined by coupling two [[0562 Liouville theory|Liouville theories]] with complex conjugate central charges $c \in 13+i \mathbb{R}$ on the worldsheet. We compute its amplitudes from first principles and establish a duality with a double-scaled two-matrix integral. We also analyze general worldsheet boundaries and non-perturbative effects in the genus expansion. This theory is capable of capturing aspects of de Sitter quantum gravity in both two and three dimensions, which leads to a precise version of [[0545 de Sitter quantum gravity|de Sitter holography]].\] # Collier, Eberhardt, Muhlmann, Rodriguez (Sep, b) ## The complex Liouville string: the worldsheet \[Links: [arXiv](https://arxiv.org/abs/2409.18759), [PDF](https://arxiv.org/pdf/2409.18759)\] \[Abstract: We introduce a new two-dimensional string theory defined by coupling two copies of Liouville CFT with complex central charge $c=13\pm i \lambda$ on the worldsheet. This string theory defines a novel, consistent and controllable model of two-dimensional quantum gravity. We use the exact solution of the worldsheet theory to derive stringent constraints on the analytic structure of the string amplitudes as a function of the vertex operator momenta. Together with other worldsheet constraints, this allows us to completely pin down the string amplitudes without explicitly computing the moduli space integrals. We focus on the case of the sphere four-point amplitude and torus one-point amplitude as worked examples. This is the first in a series of papers on the [[0650 Complex Liouville string|complex Liouville string]]: three subsequent papers will elucidate the holographic duality with a two-matrix integral, discuss worldsheet boundaries and non-perturbative effects, and connect the theory to [[0545 de Sitter quantum gravity|de Sitter quantum gravity]].\] # Collier, Eberhardt, Muhlmann, Rodriguez (Oct, a) ## The complex Liouville string: the matrix integral \[Links: [arXiv](https://arxiv.org/abs/2410.07345), [PDF](https://arxiv.org/pdf/2410.07345)\] \[Abstract: We propose a duality between the [[0650 Complex Liouville string|complex Liouville string]] and a two-matrix integral. The complex Liouville string is defined by coupling two Liouville theories with complex central charges $c = 13 \pm i \lambda$ on the worldsheet. The matrix integral is characterized by its spectral curve which allows us to compute the perturbative string amplitudes recursively via topological recursion. This duality constitutes a controllable instance of holographic duality. The leverage on the theory is provided by the rich analytic structure of the string amplitudes that we discussed in [arXiv:2409.18759](https://arxiv.org/abs/2409.18759) and allows us to perform numerous tests on the duality.\] # Collier, Eberhardt, Muhlmann, Rodriguez (Oct, b) ## The complex Liouville string: worldsheet boundaries and non-perturbative effects \[Links: [arXiv](https://arxiv.org/abs/2410.09179), [PDF](https://arxiv.org/pdf/2410.09179)\] \[Abstract: We investigate general observables of the [[0650 Complex Liouville string|complex Liouville string]] with worldsheet boundaries. We develop a universal formalism that reduces such observables to ordinary closed string amplitudes without boundaries, applicable to any worldsheet string theory, but particularly simple in the context of 2d or minimal string theories. We apply this formalism to the duality of the complex Liouville string with the matrix integral proposed in [arXiv:2409.18759](https://arxiv.org/abs/2409.18759) and [arXiv:2410.07345](https://arxiv.org/abs/2410.07345) and showcase the formalism by finding appropriate boundary conditions for various matrix model quantities of interest, such as the resolvent or the partition function. We also apply this formalism towards the computation of non-perturbative effects on the worldsheet mediated by ZZ-instantons. These are known to be plagued by extra subtleties which need input from string field theory to resolve. These computations probe and uncover the duality between the complex Liouville string and the matrix model at the non-perturbative level.\] # Collier, Eberhardt, Zhang ## 3d gravity from Virasoro TQFT: Holography, wormholes and knots \[Links: [arXiv](https://arxiv.org/abs/2401.13900), [PDF](https://arxiv.org/pdf/2401.13900.pdf)\] \[Abstract: We further develop the description of [[0002 3D gravity|three-dimensional quantum gravity]] with negative cosmological constant in terms of [[0596 Virasoro TQFT|Virasoro TQFT]] formulated in our previous paper [[2023#Collier, Eberhardt, Zhang]]. We compare the partition functions computed in the Virasoro TQFT formalism to the semiclassical evaluation of Euclidean gravity partition functions. This matching is highly non-trivial, but can be checked directly in some examples. We then showcase the formalism in action, by computing the gravity partition functions of many relevant topologies. For holographic applications, we focus on the partition functions of Euclidean multi-boundary wormholes with three-punctured spheres as boundaries. This precisely quantifies the higher moments of the structure constants in the proposed ensemble boundary dual and subjects the proposal to thorough checks. Finally, we investigate in detail the example of the figure eight knot complement as a hyperbolic 3-manifold. We show that the Virasoro TQFT partition function is identical to the partition function computed in Teichmüller theory, thus giving strong evidence for the equivalence of these TQFTs. We also show how to produce a large class of manifolds via Dehn surgery on the figure eight knot.\] # Concepcion, Nomura, Ritchie, Weiss ## Complementarity for a Dynamical Black Hole \[Links: [arXiv](https://arxiv.org/abs/2405.15849), [PDF](https://arxiv.org/pdf/2405.15849)\] \[Abstract: [[0347 Black hole complementarity|Black hole complementarity]] posits that the interior of a black hole is not independent from its [[0304 Hawking radiation|Hawking radiation]]. This leads to an apparent violation of causality: the interior can be acausally affected by operators acting solely on the radiation. We argue that this perspective is misleading and that the black hole interior must be viewed as existing in the causal past of the Hawking radiation, despite the fact that they are spacelike separated in the semiclassical description. Consequently, no operation on the Hawking radiation -- no matter how complex -- can affect the experience of an infalling observer. The black hole interior and the radiation only appear spacelike separated in the semiclassical description because an infalling observer's ability to access complex information is limited; the [[0008 Quantum chaos|chaotic]] dynamics on the horizon, as viewed from the exterior, then converts any effect caused by such an observer to information in the Hawking radiation which cannot be accessed at the semiclassical level. We arrive at the picture described above by considering a unitary exterior description in which the flow of information is strictly causal, which we extend to apply throughout the entire history of black hole evolution, including its formation. This description uses the stretched event horizon as an inner edge of spacetime, on which the information inside is holographically encoded. We argue that the global spacetime picture arises from coarse-graining over [[0248 Black hole microstates|black hole microstates]], and discuss its relationship with the exterior description.\] # Cotler, Jensen ## Non-perturbative de Sitter Jackiw-Teitelboim gravity \[Links: [arXiv](https://arxiv.org/abs/2401.01925), [PDF](https://arxiv.org/pdf/2401.01925.pdf)\] \[Abstract: With non-perturbative de Sitter gravity and holography in mind, we deduce the genus expansion of de Sitter [[0050 JT gravity|Jackiw-Teitelboim]] (dS JT) gravity. We find that this simple model of quantum cosmology has an effective string coupling which is pure imaginary. This imaginary coupling gives rise to alternating signs in the genus expansion of the dS JT S-matrix, which as a result appears to be Borel-Le Roy resummable. We explain how dS JT gravity is dual to a formal matrix integral with, in a sense, a negative number of degrees of freedom.\] # Cotler, Jensen, Prohazka, Raz, Riegler, Salzer ## Quantizing Carrollian field theories \[Links: [arXiv](https://arxiv.org/abs/2407.11971), [PDF](https://arxiv.org/pdf/2407.11971)\] \[Abstract: [[0419 Carrollian CFT|Carrollian]] field theories have recently emerged as a candidate dual to flat space quantum gravity. We carefully quantize simple two-derivative Carrollian theories, revealing a strong sensitivity to the ultraviolet. They can be regulated upon being placed on a spatial lattice and working at finite inverse temperature. Unlike in conventional field theories, the details of the lattice-regulated Carrollian theories remain important at long distances even in the limit that the lattice spacing is sent to zero. We use that limit to define interacting continuum models with a tractable perturbative expansion. The ensuing theories are those of generalized free fields, with non-Gaussian correlations suppressed by positive powers of the lattice spacing, and an unbroken supertranslation symmetry.\] # Cui, Rozali ## Comments on firewalls in JT gravity with matter \[Links: [arXiv](https://arxiv.org/abs/2412.11012), [PDF](https://arxiv.org/pdf/2412.11012)\] \[Abstract: We present two discussions of [[0195 Firewall|firewalls]] in [[0050 JT gravity|JT gravity]]. First we present an alternative, arguably simpler, derivation of the gray hole conjecture, applying uniformly to all probes of the firewall probability previously discussed. This derivation is based on the wormhole shortening picture using the handle-disk geometry. However we modifies Saad's story utilizing a "Wilsonian" effective gravitational description, adapted to the time scale probed, in which high frequency modes are integrated out generating the gravitational bulk geometries (dual to the genus expansion in the matrix integral side) whereas low frequency modes are more precisely resolved by being represented as eigenvalue D-branes where JT universes can end. This treatment results in an effective "twist factor cutoff" prescription which simplifies the discussion of long time quantities including the firewall probability. In the second part we discuss effects of matter loops on the firewall probability. While such effects lead to new firewall sources, we argue that these matter loop contributions are sub-dominant at late times.\] # da Rocha ## Deformations of the AdS-Schwarzschild black brane and the shear viscosity of the quark-gluon plasma \[Links: [arXiv](https://arxiv.org/abs/2409.17325), [PDF](https://arxiv.org/pdf/2409.17325)\] \[Abstract: Deformations of the AdS$_5$-Schwarzschild black brane, implemented in the AdS/CFT [[0229 Membrane paradigm|membrane paradigm]], are scrutinized in the dual viscous hydrodynamic infrared limit. The latest experimental data analyses, regarding the [[0430 Holographic shear viscosity|shear viscosity-to-entropy density ratio]] of the quark-gluon plasma produced by heavy-ion collisions at the LHC and RHIC, are shown to constrain these deformations severely. Although corroborating with the robustness of the standard AdS$_5$-Schwarzschild black brane against deformations, there is still a margin for mild deformations which may carry 2-loop quantum corrections to gravity, whose implications to the strongly-coupled dual field theory are addressed and discussed.\] # Dar, Ganai, Kajuri ## Hawking Radiation in Jackiw-Teitelboim Gravity \[Links: [arXiv](https://arxiv.org/abs/2408.08985), [PDF](https://arxiv.org/pdf/2408.08985)\] \[Abstract: In this paper, we study [[0304 Hawking radiation|Hawking radiation]] in [[0050 JT gravity|Jackiw-Teitelboim gravity]] for minimally coupled massless and massive scalar fields. We employ a holography-inspired technique to derive the Bogoliubov coefficients. We consider both black holes in equilibrium and black holes attached to a bath. In the latter case, we compute semiclassical deviations from the thermal spectrum.\] # Das, Porey, Roy ## Brick Wall in AdS-Schwarzschild Black Hole: Normal Modes and Emerging Thermality \[Links: [arXiv](https://arxiv.org/abs/2409.05519), [PDF](https://arxiv.org/pdf/2409.05519)\] \[Abstract: This paper investigates the normal modes of a probe scalar field in a five-dimensional AdS-Schwarzschild black hole with the brick wall boundary condition near the horizon. We employ various techniques to compute the spectrum and analyze its properties. Our results reveal a linear dependence of the spectrum on the principal quantum number while demonstrating a non-trivial dependence on the angular momentum quantum number. We compute the [[0062 Spectral form factor|Spectral Form Factor]] (SFF) and find a dip-ramp-plateau structure, with the slope of the ramp approaching unity as the brick wall nears the horizon. We also observe that as the brick wall approaches the horizon, the poles of the [[0473 Retarded Green's function|retarded Green's function]] condense on the real line, leading to an emergent thermal behavior in the boundary theory. This work extends previous studies on lower-dimensional black holes to higher dimensions, providing insights into the connection between black hole microstate models and boundary [[0008 Quantum chaos|chaos]]. Our findings contribute to the ongoing discussions on the information paradox and the nature of black hole interiors in the context of [[0001 AdS-CFT|AdS/CFT]] correspondence.\] ## Related topics - [[0325 Quasi-normal modes]] # de Boer, Liska, Post ## Multiboundary wormholes and OPE statistics \[Links: [arXiv](https://arxiv.org/abs/2405.13111), [PDF](https://arxiv.org/pdf/2405.13111)\] \[Abstract: We derive higher moments in the statistical distribution of [[0030 Operator product expansion|OPE]] coefficients in holographic 2D CFTs, and show that such moments correspond to multiboundary Euclidean wormholes in pure [[0002 3D gravity|3D gravity]]. The $n$-th cyclic non-Gaussian contraction of heavy-heavy-light OPE coefficients follows from crossing symmetry of the thermal $n$-point function. We derive universal expressions for the cubic and quartic moments and demonstrate that their scaling with the microcanonical entropy agrees with a generalization of the Eigenstate Thermalization Hypothesis. Motivated by this result, we conjecture that the full statistical [[0154 Ensemble averaging|ensemble]] of OPE data is fixed by three premises: typicality, [[0021 Crossing symmetry|crossing symmetry]] and [[0612 Modular invariance|modular invariance]]. Together, these properties give predictions for non-factorizing observables, such as the generalized [[0062 Spectral form factor|spectral form factor]]. Using the [[0596 Virasoro TQFT|Virasoro TQFT]], we match these connected averages to new on-shell wormhole topologies with multiple boundary components. Lastly, we study and clarify examples where the statistics of heavy operators are not universal and depend on the light operator spectrum. We give a gravitational interpretation to these corrections in terms of Wilson loops winding around non-trivial cycles in the bulk.\] # De Luca, Garoffolo, Khoury, Trodden ## Tidal Love numbers and Green's functions in black hole space-times \[Links: [arXiv](https://arxiv.org/abs/2407.07156), [PDF](https://arxiv.org/pdf/2407.07156)\] \[Abstract: Tidal interactions play a crucial role in deciphering gravitational wave signals emitted by the coalescence of binary systems. They are usually quantified by a set of complex coefficients which include [[0581 Tidal Love numbers|tidal Love numbers]], describing the conservative response to an external perturbation. In the static case, these are found to vanish exactly for asymptotically flat black holes in general relativity in four space-time dimensions, and recently they have been generalized to dynamical interactions. In the context of response theory, the [[0473 Retarded Green's function|retarded Green's function]] provides the complete description of the behavior of dynamical systems. In this work we investigate the relation between Love numbers and Green's functions, and highlight the relevance of radiation reaction effects to their connection. As a special case, we discuss [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black holes, where the absence of radiative modes allows us to make a direct link between them.\] # De Vuyst, Eccles, Hoehn, Kirklin ## Gravitational entropy is observer-dependent \[Links: [arXiv](https://arxiv.org/abs/2405.00114), [PDF](https://arxiv.org/pdf/2405.00114.pdf)\] \[Abstract: In quantum gravity, it has been argued that a proper accounting of the role played by an observer promotes the [[0415 Von Neumann algebra|von Neumann algebra]] of observables in a given spacetime subregion from Type III to Type II. While this allows for a mathematically precise definition of its entropy, we show that this procedure depends on which observer is employed. We make this precise by considering a setup in which many possible observers are present; by generalising previous approaches, we derive density operators for the subregion relative to different observers (and relative to arbitrary collections of observers), and we compute the associated entropies in a semiclassical regime, as well as in some specific examples that go beyond this regime. We find that the entropies seen by distinct observers can drastically differ. Our work makes extensive use of the formalism of quantum reference frames (QRF); indeed, as we point out, the 'observers' considered here and in the previous works are nothing but QRFs. In the process, we demonstrate that the description of physical states and observables invoked by Chandrasekaran et al. ([[2022#Chandrasekaran, Longo, Penington, Witten]]) is equivalent to the Page-Wootters formalism, leading to the informal slogan "PW=CLPW". It is our hope that this paper will help motivate a long overdue union between the QRF and quantum gravity communities. Further details will appear in a companion paper.\] # Deddo, Liu, Zayas, Saskowski ## Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows \[Links: [arXiv](https://arxiv.org/abs/2404.15077), [PDF](https://arxiv.org/pdf/2404.15077.pdf)\] \[Abstract: We revisit the existence of monotonic quantities along renormalization group flows using only the [[0480 Null energy condition|Null Energy Condition]] and the [[0007 RT surface|Ryu-Takayanagi formula]] for the [[0301 Entanglement entropy|entanglement entropy]] of field theories with anti-de Sitter gravity duals. In particular, we consider flows within the same dimension and holographically reprove the c-, F-, and a-theorems in dimensions two, three, and four. We focus on the family of maximally spherical entangling surfaces, define a quasi-constant of motion corresponding to the breaking of conformal invariance, and use a properly defined distance between minimal surfaces to construct a [[0257 Holographic RG flow|holographic c-function]] that is monotonic along the flow. We then apply our method to the case of flows across dimensions: There, we reprove the monotonicity of flows from $\mathrm{AdS}_{D+1}$ to $\mathrm{AdS}_3$ and prove the novel case of flows from $\mathrm{AdS}_5$ to $\mathrm{AdS}_4$.\] # Dey, Pal, Qiao ## A universal inequality on the unitary 2D CFT partition function \[Links: [arXiv](https://arxiv.org/abs/2410.18174), [PDF](https://arxiv.org/pdf/2410.18174)\] \[Abstract: We prove the conjecture proposed by Hartman, Keller and Stoica [HKS14]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension $\frac{c}{12}+\epsilon$ and below the twist $\frac{c}{12}$ is universal in the large $c$ limit for all $\beta_L\beta_R \neq 4\pi^2$. The technique of the proof allows us to derive a one-parameter (with parameter $\alpha\in(0,1])$ family of universal inequalities on the unitary 2D CFT partition function with general central charge $c\geqslant 0$, using analytical modular bootstrap. We derive an iterative equation for the domain of validity of the inequality on the $(\beta_L,\beta_R)$ plane. The infinite iteration of this equation gives the boundary of maximal-validity domain, which depends on the parameter \alpha in the inequality. In the $c \to \infty$ limit, with the additional assumption of a sparse spectrum below the scaling dimension $\frac{c}{12} + \epsilon$ and the twist $\frac{\alpha c}{12}$ (with $\alpha \in (0,1]$ fixed), our inequality shows that the grand-canonical free energy exhibits a universal large $c$ behavior in the maximal-validity domain. This domain, however, does not cover the entire $(\beta_L, \beta_R)$ plane, except in the case of $\alpha = 1.$ For $\alpha = 1$, this proves the conjecture proposed by [HKS14], and for $\alpha < 1$, it quantifies how sparseness in twist affects the regime of universality. Furthermore, this implies a precise lower bound on the temperature of near-extremal [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black holes, above which we can trust the black hole thermodynamics.\] # Dodelson ## Ringdown in the SYK model \[Links: [arXiv](https://arxiv.org/abs/2408.05790), [PDF](https://arxiv.org/pdf/2408.05790)\] \[Abstract: We analyze thermal correlators in the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] model away from the maximally [[0008 Quantum chaos|chaotic]] limit. Despite the absence of a weakly curved black hole dual, the two point function decomposes into a sum over a discrete set of [[0325 Quasi-normal modes|quasinormal modes]]. To compute the spectrum of modes, we analytically solve the Schwinger-Dyson equations to a high order in perturbation theory, and then numerically fit to a sum of exponentials using a technique analogous to the double cone construction. The resulting spectrum has a tree-like structure which is reminiscent of AdS black holes with curvature singularities. We present a simple toy model of stringy black holes that qualitatively reproduces some aspects of this structure.\] # Dong, Kudler-Flam, Rath ## Entanglement Negativity and Replica Symmetry Breaking in General Holographic States \[Links: [arXiv](https://arxiv.org/abs/2409.13009), [PDF](https://arxiv.org/pdf/2409.13009)\] \[Abstract: The [[0210 Entanglement negativity|entanglement negativity]] $\mathcal{E}(A:B)$ is a useful measure of quantum entanglement in bipartite mixed states. In [[0368 Random tensor network|random tensor networks]] (RTNs), which are related to fixed-area states, it was found in [[2021#Dong, Qi, Walter]] that the dominant saddles computing the even Rényi negativity $\mathcal{E}^{(2k)}$ generically break the $\mathbb{Z}_{2k}$ replica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques that assumed $\mathbb{Z}_{2k}$ replica symmetry and proposed that the negativity was related to the [[0319 Entanglement wedge cross-section|entanglement wedge cross section]]. In this paper, we resolve this issue by showing that in general holographic states, the saddles computing $\mathcal{E}^{(2k)}$ indeed break the $\mathbb{Z}_{2k}$ replica symmetry. Our argument involves an identity relating $\mathcal{E}^{(2k)}$ to the $k$-th Rényi entropy on subregion $AB^*$ in the doubled state $|{\rho_{AB}}\rangle_{AA^*BB^*}$, from which we see that the $\mathbb{Z}_{2k}$ replica symmetry is broken down to $\mathbb{Z}_{k}$. For $k<1$, which includes the case of $\mathcal{E}(A:B)$ at $k=1/2$, we use a modified cosmic brane proposal to derive a new holographic prescription for $\mathcal{E}^{(2k)}$ and show that it is given by a new saddle with multiple cosmic branes anchored to subregions A and B in the original state. Using our prescription, we reproduce known results for the PSSY model and show that our saddle dominates over previously proposed CFT calculations near $k=1$. Moreover, we argue that the $\mathbb{Z}_{2k}$ symmetric configurations previously proposed are not gravitational saddles, unlike our proposal. Finally, we contrast holographic calculations with those arising from RTNs with non-maximally entangled links, demonstrating that the qualitative form of backreaction in such RTNs is different from that in gravity.\] # Derda, Helset, Parra-Martinez ## Soft Scalars in Effective Field Theory \[Links: [arXiv](https://arxiv.org/abs/2403.12142), [PDF](https://arxiv.org/pdf/2403.12142)\] \[Abstract: We derive a [[0009 Soft theorems|soft theorem]] for a massless scalar in an effective field theory with generic field content using the geometry of field space. This result extends the geometric soft theorem for scalar effective field theories by allowing the massless scalar to couple to other scalars, fermions, and gauge bosons. The soft theorem keeps its geometric form, but where the field-space geometry now involves the full field content of the theory. As a bonus, we also present novel double soft theorems with fermions, which mimic the geometric structure of the double soft theorem for scalars.\] # Donnay, Freidel, Herfray ## Carrollian $Lw_{1+\infty}$ representation from twistor space \[Links: [arXiv](https://arxiv.org/abs/2402.00688), [PDF](https://arxiv.org/pdf/2402.00688.pdf)\] \[Abstract: We construct an explicit realization of the action of the $Lw_{1+\infty}$ loop algebra on fields at null infinity. This action is directly derived by Penrose transform of the geometrical action of $Lw_{1+\infty}$ symmetries in [[0330 Twistor theory|twistor space]], ensuring that it forms a representation of the algebra. Finally, we show that this action coincides with the canonical action of $Lw_{1+\infty}$ Noether charges on the asymptotic phase space.\] ## Refs - [[0328 w(1+infinity)]] # Du, Stefanyszyn ## Soft Theorems for Boostless Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2403.05459), [PDF](https://arxiv.org/pdf/2403.05459.pdf)\] \[Abstract: We consider effective field theories (EFTs) of scalar fields with broken Lorentz boosts, which arise by taking the decoupling and flat-space limits of the EFT of inflation, and derive constraints that must be satisfied by the corresponding scattering amplitudes if there is an underlying non-linearly realised symmetry. We primarily concentrate on extended shift symmetries which depend on the space-time coordinates, and find that combinations of scattering amplitudes obey enhanced Adler zeros. That is, such combinations vanish as one external momentum is taken soft, with the rate at which they vanish dictated by the corresponding symmetry. In our [[0009 Soft theorems|soft theorem]] derivation, we pay particular care to the energy and momentum-conserving delta functions that arise due to space-time translations, and show that when acted upon by derivatives with respect to spatial momenta, they yield a tower of soft theorems which are ultimately required for closure of the underlying symmetry algebra. All of our soft theorems correspond to constraints that must be satisfied by on-shell amplitudes and, even for symmetries that depend on the time coordinate, our soft theorems only require derivatives to be taken with respect to spatial momenta. We perform a soft bootstrap procedure to find solutions to our soft theorems, and compare these solutions to what we find from an off-shell analysis using the coset construction.\] # Du, Sun ## Towards bit threads in general gravitational spacetimes \[Links: [arXiv](https://arxiv.org/abs/2406.04092), [PDF](https://arxiv.org/pdf/2406.04092)\] \[Abstract: The concept of the generalized entanglement wedge was recently proposed by Bousso and Penington, which states that any bulk gravitational region a possesses an associated generalized entanglement wedge $E(a) \supset a$ on a static Cauchy surface $M$ in general gravitational spacetimes, where $E(a)$ may contain an entanglement [[0213 Islands|island]] $I(a)$. It suggests that the fine-grained entropy for bulk region a is given by the generalized entropy $S_{\text{gen}}(E(a))$. Motivated by this proposal, we extend the quantum [[0211 Bit thread|bit thread]] description to general gravitational spacetimes, no longer limited to the AdS spacetime. By utilizing the convex optimization techniques, a dual flow description for the generalized entropy $S_{\text{gen}}(E(a))$ of a bulk gravitational region a is established on the static Cauchy surface M, such that $S_{\text{gen}}(E(a))$ is equal to the maximum flux of any flow that starts from the boundary $\partial M$ and ends at bulk region $a$, or equivalently, the maximum number of bit threads that connect the boundary $\partial M$ to the bulk region $a$. In addition, the nesting property of flows is also proved. Thus the basic properties of the entropy for bulk regions, i.e. the monotonicity, subadditivity, Araki-Lieb inequality and [[0218 Strong subadditivity|strong subadditivity]], can be verified from flow perspectives by using properties of flows, such as the nesting property. Moreover, in max thread configurations, we find that there exists some lower bounds on the bulk entanglement entropy of matter fields in the region $E(a)\setminus a$, particularly on an entanglement island region $I(a) \subset (E(a)\setminus a)$, as required by the existence of a nontrivial generalized entanglement wedge. Our quantum bit thread formulation may provide a way to investigate more fine-grained entanglement structures in general spacetimes.\] # Duary, Maji ## Spectral representation in Klein space: simplifying celestial leaf amplitudes \[Links: [arXiv](https://arxiv.org/abs/2406.02342), [PDF](https://arxiv.org/pdf/2406.02342)\] \[Abstract: In this paper, we explore the spectral representation in Klein space which is the split (2,2) signature flat spacetime. The Klein space can be foliated into Lorentzian $\mathrm{AdS}_3 /\mathbb{Z}$ slices, and its identity resolution has both continuous and discrete parts. We calculate the identity resolution, and the plancherel measure in these slices. Using the foliation of Klein space into the slices, and the identity resolution, and the plancherel measure in each slices, we compute the spectral representation of the massive bulk-to-bulk propagator in Klein space. It can be expressed as the sum of product of two massive (or tachyonic) conformal primary wavefunctions, with both continuous and discrete parts, and sharing a common boundary coordinate. An interesting point in Klein space is that since the identity resolution has both discrete and continuous parts, a new type of conformal primary wavefunction naturally arises for the massive (or tachyonic) case. For the [[0148 Conformal basis|conformal primary wavefunctions]], both the discrete and continuous parts involve integrating over the common boundary coordinate and the real (or imaginary) mass. In the discrete part, the conformal dimension is summed, whereas in the continuous part, it is integrated. The spectral representation in Klein space is a computational tool to derive conformal block expansions for celestial amplitude in Klein space and its building blocks called [[0613 Leaf amplitudes|celestial leaf amplitudes]], by integrating the particle interaction vertex over a single slice of foliation.\] # Duary, Upadhyay ## Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and antipodal matching of Liénard-Wiechert fields \[Links: [arXiv](https://arxiv.org/abs/2411.08540), [PDF](https://arxiv.org/pdf/2411.08540)\] \[Abstract: We revisit the [[0454 Flat holography from AdS-CFT|flat limit]] of AdS/CFT from the point of view of geodesics in AdS. We show that the flat space scattering amplitudes can be constructed from operator insertions where the geodesics of the particles corresponding to the operators hit the conformal boundary of AdS. Further, we compute the Liénard-Wiechert solutions in AdS by boosting a static charge using AdS isometries and show that the solutions are antipodally matched between two regions, separated by a global time difference of $\Delta\tau=\pi$. Going to the boundary of AdS along null geodesics, in the flat limit, this antipodal matching leads to the flat space antipodal matching near spatial infinity.\] # Dymarsky, Shapere ## Bulk derivation of TQFT gravity \[Links: [arXiv](https://arxiv.org/abs/2405.20366), [PDF](https://arxiv.org/pdf/2405.20366)\] \[Abstract: We outline a general derivation of holographic duality between "TQFT gravity" - the path integral of a 3d [[0607 Topological QFT|TQFT]] summed over different topologies - and an [[0154 Ensemble averaging|ensemble]] of boundary 2d CFTs. The key idea is to place the boundary ensemble on a Riemann surface of very high genus, where the duality trivializes. The duality relation at finite genus is then obtained by genus reduction. Our derivation is generic and does not rely on an explicit form of the bulk or boundary partition functions. It guarantees unitarity and suggests that the bulk sum should include all possible topologies. In the case of Abelian Chern-Simons theory with compact gauge group we show that the weights of the boundary ensemble are equal, while the bulk sum reduces to a finite sum over equivalence classes of topologies, represented by handlebodies with possible line defects.\] # Engelhardt, Folkestad, Levine, Verheijden, Yang ## Spoofing Entanglement in Holography \[Links: [arXiv](https://arxiv.org/abs/2407.14589), [PDF](https://arxiv.org/pdf/2407.14589)\] \[Abstract: A defining property of [[0304 Hawking radiation|Hawking radiation]] is that states with very low entanglement masquerade as highly mixed states; this property is captured by a quantum computational phenomenon known as spoofing entanglement. Motivated by the potential implications for [[0131 Information paradox|black hole information]] and the emergence of spacetime connectivity, as well as possible applications of spoofing entanglement, we investigate the geometrization of two types of entanglement spoofers in [[0001 AdS-CFT|AdS/CFT]]: so-called EFI pairs and pseudoentangled state ensembles. We show that (a strengthened version of) EFI pairs with a semiclassical bulk dual have a [[0196 Python's lunch|Python's Lunch]]; the maximally mixed state over the pseudoentangled state ensemble likewise features a Python's Lunch. Since a Python's Lunch must lie behind an event horizon, we find that black holes are the exclusive gravitational source of entanglement spoofing in the semiclassical limit. Finally, we use an extant construction of holographic pseudorandom states to yield a candidate example of a pseudoentangled state ensemble with a semiclassical bulk dual.\] # Fan ## Massless limit and conformal soft limit for celestial massive amplitudes \[Links: [arXiv](https://arxiv.org/abs/2404.05137), [PDF](https://arxiv.org/pdf/2404.05137)\] \[Abstract: In [[0010 Celestial holography|celestial holography]], the [[0256 Massive particles in CCFT|massive]] and massless scalars in 4d space-time are represented by the Fourier transform of the bulk-to-boundary propagators and the [[0079 Mellin transform|Mellin transform]] of plane waves respectively. Recently, the 3pt celestial amplitude of one massive scalar and two massless scalars was discussed in [arXiv:2312.08597](https://arxiv.org/abs/2312.08597). In this paper, we compute the 3pt celestial amplitude of two massive scalars and one massless scalar. Then we take the massless limit $m\to 0$ for one of the massive scalars, during which process the gamma function $\Gamma(1-\Delta)$ appears. By requiring the resulting amplitude to be well-defined, that is it goes to the 3pt amplitude of [arXiv:2312.08597](https://arxiv.org/abs/2312.08597), the scaling dimension of this massive scalar has to be conformally soft $\Delta \to 1$. The pole $1/(1-\Delta)$ coming from $\Gamma(1-\Delta)$ is crucial for this massless limit. Without it the resulting amplitude would be zero. This can be compared with the conformal soft limit in celestial gluon amplitudes, where a singularity $1/(\Delta -1)$ arises and the leading contribution comes from the soft energy $\omega\to 0$. The phase factors in the massless limit of massive conformal primary wave functions, dicussed in [arXiv:1705.01027](https://arxiv.org/abs/1705.01027), plays an import and consistent role in the celestial massive amplitudes. In this massless limit, the subleading terms $m^{2n}$ can also contribute poles when the scaling dimension is analytically continued to $\Delta=1-n$.\] # Faulkner, Speranza ## Gravitational algebras and the generalized second law \[Links: [arXiv](https://arxiv.org/abs/2405.00847), [PDF](https://arxiv.org/pdf/2405.00847.pdf)\] \[Abstract: We derive the [[0082 Generalised second law|generalized second law]] (GSL) for arbitrary cuts of Killing horizons from the perspective of crossed-product gravitational algebras, making use of a recent proposal by one of us for the construction of local gravitational algebras. This construction relies on the existence of a state whose [[0416 Modular Hamiltonian|modular flow]] is geometric on the horizon. In both free and interacting quantum field theories, such states are guaranteed to exist by the properties of half-sided translations on the horizon. Using geometric identities derived from the canonical analysis of general relativity on null surfaces, we show that the crossed product entropy agrees with the generalized entropy of the horizon cut in a semiclassical limit, and further reproduce Wall's result relating the GSL to monotonicity of [[0199 Relative entropy|relative entropy]] of the quantum field algebras. We also give a novel generalization of the GSL for interacting theories in asymptotically flat spacetimes involving the concept of an algebra at infinity for a half-sided translation, which accounts for triviality of the algebra of fields smeared only on the horizon. Going beyond the semiclassical limit, we compute subleading corrections to the crossed product entropy, but are unable to determine if the GSL continues to hold after accounting for these. We speculate that an improved GSL could follow from a hidden subalgebra structure of the crossed products, assuming the existence of an operator-valued weight between horizon cut algebras.\] # Fegebank, Kuzenko ## On equivalence of gauge-invariant models for massive integer-spin fields \[Links: [arXiv](https://arxiv.org/abs/2406.02573), [PDF](https://arxiv.org/pdf/2406.02573)\] \[Abstract: There are several approaches to formulate gauge-invariant models for massive [[0588 Higher-spin fields|integer-spin field]] in $d$ dimensions including the following: (i) in terms of symmetric tensor fields $\phi_{\mu_1 \dots \mu_k}$, with $k = s, s-1, \dots , 0$, restricted to be double traceless for $k\geq 4$; and (ii) in terms of a quartet of traceful symmetric tensor fields $\psi_{\mu_1 \dots \mu_k}$, of rank $k=s,s-1,s-2, s-3$. We demonstrate that these formulations in Minkowski space ${\mathbb M}^d$ are equivalent to the gauge-invariant theory for a massive integer-spin field proposed in 1989 by Pashnev. We also make use of the Klishevich-Zinoviev theory in ${\mathbb M}^d$ to derive a generalisation of the Singh-Hagen model for a massive integer-spin field in $d>4$ dimensions.\] # Ferrari ## Jackiw-Teitelboim Gravity, Random Disks of Constant Curvature, Self-Overlapping Curves and Liouville $\text{CFT}_{1}$ \[Links: [arXiv](https://arxiv.org/abs/2402.08052), [PDF](https://arxiv.org/pdf/2402.08052.pdf)\] \[Abstract: We propose a microscopic definition of finite cut-off [[0050 JT gravity|JT]] quantum gravity on the disk, both in the discretized and in the continuum points of view. The discretized formulation involves a new model of so-called self-overlapping random polygons. The measure is not uniform, implying that the degrees of freedom are not in one-to-one correspondence with the shape of the boundary. The continuum formulation is based on a boundary $\text{CFT}_{1}$ from which we predict some critical exponents of the self-overlapping polygon model. The coupling to an arbitrary bulk matter CFT is also discussed.\] # Ferrero, Francia, Heissenberg, Romoli ## Double-Copy Supertranslations \[Links: [arXiv](https://arxiv.org/abs/2402.11595), [PDF](https://arxiv.org/pdf/2402.11595.pdf)\] \[Abstract: In the framework of the convolutional [[0067 Double copy|double copy]], we investigate the [[0060 Asymptotic symmetry|asymptotic symmetries]] of the gravitational multiplet stemming from the residual symmetries of its single-copy constituents at null infinity. We show that the asymptotic symmetries of Maxwell fields in $D=4$ imply "double-copy supertranslations", i.e. [[0064 BMS group|BMS supertranslations]] and two-form asymptotic symmetries, together with the existence of infinitely many conserved charges involving the double-copy scalar. With the vector fields in Lorenz gauge, the double-copy parameters display a radial expansion involving logarithmic subleading terms, essential for the corresponding charges to be nonvanishing.\] # Fields, Glazebrook, Marciano, Zappala ## ER = EPR is an operational theorem \[Links: [arXiv](https://arxiv.org/abs/2410.16496), [PDF](https://arxiv.org/pdf/2410.16496)\] \[Abstract: We show that in the operational setting of a two-agent, local operations, classical communication (LOCC) protocol, Alice and Bob cannot operationally distinguish monogamous entanglement from a topological identification of points in their respective local spacetimes, i.e. that [[0220 ER=EPR|ER = EPR]] can be recovered as an operational theorem. Our construction immediately implies that in this operational setting, the local topology of spacetime is observer-relative. It also provides a simple demonstration of the non-traversability of ER bridges. As our construction does not depend on an embedding geometry, it generalizes previous geometric approaches to ER = EPR.\] # Fliss, Frenkel, Hartnoll, Soni ## Minimal Areas from Entangled Matrices \[Links: [arXiv](https://arxiv.org/abs/2408.05274), [PDF](https://arxiv.org/pdf/2408.05274)\] \[Abstract: We define a relational notion of a subsystem in theories of matrix quantum mechanics and show how the corresponding [[0301 Entanglement entropy|entanglement entropy]] can be given as a minimisation, exhibiting many similarities to the [[0007 RT surface|Ryu-Takayanagi formula]]. Our construction brings together the physics of entanglement [[0556 Edge mode|edge modes]], noncommutative geometry and quantum internal reference frames, to define a subsystem whose reduced state is (approximately) an incoherent sum of density matrices, corresponding to distinct spatial subregions. We show that in states where geometry emerges from semiclassical matrices, this sum is dominated by the subregion with minimal boundary area. As in the Ryu-Takayanagi formula, it is the computation of the entanglement that determines the subregion. We find that coarse-graining is essential in our microscopic derivation, in order to control the proliferation of highly curved and disconnected non-geometric subregions in the sum.\] # Forste, Natu ## Half-Wormholes in a Supersymmetric SYK Model \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/)\] \[Abstract: We identify [[0308 Half-wormhole|half-wormhole]] contributions to the non-averaged $\mathscr{N} =1$ supersymmetric [[0201 Sachdev-Ye-Kitaev model|SYK]] model in which time has been reduced to a point. As in previously studied examples, the inclusion of half-wormholes restores [[0249 Factorisation problem|factorisation]] in the large $N$ limit. Wormholes as well as half-wormholes break supersymmetry.\] # Fragoso, Guo ## The fermionic double smeared null energy condition \[Links: [arXiv](https://arxiv.org/abs/2405.10228), [PDF](https://arxiv.org/pdf/2405.10228)\] \[Abstract: [[0247 Energy conditions|Energy conditions]] are crucial for understanding why exotic phenomena such as traversable wormholes and [[0570 Time machine|closed timelike curves]] remain elusive. In this paper, we prove the Double Smeared Null Energy Condition (DSNEC) for the fermionic free theory in 4-dimensional flat Minkowski space-time, extending previous work on the same energy condition for the bosonic case \[1\]\[2\] by adapting Fewster and Mistry's method \[3\] to the energy-momentum tensor $T_{++}$. A notable difference from previous works lies in the presence of the $\gamma_0 \gamma_+$ matrix in $T_{++}$, causing a loss of symmetry. This challenge is addressed by making use of its square-root matrix. We provide explicit analytic results for the massless case as well as numerical insights for the mass-dependence of the bound in the case of Gaussian smearing.\] # Franken, Mori ## Horizon causality from holographic scattering in asymptotically dS$_3$ \[Links: [arXiv](https://arxiv.org/abs/2410.09050), [PDF](https://arxiv.org/pdf/2410.09050)\] \[Abstract: In the [[0001 AdS-CFT|AdS/CFT]] correspondence, a direct scattering in the bulk may not have a local boundary analog. A nonlocal implementation on the boundary requires $O(1/G_N)$ [[0300 Mutual information|mutual information]]. This statement is formalized by the connected wedge theorem, which can be proven using general relativity within AdS$_3$ but also argued for using quantum information theory on the boundary, suggesting that the theorem applies to any holographic duality. We examine scattering within the static patch of asymptotically dS$_3$ spacetime, which is conjectured to be described by a quantum theory on the stretched horizon in static patch holography. We show that causality on the horizon induced from null infinities $\mathcal{I}^{\pm}$ is consistent with the theorem. Specifically, signals propagating in the static patch are associated with local operators at $\mathcal{I}^{\pm}$. Our results suggest a novel connection between static patch holography and the [[0545 de Sitter quantum gravity|dS/CFT correspondence]].\] # Friedrich, Hebecker ## The Boundary Proposal \[Links: [arXiv](https://arxiv.org/abs/2403.18892), [PDF](https://arxiv.org/pdf/2403.18892)\] \[Abstract: One of the leading ideas for the beginning of the Universe is the Hartle-Hawking '[[0162 No-boundary wavefunction|No-Boundary Proposal]].' Since the Cobordism Conjecture claims that any spacetime allows for a dynamical boundary, we suggest that one may equally well consider a 'Boundary Proposal'. Specifically, the corresponding euclidean instanton is a sphere with two holes around north and south pole cut out. Analogously to the Hartle-Hawking proposal, the sphere is then cut in two at the equator and half of it is dropped. The equator is glued to an expanding Lorentzian de Sitter space, implementing a beginning of the Universe with a spacelike spherical boundary at its earliest moment. This process is in principle on equal footing with the one based on the no-boundary instanton. In fact, if the Linde-Vilenkin sign choice is used, this 'Boundary' creation process may even dominate. An intriguing implication arises if tensionless end-of-the-world branes, as familiar from type-IIA or M-theory, are available: Analogously to the Boundary Proposal, one may then be able to create a compact, flat torus universe from nothing, without any exponential suppression or enhancement factors.\] # Fumagalli, Gorbenko, Kames-King ## De Sitter Bra-Ket Wormholes \[Links: [arXiv](https://arxiv.org/abs/2408.08351), [PDF](https://arxiv.org/pdf/2408.08351)\] \[Abstract: We study a model for the initial state of the universe based on a [[0555 Gravitational path integral|gravitational path integral]] that includes connected geometries which simultaneously produce [[0216 Bra-ket wormholes|bra and ket]] of the wave function. We argue that a natural object to describe this state is the Wigner distribution, which is a function on a classical phase space obtained by a certain integral transform of the density matrix. We work with Lorentzian de Sitter [[0050 JT gravity|Jackiw-Teitelboim gravity]] in which we find semiclassical saddle-points for pure gravity, as well as when we include matter components such as a CFT and a classical inflaton field. We also discuss different choices of fixing time reparametrizations. In the regime of large universes our connected geometry dominates over the [[0162 No-boundary wavefunction|Hartle-Hawking saddle]] and gives a distribution that has a meaningful probabilistic interpretation for local observables. It does not, however, give a normalizable probability measure on the entire phase space of the theory.\] # Gadde, Harper, Krishna ## Multi-invariants and Bulk Replica Symmetry \[Links: [arXiv](https://arxiv.org/abs/2411.00935), [PDF](https://arxiv.org/pdf/2411.00935)\] \[Abstract: In this paper, we analyze the question of replica symmetry in the bulk for [[0264 Multi-partite entanglement|multi-partite entanglement]] measures in the vacuum state of two dimensional holographic CFTs. We first define a class of multi-partite local unitary invariants, multi-invariants, with a given replica symmetry that acts freely and transitively on the replicas. We look for a subclass of measures such that the dual bulk geometry also preserves replica symmetry. We obtain the most general solution to this problem if we require the bulk to preserve replica symmetry for general configurations of the regions. Orbifolding the bulk solution with the replica symmetry gives us a bulk geometry with a network of conical singularities. Our approach makes it clear that there are infinitely many infinitely large families of multi-invariants such that each family evaluates identically on the holographic state. Geometrically, these are equalities involving volumes of handlebodies, possibly of different genus, at particular points in the moduli space. In certain cases, we check our bulk computation with an explicit calculation in CFT. Finally we comment on the generalization to higher dimension.\] # Galloway, Ling ## Rigidity aspects of Penrose's singularity theorem \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: In this paper, we study rigidity aspects of [[0225 Singularity theorems|Penrose's singularity theorem]]. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces instead of trapped surfaces, then what can be said about the global spacetime structure if the spacetime is null geodesically complete? In this setting, we show that we obtain a foliation of [[0298 MOTS|MOTS]] which generate totally geodesic null hypersurfaces. Depending on our starting assumptions, we obtain either local or global rigidity results. We apply our arguments to cosmological spacetimes (i.e., spacetimes with compact Cauchy surfaces) and scenarios involving topological censorship.\] # Gao ## Modular flow in JT gravity and entanglement wedge reconstruction \[Links: [arXiv](https://arxiv.org/abs/2402.18655), [PDF](https://arxiv.org/pdf/2402.18655.pdf)\] \[Abstract: It has been shown in recent works that [[0050 JT gravity|JT gravity]] with matter with two boundaries has a type II$_\infty$ [[0415 Von Neumann algebra|algebra]] on each side. As the bulk spacetime between the two boundaries fluctuates in quantum nature, we can only define the entanglement wedge for each side in a pure algebraic sense. As we take the semiclassical limit, we will have a fixed long wormhole spacetime for a generic partially entangled thermal state (PETS), which is prepared by inserting heavy operators on the Euclidean path integral. Under this limit, with appropriate assumptions of the matter theory, geometric notions of the causal wedge and entanglement wedge emerge in this background. In particular, the causal wedge is manifestly [[0143 Causal wedge inclusion|nested]] in the entanglement wedge. Different PETS are orthogonal to each other, and thus the Hilbert space has a direct sum structure over sub-Hilbert spaces labeled by different Euclidean geometries. The full algebra for both sides is decomposed accordingly. From the algebra viewpoint, the causal wedge is dual to an emergent type III$_1$ subalgebra, which is generated by boundary light operators. To reconstruct the entanglement wedge, we consider the [[0416 Modular Hamiltonian|modular flow]] in a generic PETS for each boundary. We show that the modular flow acts locally and is the boost transformation around the global [[0007 RT surface|RT surface]] in the semiclassical limit. It follows that we can extend the causal wedge algebra to a larger type III$_1$ algebra corresponding to the entanglement wedge. Within each sub-Hilbert space, the original type II$_\infty$ reduces to type III$_1$.\] # Garattini, Zatrimaylov ## On the Wormhole--Warp Drive Correspondence \[Links: [arXiv](https://arxiv.org/abs/2401.15136), [PDF](https://arxiv.org/pdf/2401.15136.pdf)\] \[Abstract: We propose a correspondence between the Morris--Thorne wormhole metric and a [[0263 Warp drives|warp drive]] metric, which generalizes an earlier result by H. Ellis regarding the Schwarzschild black hole metric and makes it possible to embed a warp drive in a wormhole background. We demonstrate that in order to do that, one needs to also generalize the Natario--Alcubierre definition of warp drive and introduce nonzero intrinsic curvature. However, we also find out that in order to be [[0083 Traversable wormhole|traversable]] by a warp drive, the wormhole should have a horizon: in other words, humanly traversable wormholes cannot be traversed by a warp drive, and vice versa. We also discuss possible loopholes in this "no-go" theorem.\] # Garcia-Garcia, Verbaarschot, Zheng ## The Lyapunov exponent as a signature of dissipative many-body quantum chaos \[Links: [arXiv](https://arxiv.org/abs/2403.12359), [PDF](https://arxiv.org/pdf/2403.12359)\] \[Abstract: A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain [[0482 Out-of-time-order correlator|out-of-time-order-correlation]] (OTOC) functions around the Ehrenfest time with a rate given by a [[0466 Lyapunov exponent|Lyapunov exponent]]. Physically, the OTOCs describe the growth of quantum uncertainty that crucially depends on the nature of the quantum motion. Here, we employ the OTOC in order to provide a precise definition of dissipative [[0008 Quantum chaos|quantum chaos]]. For this purpose, we compute analytically the Lyapunov exponent for the ==vectorized formulation== of the large $q$-limit of a $q$-body [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] model coupled to a Markovian bath. These analytic results are confirmed by an explicit numerical calculation of the Lyapunov exponent for several values of $q \geq 4$ based on the solutions of the Schwinger-Dyson and Bethe-Salpeter equations. We show that the Lyapunov exponent decreases monotonically as the coupling to the bath increases and eventually becomes negative at a critical value of the coupling signaling a transition to a dynamics which is no longer quantum chaotic. Therefore, a positive Lyapunov exponent is a defining feature of dissipative many-body quantum chaos. The observation of the breaking of the exponential growth for sufficiently strong coupling suggests that dissipative quantum chaos may require in certain cases a sufficiently weak coupling to the environment.\] # Ge, Matsumoto, Zhang ## Duality between Seiberg-Witten Theory and Black Hole Superradiance \[Links: [arXiv](https://arxiv.org/abs/2402.17441), [PDF](https://arxiv.org/pdf/2402.17441.pdf)\] \[Abstract: The newly established [[0371 SW-QNM correspondence|Seiberg-Witten (SW)/Quasinormal Modes (QNM) correspondence]] offers an efficient analytical approach to calculate the [[0325 Quasi-normal modes|QNM]] frequencies, which was only available numerically before. This is based on the fact that both sides are characterized by Heun-type equations. We find that a similar duality exists between [[0542 Seiberg-Witten theory|Seiberg-Witten theory]] and black hole [[0616 Superradiance|superradiance]], since the latter can also be linked to confluent Heun equation after proper transformation. Then a dictionary is constructed, with the superradiance frequencies written in terms of gauge parameters. Further by instanton counting, and taking care of the boundary conditions through connection formula, the relating frequencies are obtained analytically, which show consistency with known numerical results.\] # Geiller ## Celestial w$_{1+\infty}$ charges and the subleading structure of asymptotically-flat spacetimes \[Links: [arXiv](https://arxiv.org/abs/2403.05195), [PDF](https://arxiv.org/pdf/2403.05195.pdf)\] \[Abstract: We study the subleading structure of asymptotically-flat spacetimes and its relationship to the [[0328 w(1+infinity)|w]]$_{1+\infty}$ loop algebra of higher spin charges. We do so using both the Bondi-Sachs and the [[0456 Newman-Penrose charges|Newman-Penrose]] formalism, via a dictionary built from a preferred choice of tetrad. This enables us to access properties of the so-called higher Bondi aspects, such as their evolution equations, their transformation laws under [[0060 Asymptotic symmetry|asymptotic symmetries]], and their relationship to the Newman-Penrose and the higher spin charges. By studying the recursive Einstein evolution equations defining these higher spin charges, we derive the general form of their transformation behavior under BMSW symmetries. This leads to an immediate proof that the spin $0,1$ and spin $s$ brackets reproduce upon linearization the structure expected from the w$_{1+\infty}$ algebra. We then define renormalized higher spin charges which are conserved in the radiative vacuum at quadratic order, and show that they satisfy for all spins the w$_{1+\infty}$ algebra at linear order in the radiative data.\] # Geng, Jiang ## Microscopic Origin of the Entropy of Single-sided Black Holes \[Links: [arXiv](https://arxiv.org/abs/2409.12219), [PDF](https://arxiv.org/pdf/2409.12219)\] \[Abstract: In this paper, we provide a state-counting derivation of the Bekenstein-Hawking entropy formula for single-sided black holes. We firstly articulate the concept of the [[0248 Black hole microstates|black hole microstates]]. Then we construct explicit mircostates of single-sided black holes in (2+1)-dimensional spacetimes with a negative cosmological constant. These microstates are constructed by putting a [[0452 Karch-Randall braneworld|Karch-Randall brane]] behind the black hole horizon. Their difference is described by different interior excitations which gravitationally backreact. We show that these microstates have nonperturbatively small overlaps with each other. As a result, we use this fact to give a state-counting derivation of the Bekenstein-Hawking entropy formula for single-sided black holes. At the end, we notice that there are no negative norm states in the resulting Hilbert space of the black hole microstates which in turn ensures unitarity. All calculations in this paper are analytic and can be easily generalized to higher spacetime dimensions.\] # Gesteau, Marcolli, McNamara ## Wormhole Renormalization: The gravitational path integral, holography, and a gauge group for topology change \[Links: [arXiv](https://arxiv.org/abs/2407.20324), [PDF](https://arxiv.org/pdf/2407.20324)\] \[Abstract: We study the [[0249 Factorisation problem|Factorization Paradox]] from the bottom up by adapting methods from perturbative renormalization. Just as quantum field theories are plagued with loop divergences that need to be cancelled systematically by introducing counterterms, gravitational path integrals are plagued by [[0278 Euclidean wormholes|wormhole]] contributions that spoil the factorization of the holographic dual. These wormholes must be cancelled by some stringy effects in a UV complete, holographic theory of quantum gravity. In a simple model of two-dimensional topological gravity, we outline a gravitational analog of the recursive BPHZ procedure in order to systematically introduce ''counter-wormholes" which parametrize the unknown stringy effects that lead to factorization. Underlying this procedure is a Hopf algebra of symmetries which is analogous to the Connes--Kreimer Hopf algebra underlying perturbative renormalization. The group dual to this Hopf algebra acts to reorganize contributions from spacetimes with distinct topology, and can be seen as a gauge group relating various equivalent ways of constructing a factorizing [[0555 Gravitational path integral|gravitational path integral]].\] # Glorioso, Qi, Yang ## Space-time generalization of mutual information \[Links: [arXiv](https://arxiv.org/abs/2401.02475), [PDF](https://arxiv.org/pdf/2401.02475.pdf)\] \[Abstract: The [[0300 Mutual information|mutual information]] characterizes correlations between spatially separated regions of a system. Yet, in experiments we often measure dynamical correlations, which involve probing operators that are also separated in time. Here, we introduce a space-time generalization of mutual information which, by construction, satisfies several natural properties of the mutual information and at the same time characterizes correlations across subsystems that are separated in time. In particular, this quantity, that we call the *space-time mutual information*, bounds all dynamical correlations. We construct this quantity based on the idea of the quantum hypothesis testing. As a by-product, our definition provides a transparent interpretation in terms of an experimentally accessible setup. We draw connections with other notions in quantum information theory, such as quantum channel discrimination. Finally, we study the behavior of the space-time mutual information in several settings and contrast its long-time behavior in many-body localizing and thermalizing systems.\] # Godet ## Quantum cosmology as automorphic dynamics \[Links: [arXiv](https://arxiv.org/abs/2405.09833), [PDF](https://arxiv.org/pdf/2405.09833)\] \[Abstract: We revisit pure [[0545 de Sitter quantum gravity|quantum cosmology]] in three dimensions. The Wheeler-DeWitt equation can be solved perturbatively and the dynamics reduces to a particle on moduli space. Its time evolution is equivalent to the $T\overline{T}$ deformation. Focusing on spacetimes with torus slices, we show that inflationary cosmologies correspond to particle trajectories in Artin's billiard. The resulting automorphic dynamics is developed both from a first and second quantized perspectives. Our main application is to give an interpretation for the Hartle-Hawking state which is here the analytic continuation of the Maloney-Witten partition function. We obtain its spectral decomposition and an exact representation as an average involving the Möbius function.\] # Goldar, Kajuri ## Bulk Reconstruction in De Sitter Spacetime \[Links: [arXiv](https://arxiv.org/abs/2405.16832), [PDF](https://arxiv.org/pdf/2405.16832)\] \[Abstract: The [[0026 Bulk reconstruction|bulk reconstruction]] program involves expressing local bulk fields as non-local operators on the boundary. It was initiated in the context of [[0001 AdS-CFT|AdS/CFT]] correspondence. Attempts to extend it to de Sitter have been successful for heavy (principal series) scalar fields. For other fields, the construction ran into issues. In particular, divergences were found to appear for [[0588 Higher-spin fields|higher spin fields]]. In this paper, we resolve these issues and obtain boundary representations for scalars of all masses as well as higher spin fields. We trace the origin of the previously discovered divergences and show that the smearing function becomes distributional for certain values of mass, spin and dimension. We also extend the construction from Bunch-Davies vacuum to all \alpha-vacua.\] # Gomez ## The Algebraic Page Curve \[Links: [arXiv](https://arxiv.org/abs/2403.09165), [PDF](https://arxiv.org/pdf/2403.09165.pdf)\] \[Abstract: The [[0131 Information paradox|Page curve]] describing the process of black hole evaporation is derived in terms of a family, parametrized in terms of the evaporation time, of finite type II$_1$ factors, associated, respectively, to the entanglement wedges of the black hole and the radiation. The so defined Page curve measures the relative continuous dimension of the black hole and the radiation along the evaporation process. The transfer of information is quantitatively defined in terms of the Murray von Neumann parameter describing the change of the spatial properties of the factors during the evaporation. In the simplest case the generator of the evaporation process is defined in terms of the action of the fundamental group of the hyperfinite type II$_1$ factor. In this setup the Page curve describes a phase transition with the transfer of information as order parameter. We discuss the limits of either a type I or a type III description of the black hole evaporation.\] # Goodhew, Thavanesan, Wall ## The Cosmological CPT Theorem \[Links: [arXiv](https://arxiv.org/abs/2408.17406), [PDF](https://arxiv.org/pdf/2408.17406)\] \[Abstract: The [[0635 CPT theorem|CPT theorem]] states that a unitary and Lorentz-invariant theory must also be invariant under a discrete symmetry CRT which reverses charge, time, and one spatial direction. In this article, we study a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry group, in which two of the nontrivial symmetries (''Reflection Reality'' and a 180 degree rotation) are implied by Unitarity and Lorentz Invariance respectively, while the third is CRT. (In cosmology, Scale Invariance plays the role of Lorentz Invariance.) This naturally leads to converses of the CPT theorem, as any two of the discrete $\mathbb{Z}_2$ symmetries will imply the third one. Furthermore, in many field theories, the Reflection Reality $\mathbb{Z}_2$ symmetry is actually sufficient to imply the theory is fully unitary, over a generic range of couplings. Building upon previous work on the Cosmological Optical Theorem, we derive non-perturbative reality conditions associated with bulk Reflection Reality (in all flat FLRW models) and CRT (in de Sitter spacetime), in arbitrary dimensions. Remarkably, this CRT constraint suffices to fix the phase of all wavefunction coefficients at future infinity (up to a real sign) -- without requiring any analytic continuation, or comparison to past infinity -- although extra care is required in cases where the bulk theory has logarithmic UV or IR divergences. This result has significant implications for [[0545 de Sitter quantum gravity|de Sitter holography]], as it allows us to determine the phases of arbitrary $n$-point functions in the dual CFT.\] # Grabovsky ## Heavy States in 3d Gravity and 2d CFT \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: We discuss correlators of light fields in heavy states in [[0002 3D gravity|3d gravity]] and holographic [[0003 2D CFT|2d CFTs]]. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black hole can be obtained by solving the wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in [[0032 Virasoro algebra|Virasoro]] blocks to our bulk results, we determine the [[0030 Operator product expansion|OPE]] coefficients of all contributing states in both the $s$ and $t$ channels. In the $s$ channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The $t$-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.\] # Grado-White, Grimaldi, Headrick, Hubeny ## Testing holographic entropy inequalities in 2+1 dimensions \[Links: [arXiv](https://arxiv.org/abs/2407.07165), [PDF](https://arxiv.org/pdf/2407.07165)\] \[Abstract: We address the question of whether [[0259 Holographic entropy cone|holographic entropy inequalities]] obeyed in static states (by the [[0007 RT surface|RT formula]]) are always obeyed in time-dependent states (by the HRT formula), focusing on the case where the bulk spacetime is $2+1$ dimensional. An affirmative answer to this question was previously claimed by Czech-Dong. We point out an error in their proof when the bulk is multiply connected. We nonetheless find strong support, of two kinds, for an affirmative answer in that case. We extend the Czech-Dong proof for simply-connected spacetimes to spacetimes with $\pi_1=\mathbb{Z}$ (i.e. 2-boundary, genus-0 wormholes). Specializing to vacuum solutions, we also numerically test thousands of distinct inequalities (including all known RT inequalities for up to 6 regions) on millions of randomly chosen configurations of regions and bulk spacetimes, including three different multiply-connected topologies; we find no counterexamples. In an appendix, we prove some (dimension-independent) facts about degenerate HRT surfaces and symmetry breaking.\] ## Assumptions - needs [[0480 Null energy condition|NEC]] # Gray, Keeler, Kubiznak, Martin ## Love symmetry in higher-dimensional rotating black hole spacetimes \[Links: [arXiv](https://arxiv.org/abs/2409.05964), [PDF](https://arxiv.org/pdf/2409.05964)\] \[Abstract: We develop a method for constructing a 1-parameter family of globally-defined [[0581 Tidal Love numbers|Love]] symmetry generators in rotating black hole spacetimes of general dimension. The key ingredient is to focus on the vicinity of the (physical) outer horizon, matching only the radial derivative and the outer horizon pole pieces of the Klein--Gordon operator in the black hole spacetime to the $SL(2,\mathbb{R})$ Casimir operator. After revisiting the 4D Kerr and 5D Myers--Perry cases, the procedure is illustrated on generalized Lense--Thirring spacetimes which describe a wide variety of slowly rotating black hole metrics in any number of dimensions. Such spacetimes are known to admit an extended tower of Killing tensor and Killing vector symmetries and, as demonstrated in this paper, allow for separability of the massive scalar wave equation in Myers--Perry-like coordinates. Interestingly, separability also occurs in the horizon-penetrating Painlevé--Gullstrand coordinates associated with the freely infalling observer who registers flat space around her all the way to singularity.\] # Griguolo, Papalini, Russo, Seminara ## Asymptotics of Weil-Petersson volumes and two-dimensional quantum gravities \[Links: [arXiv](https://arxiv.org/abs/2402.07276), [PDF](https://arxiv.org/pdf/2402.07276.pdf)\] \[Abstract: We propose a refined expression for the large genus asymptotics of the Weil-Petersson volumes of the moduli space of super-Riemann surfaces with an arbitrary number of boundaries. Our formula leverages the connection between [[0050 JT gravity|JT supergravity]] and its [[0197 Matrix model|matrix model]] definition, utilizing some basic tools of resurgence theory. The final result holds for arbitrary boundary lengths and preserves the polynomial structure of the super-volumes. As a byproduct we also obtain a prediction for the large genus asymptotics of generalized $\Theta$-class intersection numbers. We extend our proposal to the case of the quantum volumes relevant for the Virasoro minimal string/[[0562 Liouville theory|Liouville gravity]]. Performing the classical limit on the quantum volumes, we recover a formula for the ordinary Weil-Petersson building blocks of JT gravity.\] # Grozdanov, Vrbica ## Duality constraints on thermal spectra of 3d CFTs and 4d quasinormal modes \[Links: [arXiv](https://arxiv.org/abs/2406.19790), [PDF](https://arxiv.org/pdf/2406.19790)\] \[Abstract: Thermal spectra of correlation functions in holographic 3d large-$N$ CFTs correspond to [[0325 Quasi-normal modes|quasinormal modes]] of classical gravity and other fields in asymptotically anti-de Sitter black hole spacetimes. Using general properties of such spectra along with constraints imposed by the S-duality (or the particle-vortex duality), we derive a spectral duality relation that all such spectra must obey. Its form is universal in that each such relation (expressed as an infinite product over QNMs) only depends on a single function of a spatial wavevector that corresponds to the bulk algebraically special frequencies. In the process, we also derive a new sum rule constraining products over QNMs. The spectral duality relation, which imposes an infinite set of constraints on the QNMs, is then investigated and a number of well-known holographic examples that demonstrate its validity are examined. Our results also allow us to understand several new aspects of the [[0179 Pole skipping|pole-skipping]] phenomenon.\] # Guevara, Hu, Pasterski ## Multiparticle Contributions to the Celestial OPE \[Links: [arXiv](https://arxiv.org/abs/2402.18798), [PDF](https://arxiv.org/pdf/2402.18798.pdf)\] \[Abstract: We start by defining two-particle operators that appear in [[0010 Celestial holography|celestial CFT]]. We then show how to compute their [[0030 Operator product expansion|OPE]] coefficients with the known single-particle operators at tree level from multiparticle factorization channels, focusing on the leading contribution involving the two-particle states. These factorization channels only give us single-particle exchanges. To extract the multiparticle exchanges, we look at the $\overline{\rm MHV}$ gluon amplitudes and show how non-factorization channels contribute to two-particle terms in the single-helicity sector. This is a first step towards systematically computing the full [[0114 Celestial OPE|celestial OPE]].\] # Guo, He, Zhang ## Relation between timelike and spacelike entanglement entropy \[Links: [arXiv](https://arxiv.org/abs/2402.00268), [PDF](https://arxiv.org/pdf/2402.00268)\] \[Abstract: In this study, we establish a connection between [[0606 Timelike entanglement|timelike]] and [[0301 Entanglement entropy|spacelike entanglement entropy]]. Specifically, for a diverse range of states, the timelike entanglement entropy is uniquely determined by a linear combination of the spacelike entanglement entropy and its first-order temporal derivative. This framework reveals that the imaginary component of the timelike entanglement entropy primarily originates from the non-commutativity between the twist operator and its first-order temporal derivative. Furthermore, we analyze the constraints of this relation and highlight the possible extension to accommodate more complex state configurations.\] # Guo, Xu ## Imaginary part of timelike entanglement entropy \[Links: [arXiv](https://arxiv.org/abs/2410.22684), [PDF](https://arxiv.org/pdf/2410.22684)\] \[Abstract: In this paper, we explore the imaginary part of the [[0606 Timelike entanglement|timelike entanglement entropy]]. In the context of field theory, it is more appropriate to obtain the timelike entanglement entropy through the Wick rotation of the twist operators. It is found that, in certain special cases, the imaginary part of the timelike entanglement entropy is related to the commutator of the twist operator and its first-order temporal derivative. To evaluate these commutators, we employ the [[0030 Operator product expansion|operator product expansion]] of the twist operators, revealing that the commutator is generally universal across most scenarios. However, in more general cases, the imaginary part of the timelike entanglement entropy proves to be more complex. We compute the commutator of the twist operators along with its higher-order temporal derivatives. Utilizing these results, we derive a modified formula for the imaginary part of the timelike entanglement entropy. Furthermore, we extend this formula to the case of strip subregion in higher dimensions. Our analysis shows that for the strip geometry, the imaginary part of the timelike entanglement entropy is solely related to the commutators of the twist operator and its first-order temporal derivative. The findings presented in this paper provide valuable insights into the imaginary part of timelike entanglement entropy and its physical significance.\] # Haneder, Urbina, Moreno, Weber, Richter ## Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions \[Links: [arXiv](https://arxiv.org/abs/2410.02270), [PDF](https://arxiv.org/pdf/2410.02270)\] \[Abstract: Based on periodic orbit theory we address the individual-system versus [[0154 Ensemble averaging|ensemble]] interpretation of quantum gravity from a [[0008 Quantum chaos|quantum chaos]] perspective. To this end we show that the spectrum of geodesic motion on high-dimensional hyperbolic manifolds, described by the Selberg trace formula, displays a Schwarzian $(\sinh 2\pi\sqrt{E})$ mean level density. Due to its chaotic classical limit, this quantum system also shows all universal signatures of quantum chaos. These two properties imply a possible duality to [[0050 JT gravity|Jackiw-Teitelboim]]-type quantum gravity at the level of a single system instead of an ensemble of systems like matrix theories and [[0201 Sachdev-Ye-Kitaev model|SYK models]]. Beyond the universal regime we show how the full wormhole geometry on the gravity side emerges from the discreteness of the set of periodic orbits. Thereby, we take initial steps towards a duality between gravitational and mesoscopic chaotic quantum systems through the topological, respectively, periodic orbit expansions of their correlators.\] # Hao ## Holographic reconstruction of flat spacetime \[Links: [arXiv](https://arxiv.org/abs/2404.01113), [PDF](https://arxiv.org/pdf/2404.01113)\] \[Abstract: The flat/CFT dictionary between the bulk gravitational theory and boundary conformal field theory is systematically developed in this paper. Asymptotically flat spacetime is built up by asymptotically AdS hyperboloid slices in terms of [[0011 Fefferman-Graham expansion|Fefferman Graham]] coordinates together with soft modes propagating between different slices near the null boundary. Then we construct the flat holography dictionary based on studying Einstein equation at zero and first order and it turns out that these correspond to the description of hard and soft sector for the field theory from the boundary point of view. The explicit expression for energy-stress tensor is also determined by performing [[0209 Holographic renormalisation|holographic renormalisation]] on the Einstein Hilbert action. By studying the anomalies of the energy-stress tensor, we obtain the leading and subleading contribution to the [[0033 Central charge|central charge]]. Einstein equations in the bulk are related to the [[0106 Ward identity|Ward identities]] of the boundary theory and we find that the boundary CFT energy-stress tensor is not conserved due to the existence of radiative soft modes which will generate the energy flow through the null boundary.\] # Harper, Kanda, Takayanagi, Tasuki ## The g-theorem from Strong Subadditivity \[Links: [arXiv](https://arxiv.org/abs/2403.19934), [PDF](https://arxiv.org/pdf/2403.19934)\] \[Abstract: We show that [[0218 Strong subadditivity|strong subadditivity]] provides a simple derivation of the [[0351 Irreversibility theorems|g-theorem]] for the boundary renormalization group flow in two-dimensional conformal field theories. We work out its [[0257 Holographic RG flow|holographic interpretation]] and also give a derivation of the g-theorem for the case of an [[0065 Defect CFT|interface in two-dimensional conformal field theories]]. We also geometrically confirm strong subadditivity for [[0181 AdS-BCFT|holographic duals of conformal field theories on manifolds with boundaries]].\] # Harper, Takayanagi, Tsuda ## Multi-entropy at low Renyi index in 2d CFTs \[Links: [arXiv](https://arxiv.org/abs/2401.04236), [PDF](https://arxiv.org/pdf/2401.04236.pdf)\] \[Abstract: For a static time slice of AdS$_3$ we describe a particular class of minimal surfaces which form trivalent networks of geodesics. Through geometric arguments we provide evidence that these surfaces describe a measure of [[0264 Multi-partite entanglement|multipartite entanglement]]. By relating these surfaces to [[0007 RT surface|Ryu-Takayanagi surfaces]] it can be shown that this multipartite contribution is related to the angles of intersection of the bulk geodesics. A proposed boundary dual, the multi-entropy, generalizes replica trick calculations involving twist operators by considering monodromies with finite group symmetry beyond the cyclic group used for the computation of entanglement entropy. We make progress by providing explicit calculations of Renyi multi-entropy in two dimensional CFTs and geometric descriptions of the replica surfaces for several cases with low genus. We also explore aspects of the free fermion and free scalar CFTs. For the free fermion CFT we examine subtleties in the definition of the twist operators used for the calculation of Renyi multi-entropy. In particular the standard bosonization procedure used for the calculation of the usual entanglement entropy fails and a different treatment is required.\] # Hartman, Mathys ## Light-ray sum rules and the $c$-anomaly \[Links: [arXiv](https://arxiv.org/abs/2405.10137), [PDF](https://arxiv.org/pdf/2405.10137)\] \[Abstract: In a four-dimensional quantum field theory that flows between two fixed points under the [[0351 Irreversibility theorems|renormalization group]], the change in the conformal anomaly $\Delta a$ has been related to the [[0417 Averaged null energy condition|average null energy]]. We extend this result to derive a sum rule for the other [[0306 Weyl anomaly|anomaly]] coefficient, $\Delta c$, in terms of the stress tensor three-point function. While the sum rule for $\Delta a$ is an expectation value of the averaged null energy operator, and therefore positive, the result for $\Delta c$ involves the off-diagonal matrix elements, so it does not have a fixed sign.\] # Have, Nguyen, Prohazka, Salzer ## Massive carrollian fields at timelike infinity \[Links: [arXiv](https://arxiv.org/abs/2402.05190), [PDF](https://arxiv.org/pdf/2402.05190.pdf)\] \[Abstract: Motivated by flat space holography, we demonstrate that massive spin-$s$ fields in Minkowski space near timelike infinity are massive carrollian fields on the carrollian counterpart of anti-de Sitter space called $\mathsf{Ti}$. Its isometries form the Poincaré group, and we construct the carrollian spin-$s$ fields using the method of induced representations. We provide a dictionary between massive carrollian fields on $\mathsf{Ti}$ and massive fields in Minkowski space, as well as to fields in the [[0148 Conformal basis|conformal primary basis]] used in [[0010 Celestial holography|celestial holography]]. We show that the symmetries of the [[0419 Carrollian CFT|carrollian]] structure naturally account for the [[0064 BMS group|BMS]] charges underlying the [[0009 Soft theorems|soft graviton theorem]]. Finally, we initiate a discussion of the correspondence between massive scattering amplitudes and carrollian correlation functions on $\mathsf{Ti}$, and introduce physical definitions of detector operators using a suitable notion of conserved carrollian energy-momentum tensor.\] # He ## One-loop partition functions in $T\overline{T}$-deformed AdS$_3$ \[Links: [arXiv](https://arxiv.org/abs/2401.09879), [PDF](https://arxiv.org/pdf/2401.09879.pdf)\] \[Abstract: We study the geometry of $T\bar{T}$-[[0170 TTbar|deformed]] [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black hole and find it can be regarded as a quotient of hyperbolic space. We then consider the massive scalar field propagating in the $T\bar{T}$-deformed BTZ black hole background. The one-loop partition function of scalar field is calculated using the heat kernel method and the [[0653 Wilson spool|Wilson spool]] proposal. These two methods give consistent result which implies the Wilson spool proposal still holds under $T\bar{T}$ deformation. Moreover, we also calculate the one-loop partition function of graviton in $T\bar{T}$-deformed BTZ black hole. We find the deformed one-loop partition functions are modified in a simple way, which corresponds to a replacement of the modular parameter. The result precisely matches the large $c$ expansion of $T\bar{T}$-deformed CFT partition function. These results provide a further check about the correspondence between $T\bar{T}$-deformed CFT$_2$ and AdS$_3$ with mixed boundary condition.\] # He, Lau, Zhao ## Detecting quantum chaos via pseudo-entropy and negativity \[Links: [arXiv](https://arxiv.org/abs/2403.05875), [PDF](https://arxiv.org/pdf/2403.05875.pdf)\] \[Abstract: [[0290 Quantum information measures|Quantum informatic quantities]] such as [[0301 Entanglement entropy|entanglement entropy]] are useful in detecting quantum phase transitions. Recently, a new entanglement measure called pseudo-entropy was proposed which is a generalization of the more well-known entanglement entropy. It has many nice properties and is useful in the study of post-selection measurements. In this paper, one of our goals is to explore the properties of pseudo-entropy and study the effectiveness of it as a [[0008 Quantum chaos|quantum chaos]] diagnostic, i.e. as a tool to distinguish between chaotic and integrable systems. Using various variants of the [[0201 Sachdev-Ye-Kitaev model|SYK]] model, we study the signal of quantum chaos captured in the pseudo-entropy and relate it to the [[0062 Spectral form factor|spectral form factor]] (SFF) and local operator entanglement (LOE). We also explore another quantity called the [[0210 Entanglement negativity|negativity of entanglement]] which is a useful entanglement measure for a mixed state. We generalized it to accommodate the transition matrix and called it pseudo-negativity in analogy to pseudo-entropy. We found that it also nicely captures the spectral properties of a chaotic system and hence also plays a role as a tool of quantum chaos diagnostic.\] # He, Li, Xie ## Holographic stress tensor correlators on higher genus Riemann surfaces \[Links: [arXiv](https://arxiv.org/abs/2406.04042), [PDF](https://arxiv.org/pdf/2406.04042)\] \[Abstract: In this work, we present a comprehensive study of holographic stress tensor correlators on general Riemann surfaces, extending beyond the previously well-studied torus cases to explore higher genus conformal field theories (CFTs) within the framework of the [[0001 AdS-CFT|Anti-de Sitter/conformal field theory]] (AdS/CFT) correspondence. We develop a methodological approach to compute holographic stress tensor correlators, employing the Schottky uniformization technique to address the handlebody solutions for higher genus Riemann surfaces. Through rigorous calculations, we derive four-point stress tensor correlators, alongside recurrence relations for higher-point correlators, within the [[0073 AdS3-CFT2|AdS3/CFT2]] context. Additionally, our research delves into the holography of cutoff $\mathrm{AdS}_3$ spaces, offering novel insights into the lower-point correlators of the $T\bar{T}$-deformed theories on higher genus Riemann surfaces up to the first deformation order.\] # He, Mitra, Sivaramakrishnan, Zurek ## An On-Shell Derivation of the Soft Effective Action in Abelian Gauge Theories \[Links: [arXiv](https://arxiv.org/abs/2403.14502), [PDF](https://arxiv.org/pdf/2403.14502)\] \[Abstract: We derive the soft effective action in ($d+2$)-dimensional abelian gauge theories from the on-shell action obeying Neumann boundary conditions at timelike and null infinity and Dirichlet boundary conditions at spatial infinity. This allows us to identify the on-shell degrees of freedom on the boundary with the soft modes living on the [[0022 Celestial sphere|celestial sphere]]. Following the work of Donnelly and Wall, this suggests that we can interpret soft modes as entanglement [[0556 Edge mode|edge modes]] on the celestial sphere and study entanglement properties of soft modes in abelian gauge theories.\] # He, Yang ## Geodesics connecting end points of time-like interval in asymptotically AdS spacetime \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/)\] \[Abstract: This paper studies the geodesics connecting two time-like separated boundary points in asymptotically anti-de Sitter (AdS) spacetime. We find that in spherically symmetry Schwarzschild AdS black hole, smooth space-like geodesics can connect timelike-separated points by winding around the horizon multiple times. Similar result will also happen in modified BTZ black hole which contains photon ring in the bulk. According to recent holographic proposal on time-like entanglement entropy, our result suggests that, if there is photon ring/sphere in the bulk, then the [[0606 Timelike entanglement|time-like entanglement entropy]] AdS3/CFT2 duality may not have an imaginary part and so further understanding may be necessary.\] # Held, Kaplan, Marolf, Wu ## Link-area commutators in AdS${}_3$ area-networks \[Links: [arXiv](https://arxiv.org/abs/2401.02487), [PDF](https://arxiv.org/pdf/2401.02487.pdf)\] \[Abstract: [[0368 Random tensor network|Random tensor networks]] (RTNs) have proved to be fruitful tools for modelling the [[0001 AdS-CFT|AdS/CFT]] correspondence. Due to their flat entanglement spectra, when discussing a given boundary region $R$ and its complement $\bar R$, standard RTNs are most analogous to [[0024 Fixed area states|fixed-area states]] of the bulk quantum gravity theory, in which quantum fluctuations have been suppressed for the area of the corresponding [[0007 RT surface|HRT surface]]. However, such RTNs have flat entanglement spectra for all choices of $R$, $\bar R$, while quantum fluctuations of multiple HRT-areas can be suppressed only when the corresponding HRT-area operators mutually commute. We probe the severity of such obstructions in pure AdS$_3$ [[0554 Einstein gravity|Einstein-Hilbert gravity]] by constructing networks whose links are codimension-2 extremal-surfaces and by explicitly computing semiclassical commutators of the associated link-areas. Since $d=3$, codimension-2 extremal-surfaces are geodesics, and codimension-2 'areas' are lengths. We find a simple 4-link network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT surface for which all link-areas commute. However, the algebra generated by the link-areas of more general networks tends to be non-Abelian. One such non-Abelian example is associated with [[0319 Entanglement wedge cross-section|entanglement-wedge cross sections]] and may be of more general interest.\] # Held, Maxfield ## The Hilbert space of de Sitter JT: a case study for canonical methods in quantum gravity \[Links: [arXiv](https://arxiv.org/abs/2410.14824), [PDF](https://arxiv.org/pdf/2410.14824)\] \[Abstract: We study [[0545 de Sitter quantum gravity|de Sitter]] [[0050 JT gravity|JT gravity]] in the canonical formulation to illustrate constructions of Hilbert spaces in quantum gravity, which is challenging due to the Hamiltonian constraints. The key ideas include representing states as "invariants" (solutions to the Wheeler-DeWitt equation) or dual "co-invariants" (equivalence classes under gauge transformations), defining a physical inner product by group averaging, and relating this to Klein-Gordon inner products via gauge-fixing conditions. We identify a rich Hilbert space with positive-definite inner product which splits into distinct sectors, mirroring a similar structure in the classical phase space. Many (but not all) of these sectors are described exactly (in a constant extrinsic curvature gauge) by a mini-superspace theory, a quantum mechanical theory with a single constraint.\] # Heller, Ori, Serantes ## Geometric interpretation of timelike entanglement entropy \[Links: [arXiv](https://arxiv.org/abs/2408.15752), [PDF](https://arxiv.org/pdf/2408.15752)\] \[Abstract: Analytic continuations of [[0007 RT surface|holographic entanglement entropy]] in which the boundary subregion extends along a timelike direction have brought a promise of a novel, time-centric probe of the emergence of spacetime. We propose that the bulk carriers of this holographic [[0606 Timelike entanglement|timelike entanglement entropy]] are boundary-anchored extremal surfaces probing analytic continuation of holographic spacetimes into complex coordinates. This proposal not only provides a geometric interpretation of all the known cases obtained by direct analytic continuation of closed-form expressions of holographic entanglement entropy of a strip subregion but crucially also opens a window to study holographic timelike entanglement entropy in full generality. We initialize the investigation of complex extremal surfaces anchored on a timelike strip at the boundary of anti-de Sitter black branes. We find multiple complex extremal surfaces and discuss possible principles singling out the physical contribution.\] # Hernandez-Cuenca (Apr) ## Wormholes and Factorization in Exact Effective Theory \[Links: [arXiv](https://arxiv.org/abs/2404.10035), [PDF](https://arxiv.org/pdf/2404.10035)\] \[Abstract: We study the general framework of effective theories obtained via exact path integration of a complete theory over some sector of its degrees of freedom. Theories constructed this way contain multi-integrals which couple fields arbitrarily far apart, and in certain settings even on path-disconnected components of the space. These are not just entanglement, but genuine non-local interactions that we dub quantum wormholes. Any state the path integral of such an effective theory prepares is shown to be a partial trace of a state of the complete theory over the integrated-out sector. The resulting reduced density operator is generally mixed due to [[0216 Bra-ket wormholes|bra-ket wormholes]]. An infinite family of ensembles of pure states of the complete theory giving the same effective state is identified. These allow one to equivalently interpret any effective state as being prepared by an ensemble of theories. When computing entropic quantities, bra-ket wormholes give rise to [[0206 Replica wormholes|replica wormholes]]. This causes replica path integrals for the effective theory to not factorize even when the underlying manifold does, as expected from mixing. In contrast, effective theories obtained by derivative expansions have no quantum wormholes and prepare pure states. There exist operators in the algebra of effective theories which can distinguish mixed from pure states, implying a breakdown of non-exact effective theories for sufficiently complex observables. This framework unifies and provides new insights into much of the phenomena observed in quantum gravity, including the interplay between wormholes and unitarity, the breakdown of bulk effective theory, the factorization puzzle, state ensembles, [[0154 Ensemble averaging|theory ensembles]], [[0146 Quantum error correction|quantum error correction]], and [[0051 Baby universes|baby universes]]. Some interesting lessons are drawn accounting also for characteristic aspects of gravity concerning IR/UV mixing and [[0169 Kaluza-Klein|Kaluza-Klein reductions]].\] # Hernandez-Cuenca (Jul) ## Entropy and Spectrum of Near-Extremal Black Holes: semiclassical brane solutions to non-perturbative problems \[Links: [arXiv](https://arxiv.org/abs/2407.20321), [PDF](https://arxiv.org/pdf/2407.20321)\] \[Abstract: The [[0004 Black hole entropy|black hole entropy]] has been observed to generically turn negative at exponentially low temperatures $T\sim e^{-S_0}$ in the extremal Bekenstein-Hawking entropy $S_0$, a seeming pathology often attributed to missing non-perturbative effects. In fact, we show that this negativity must happen for any effective theory of quantum gravity with an [[0154 Ensemble averaging|ensemble]] description. To do so, we identify the usual gravitational entropy as an annealed entropy $S_a$, and prove that this quantity gives $S_0$ at extremality if and only if the ground-state energy is protected by supersymmetry, and diverges negatively otherwise. The actual thermodynamically-behaved quantity is the average or quenched entropy $S_q$, whose calculation is poorly understood in gravity: it involves [[0206 Replica wormholes|replica wormholes]] in a regime where the topological expansion breaks down. Using matrix integrals we find new instanton saddles that dominate gravitational correlators at $T\sim e^{-S_0}$ and are dual to semiclassical wormholes involving dynamical branes. These brane solutions give the leading contribution to any black hole very near extremality, and a duality with matrix ensembles would not make sense without them. In the non-BPS case, they are required to make $S_q$ non-negative and also enhance the negativity of $S_a$, both effects consistent with matrix integrals evaluated exactly. Our instanton results are tested against the on-shell action of D3-branes dual to multiply wrapped Wilson loops in $\mathcal{N}=4$ super-YM, and a precise match is found. Our analysis of low-energy random matrix spectra also explains the origin of spectral gaps in supersymmetric theories, not only when there are BPS states at zero energy, but also for purely non-BPS supermultiplets. In the former, our prediction for the gap in terms of the degeneracy of BPS states agrees with the R-charge scaling in gapped multiplets of $\mathcal{N}=2$ super-JT gravity.\] # Hinterbichler ## Dualities Among Massive, Partially Massless and Shift Symmetric Fields on (A)dS \[Links: [arXiv](https://arxiv.org/abs/2402.16938), [PDF](https://arxiv.org/pdf/2402.16938.pdf)\] \[Abstract: We catalog all the electromagnetic-like dualities that exist between free dynamical bosonic fields of arbitrary symmetry type and mass on (anti-) de Sitter space in all dimensions, including dualities among the partially massless and [[0500 Shift symmetry|shift]] symmetric fields. This generalizes to all these field types the well known fact that a massless $p$-form is dual to a massless $(D-p-2)$-form in $D$ spacetime dimensions. In the process, we describe the structure of the Weyl modules (the spaces of local operators linear in the fields and their derivative relations) for all the massive, partially massless and shift symmetric fields.\] # Hollands, Wald, Zhang ## The Entropy of Dynamical Black Holes \[Links: [arXiv](https://arxiv.org/abs/2402.00818), [PDF](https://arxiv.org/pdf/2402.00818.pdf)\] \[Abstract: We propose a new formula for the entropy of a dynamical black hole-valid to leading order for perturbations off of a stationary black hole background-in an arbitrary classical diffeomorphism covariant Lagrangian theory of gravity in n dimensions. In stationary eras, this formula agrees with the usual Noether charge formula, but in nonstationary eras, we obtain a nontrivial correction term. In general relativity, our formula for the entropy of a dynamical black hole is 1/4 of the horizon area plus a term involving the integral of the expansion of the null generators of the horizon, which we show is 1/4 of the area of the apparent horizon to leading order. Our formula for entropy in a general theory of gravity obeys a "local physical process version" of the first law of black hole thermodynamics. For first order perturbations sourced by external matter that satisfies the [[0480 Null energy condition|null energy condition]], our entropy obeys the [[0005 Black hole second law|second law of black hole thermodynamics]]. For vacuum perturbations, the second law is obeyed at leading order if and only if the "modified canonical energy flux" is positive (as is the case in general relativity but presumably would not hold in general theories). We obtain a general relationship between our formula for the entropy of a dynamical black hole and a formula proposed independently by Dong and by Wall. We then consider the generalized second law in semiclassical gravity for first order perturbations of a stationary black hole. We show that the validity of the [[0405 Quantum null energy condition|quantum null energy condition]] (QNEC) on a Killing horizon is equivalent to the [[0082 Generalised second law|generalized second law]] using our notion of [[0004 Black hole entropy|black hole entropy]] but using a modified notion of [[0301 Entanglement entropy|von Neumann entropy]] for matter. On the other hand, the generalized second law for the Dong-Wall entropy is equivalent to an integrated version of QNEC, using the unmodified von Neumann entropy for the entropy of matter.\] # Horowitz, Wang, Ye ## A new energy inequality in AdS \[Links: [arXiv](https://arxiv.org/abs/2406.13068), [PDF](https://arxiv.org/pdf/2406.13068)\] \[Abstract: We study time symmetric initial data for asymptotically AdS spacetimes with conformal boundary containing a spatial circle. Such $d$-dimensional initial data sets can contain ($d-2$)-dimensional minimal surfaces if the circle is contractible. We compute the minimum energy of a large class of such initial data as a function of the area $A$ of this minimal surface. The statement $E \ge E_{min}(A)$ is analogous to the [[0476 Penrose inequality|Penrose inequality]] which bounds the energy from below by a function of the area of a ($d-1$)-dimensional minimal surface.\] # Huang, Jepsen ## Finite Temperature at Finite Places \[Links: [arXiv](https://arxiv.org/abs/2408.04199), [PDF](https://arxiv.org/pdf/2408.04199)\] \[Abstract: This paper studies [[0001 AdS-CFT|AdS/CFT]] in its [[0084 p-adic holography|p-adic]] version (at the "finite place") in the setting where the bulk geometry is made up of the Tate curve, a discrete quotient of the Bruhat-Tits tree. Generalizing a classic result due to Zabrodin, the boundary dual of the free massive bulk theory is explicitly derived. Introducing perturbative interactions, the Wittens diagrams for the two-point and three-point correlators are computed for generic scaling dimensions at one-loop and tree level respectively. The answers obtained demonstrate how p-adic AdS/CFT on the Tate curve provides a useful toy model for real CFTs at finite temperature.\] # Hung, Jiang ## Building up quantum spacetimes with BCFT Legos \[Links: [arXiv](https://arxiv.org/abs/2404.00877), [PDF](https://arxiv.org/pdf/2404.00877)\] \[Abstract: Is it possible to read off the quantum gravity dual of a CFT directly from its operator algebra? In this essay, we present a step-by-step recipe synthesizing results and techniques from [[0036 Conformal bootstrap|conformal bootstrap]], topological symmetries, tensor networks, a novel symmetry-preserving real-space renormalization algorithm devised originally in lattice models, and the asymptotics of quantum [[0597 6j symbol|6j symbols]], thereby providing an answer in the affirmative. Quantum 2D [[0562 Liouville theory|Liouville theory]] serves as a simple and explicit example, illustrating how the quantum gravitational path integral can be built up from local pieces of [[0548 Boundary CFT|BCFT]] correlation functions, which we call the ''BCFT Legos''. The constructive map between gravity and CFT naturally and explicitly bridges local geometrical data, algebraic structures, and quantum entanglement, as envisaged by the *It from Qubit* motto.\] # Iacobacci, Sleight, Taronna ## Celestial Holography Revisited II: Correlators and Källén-Lehmann \[Links: [arXiv](https://arxiv.org/abs/2401.16591), [PDF](https://arxiv.org/pdf/2401.16591.pdf)\] \[Abstract: In this work we continue the investigation of the extrapolate [[0516 Celestial correlators|dictionary]] for [[0010 Celestial holography|celestial holography]] recently proposed in \[[2301.01810](https://arxiv.org/abs/2301.01810)\], at both the perturbative and non-perturbative level. Focusing on scalar field theories, we give a complete set of Feynman rules for extrapolate celestial correlation functions and their radial reduction in the hyperbolic slicing of Minkowski space. We prove to all orders in perturbation theory that celestial correlators can be re-written in terms of corresponding Witten diagrams in EAdS which, in the hyperbolic slicing of Minkowski space, follows from the fact that the same is true in dS space. We then initiate the study of non-perturbative properties of celestial correlators, deriving the radial reduction of the Källén-Lehmann spectral representation of the exact Minkowski two-point function. We discuss the analytic properties of the radially reduced spectral function, which is a meromorphic function of the spectral parameter, and highlight a connection with the Watson-Sommerfeld transform.\] # Iizuka, Lin, Nishida ## Black Hole Multi-Entropy Curves \[Links: [arXiv](https://arxiv.org/abs/2412.07549), [PDF](https://arxiv.org/pdf/2412.07549)\] \[Abstract: We investigate the [[0264 Multi-partite entanglement|multi-partite entanglement]] structure of an evaporating black hole and its Hawking radiation by dividing the radiation into finer subsystems. We approximate an evaporating black hole and its radiation with a Haar-random state for this purpose. Using the multi-entropy of these configurations, we define a black hole multi-entropy curve, which describes how the multi-entropy changes during the black hole evaporation. This black hole multi-entropy curve is a natural generalization of the Page curve since the multi-entropy reduces to the [[0301 Entanglement entropy|entanglement entropy]] for the bi-partite case. The multi-entropy curve keeps increasing in the early time. It reaches the maximum value at the multi-entropy time, which is later than the Page time, and starts to decrease. However, it does not decrease to zero at the end of the black hole evaporation. This non-zero value of the multi-entropy represents the secret entanglement between Hawking particles.\] # Iizuka, Nishida ## Logarithmic singularities of Renyi entropy as a sign of chaos? \[Links: [arXiv](https://arxiv.org/abs/2404.04805), [PDF](https://arxiv.org/pdf/2404.04805)\] \[Abstract: We propose that the logarithmic singularities of the [[0293 Renyi entropy|Renyi entropy]] of local-operator-excited states for replica index $n$ can be a sign of [[0008 Quantum chaos|quantum chaos]]. As concrete examples, we analyze the logarithmic singularities of the Renyi entropy in various [[0003 2D CFT|two-dimensional conformal field theories]]. We show that there are always logarithmic singularities of the Renyi entropy in [[0122 Holographic CFT|holographic CFTs]], but no such singularities in free and rational CFTs. These singularities of the Renyi entropy are also related to the logarithmic time growth of the Renyi entropy at late times.\] # Iliesiu, Levine, Lin, Maxfield, Mezei ## On the non-perturbative bulk Hilbert space of JT gravity \[Links: [arXiv](https://arxiv.org/abs/2403.08696), [PDF](https://arxiv.org/pdf/2403.08696.pdf); Talks: [Iliesiu at IAS](https://youtu.be/K_K8ComNqTU?feature=shared)\] \[Abstract: What is the bulk Hilbert space of quantum gravity? In this paper, we resolve this problem in 2d [[0050 JT gravity|JT gravity]], both with and without matter, providing the first example of an explicit definition of a non-perturbative Hilbert space specified in terms of metric variables. The states are wavefunctions of the length and matter state, but with a non-trivial and highly degenerate inner product. We explicitly identify the null states, and discuss their importance for defining operators non-perturbatively. To highlight the power of the formalism we developed, we study the non-perturbative effects for two bulk linear operators that may serve as proxies for the experience of an observer falling into a two-sided black hole: one captures the length of an Einstein-Rosen bridge and the other captures the center-of-mass collision energy between two particles falling from opposite sides. We track the behavior of these operators up to times of order $e^{S_\text{BH}}$, at which point the wavefunction spreads to the complete set of eigenstates of these operators. If these observables are indeed good proxies for the experience of an infalling observer, our results indicate an $O(1)$ probability of detecting a [[0195 Firewall|firewall]] at late times that is self-averaging and universal.\] # Ishibashi, Matsuo, Tanaka ## Quantum focusing conjecture in two-dimensional evaporating black holes \[Links: [arXiv](https://arxiv.org/abs/2403.19136), [PDF](https://arxiv.org/pdf/2403.19136)\] \[Abstract: We consider the [[0243 Quantum focusing conjecture|quantum focusing conjecture]] (QFC) for two-dimensional evaporating black holes. The QFC is closely related to the behavior of the [[0212 Quantum extremal surface|generalized entropy]] -- the sum of the area entropy for a given co-dimension two surface and the entanglement entropy for quantum fields outside the area. In the context of the black hole evaporation, the entanglement entropy of the [[0304 Hawking radiation|Hawking radiation]] is decreasing after the Page time, and therefore it is not obvious whether the QFC holds in the black hole evaporation process especially after the Page time. One of the present authors previously addressed this problem in a four-dimensional spherically symmetric dynamical black hole model and showed that the QFC is satisfied. However the background spacetime considered was approximated by the Vaidya metric, and quantum effects of matters in the semiclassical regime is not fully taken into consideration. It remains to be seen if the QFC in fact holds for exact solutions of the semiclassical Einstein equations. In this paper, we address this problem in a two-dimensional dynamical black hole of the Russo-Susskind-Thorlacius (RST) model, which allows us to solve the semiclassical equations of motion exactly. We first give a suitable definition of the quantum expansion in two-dimensions and then prove that the QFC is satisfied for evaporating black holes in the RST model with the [[0213 Islands|island]] formation taken into account.\] # Jafferis, Rozenberg, Wong ## 3d Gravity as a random ensemble \[Links: [arXiv](https://arxiv.org/abs/2407.02649), [PDF](https://arxiv.org/pdf/2407.02649)\] \[Abstract: We give further evidence that the matrix-tensor model studied in [[2023#Belin, de Boer, Jafferis, Nayak, Sonner]] is dual to [[0002 3D gravity|AdS3 gravity]] including the sum over topologies. This provides a 3D version of the [[0471 String-matrix duality|duality between JT gravity and an ensemble of random Hamiltonians]], in which the matrix and tensor provide random CFT$_2$ data subject to a potential that incorporates the bootstrap constraints. We show how the Feynman rules of the ensemble produce a sum over all three-manifolds and how surgery is implemented by the matrix integral. The partition functions of the resulting 3d gravity theory agree with [[0596 Virasoro TQFT|Virasoro TQFT]] (VTQFT) on a fixed, hyperbolic manifold. However, on non-hyperbolic geometries, our 3d gravity theory differs from VTQFT, leading to a difference in the eigenvalue statistics of the associated ensemble. As explained in [[2023#Belin, de Boer, Jafferis, Nayak, Sonner]], the Schwinger-Dyson (SD) equations of the matrix-tensor integral play a crucial role in understanding how gravity emerges in the limit that the ensemble localizes to exact CFT's. We show how the SD equations can be translated into a combinatorial problem about three-manifolds.\] # Jensen, Raju, Speranza ## Holographic observers for time-band algebras \[Links: [arXiv](https://arxiv.org/abs/2412.21185), [PDF](https://arxiv.org/pdf/2412.21185)\] \[Abstract: We study the algebra of observables in a time band on the boundary of anti-de Sitter space in a theory of quantum gravity. Strictly speaking this algebra does not have a commutant because products of operators within the time band give rise to operators outside the time band. However, we show that in a state where the bulk contains a macroscopic observer, it is possible to define a coarse-grained version of this algebra with a non-trivial commutant, and a resolution limited by the observer's characteristics. This algebra acts on a little Hilbert space that describes excitations about the observer's state and time-translated versions of this state. Our construction requires a choice of dressing that determines how elements of the algebra transform under the Hamiltonian. At leading order in gravitational perturbation theory, and with a specific choice of dressing, our construction reduces to the modular crossed-product described previously in the literature. We also prove a theorem showing that this is the only crossed product of a type III$_1$ [[0415 Von Neumann algebra|algebra]] resulting in an algebra with a trace. This trace can be used to define entropy differences between states in the little Hilbert space that are insensitive to the properties of the observer. We discuss some technical challenges in extending this construction to higher orders in perturbation theory. Lastly, we review the construction of interior operators in the eternal black hole and show that they can be written as elements of a crossed product algebra.\] # Jia, Rangamani ## Holographic thermal correlators and quasinormal modes from semiclassical Virasoro blocks \[Links: [arXiv](https://arxiv.org/abs/2408.05208), [PDF](https://arxiv.org/pdf/2408.05208)\] \[Abstract: > Motivated by its relevance for thermal correlators in strongly coupled holographic CFTs, we refine and further develop a recent exact analytic approach to black hole perturbation problem, based on the semiclassical Virasoro blocks, or equivalently via AGT relation, the Nekrasov partition functions in the Nekrasov-Shatashvili limit. Focusing on asymptotically \text{AdS}_5 black hole backgrounds, we derive new universal exact expressions for holographic thermal two-point functions, both for scalar operators and conserved currents. Relatedly, we also obtain exact quantization conditions of the associated quasinormal modes (QNMs). Our expressions for the holographic \text{CFT}_4 closely resemble the well-known results for 2d thermal CFTs on \mathbb{R}^{1,1}. This structural similarity stems from the locality of fusion transformation for Virasoro blocks. We provide numerical checks of our quantization conditions for QNMs. Additionally, we discuss the application of our results to understand specific physical properties of QNMs, including their near-extremal and asymptotic limits. The latter is related to a certain large-momentum regime of semiclassical Virasoro blocks dual to Seiberg-Witten prepotentials.\] # Jiang, Blake, Thompson ## Islands, Double Holography, and the Entanglement Membrane \[Links: [arXiv](https://arxiv.org/abs/2412.15070), [PDF](https://arxiv.org/pdf/2412.15070)\] \[Abstract: The quantum extremal [[0213 Islands|island rule]] allows us to compute the [[0131 Information paradox|Page curves]] of [[0304 Hawking radiation|Hawking radiation]] in semi-classical gravity. In this work, we study the connection between these calculations and the thermalisation of chaotic quantum many-body systems, using a coarse-grained description of [[0522 Entanglement dynamics|entanglement dynamics]] known as the [[0433 Membrane theory of entanglement dynamics|entanglement membrane]]. Starting from a double-holographic model of eternal two-sided asymptotically AdS$_d$ ($d>2$) black hole each coupled to a flat $d$-dimensional bath, we show that the entanglement dynamics in the late-time, large-subregion limit is described by entanglement membrane, thereby establishing a quantitative equivalence between a semi-classical gravity and a chaotic quantum many-body system calculation of the Page curve.\] # Jiang, Mezei, Virrueta ## The entanglement membrane in 2d CFT: reflected entropy, RG flow, and information velocity \[Links: [arXiv](https://arxiv.org/abs/2411.16542), [PDF](https://arxiv.org/pdf/2411.16542)\] \[Abstract: The time evolution of entanglement entropy in generic chaotic many-body systems has an effective description in terms of a [[0433 Membrane theory of entanglement dynamics|minimal membrane]], characterised by a tension function. For [[0003 2D CFT|2d CFTs]], a degenerate tension function reproduces several results regarding the dynamics of the entropy; this stands in contrast to higher dimensions where the tension is non-degenerate. In this paper we use holography to show that, in order to correctly capture the [[0166 Reflected entropy|reflected entropy]] in 2d CFT, one needs to add an additional degree of freedom to the membrane description. Furthermore, we show that the conventional non-degenerate membrane tension function emerges upon introducing a relevant deformation of the CFT, dual to a planar [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black hole with scalar hair and with an interior [[0126 Kasner singularity|Kasner]] universe. Finally, we also study the membrane description for reflected entropy and information velocity [arXiv:1908.06993](https://arxiv.org/abs/1908.06993) in higher dimensions.\] # Jiang, Wang, Wu, Yang (Oct) ## How Einstein's Equation Emerges From CFT$_2$ \[Links: [arXiv](https://arxiv.org/abs/2410.19711), [PDF](https://arxiv.org/pdf/2410.19711)\] \[Abstract: The *finiteness* of the mixed state entanglement entropies enables us to show that, the dynamical equation of the entanglement entropy in CFT$_2$ is precisely three dimensional Einstein's equation. A profound relation between the cosmological constant and CFT$_2$ entanglement entropy is given. Thus entanglement entropies induce internal gravitational geometries in CFT$_2$. [[0302 Gravity from entanglement|Deriving the dual metric]] from an entanglement entropy becomes a trivial procedure. Surprisingly, we find that the renormalization group equation is a geometric identity.\] # Jiang, Wang, Wu, Yang (Nov) ## Realization of "ER=EPR" \[Links: [arXiv](https://arxiv.org/abs/2411.18485), [PDF](https://arxiv.org/pdf/2411.18485)\] \[Abstract: We provide a concrete and computable realization of the [[0220 ER=EPR|ER=EPR]] conjecture, by deriving the Einstein-Rosen bridge from the quantum entanglement in the [[0574 Thermofield double|thermofield double]] CFT. The [[0004 Black hole entropy|Bekenstein-Hawking entropy]] of the wormhole is explicitly identified as an [[0301 Entanglement entropy|entanglement entropy]] between subsystems of the thermofield double state. Furthermore, our results provide a quantitative verification of Van Raamsdonk's conjecture about spacetime emergence.\] # Johnson ## Supersymmetric Virasoro Minimal Strings \[Links: [arXiv](https://arxiv.org/abs/2401.08786), [PDF](https://arxiv.org/pdf/2401.08786)\] \[Abstract: A random matrix model definition of a family of ${\cal N}{=}1$ supersymmetric extensions of the [[0657 Virasoro minimal string|Virasoro minimal string]] of Collier, Eberhardt, Mühlmann, and Rodriguez is presented. An analysis of the defining string equations shows that the models all naturally have unambiguous non-perturbative completions, which are explicitly supplied by the double-scaled orthogonal polynomial techniques employed. Perturbatively, the multi-loop correlation functions of the model define a special supersymmetric class of ''quantum volumes'', generalizing the prototype case, some of which are computed.\] # Jorstad, Pasterski ## A Comment on Boundary Correlators: Soft Omissions and the Massless S-Matrix \[Links: [arXiv](https://arxiv.org/abs/2410.20296), [PDF](https://arxiv.org/pdf/2410.20296)\] \[Abstract: We revisit the extrapolate dictionary for massless scattering in flat spacetime and identify a soft contribution that is typically dropped from the saddle point approximation. We show how to consistently regulate the extrapolation to include both the soft and hard components and identify the boundary correlation functions as a combination of electric and magnetic branch Carrollian correlators. This implies in particular that there are contributions to these boundary [[0516 Celestial correlators|correlators]] that are non-distributional on the celestial sphere. Finally, we close by exploring the utility of the magnetic branch for extracting celestial data from low point correlators: connecting our results to recent work on flat space extrapolate dictionaries and celestial shadow amplitudes.\] # Ju, Pan, Sun, Wang, Zhao ## More on the upper bound of holographic $n$-partite information \[Links: [arXiv](https://arxiv.org/abs/2411.19207), [PDF](https://arxiv.org/pdf/2411.19207)\] \[Abstract: We show that there exists a huge amount of [[0264 Multi-partite entanglement|multipartite entanglement]] in holography by studying the upper bound for holographic $n$-partite information $I_n$ that $n-1$ fixed boundary subregions participate. We develop methods to find the $n$-th region $E$ that makes $I_n$ reach the upper bound. Through the explicit evaluation, it is shown that $I_n$, an IR term without UV divergence, could diverge when the number of intervals or strips in region $E$ approaches infinity. At this upper bound configuration, we could argue that $I_n$ fully comes from the $n$-partite global quantum entanglement. Our results indicate: fewer-partite entanglement in holography emerges from more-partite entanglement; $n-1$ distant local subregions are highly $n$-partite entangling. Moreover, the relationship between the convexity of a boundary subregion and the multipartite entanglement it participates, and the difference between multipartite entanglement structure in different dimensions are revealed as well.\] # Kallosh ## Ward Identities for Superamplitudes \[Links: [arXiv](https://arxiv.org/abs/2402.03453), [PDF](https://arxiv.org/pdf/2402.03453.pdf)\] \[Abstract: We introduce [[0106 Ward identity|Ward identities]] for superamplitudes in $D$-dimensional $\mathcal{N}$-extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for an $n$-partice superamplitude take a simple universal form for half-BPS and non-BPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of the $n$ superparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on half-BPS or non-BPS superfields, given by $(D-2) L +2- \mathcal{N}$ or $(D-2) L +2- 2 \mathcal{N}$, respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree.\] # Kanai, Maeda, Noumi, Yoshida ## Cutoff Scale of Quadratic Gravity from Quantum Focusing Conjecture \[Links: [arXiv](https://arxiv.org/abs/2405.01296), [PDF](https://arxiv.org/pdf/2405.01296.pdf)\] \[Abstract: We derive the cutoff length scale of the quadratic gravity in $d \geq 5$ dimensional spacetime by demanding that the [[0243 Quantum focusing conjecture|quantum focusing conjecture]] for the smeared quantum expansion holds at the classical level. The cutoff scale has different dependence on the spacetime dimension depending on the sign of the coupling constant of the quadratic gravity. We also investigate a concrete example of the 5-dimensional Schwarzschild spacetime and directly confirm that the quantum focusing conjecture holds when the quantum expansion is smeared over the scale larger than our cutoff scale.\] # Kapec, Law, Toldo ## Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics \[Links: [arXiv](https://arxiv.org/abs/2409.14928), [PDF](https://arxiv.org/pdf/2409.14928)\] \[Abstract: Recent work on the quantum mechanics of near-extremal non-supersymmetric black holes has identified a characteristic $T^{3/2}$ scaling of the [[0608 Quantum effects for near-extremal black holes|low temperature black hole]] partition function. This result has only been derived using the path integral in the near-horizon region and relies on many assumptions. We discuss how to derive the $T^{3/2}$ scaling for the near-extremal rotating BTZ black hole from a calculation in the full black hole background using the [[0631 DHS formula|Denef-Hartnoll-Sachdev]] (DHS) formula, which expresses the 1-loop determinant of a thermal geometry in terms of a product over the [[0325 Quasi-normal modes|quasinormal mode]] spectrum. We also derive the spectral measure for fields of any spin in Euclidean BTZ and use it to provide a new proof of the DHS formula and a new, direct derivation of the BTZ heat kernel. The computations suggest a path to proving the $T^{3/2}$ scaling for the asymptotically flat 4d Kerr black hole.\] # Kar, Dhivakar, Roy, Panda, Shaikh ## Iyer-Wald ambiguities and gauge covariance of Entropy current in Higher derivative theories of gravity \[Links: [arXiv](https://arxiv.org/abs/2403.04749), [PDF](https://arxiv.org/pdf/2403.04749.pdf)\] \[Abstract: In [[2021#Bhattacharyya, Dhivakar, Dinda, Kundu, Patra, Roy]] and [[2022#Biswas, Dhivakar, Kundu]], the authors have been able to argue for an ultra-local version of the [[0005 Black hole second law|second law of black hole mechanics]], for arbitrary diffeomorphism invariant theories of gravity non-minimally coupled to matter fields, by constructing an entropy current on the dynamical horizon with manifestly positive divergence. This has been achieved by working in the horizon-adapted coordinate system. In this work, we show that the local entropy production through the divergence of the entropy current is covariant under affine reparametrizations that leave the gauge of horizon-adapted coordinates invariant. We explicitly derive a formula for how the entropy current transforms under such coordinate transformations. This extends the analysis of [[2022#Bhattacharyya, Jethwani, Patra, Roy]] for arbitrary diffeomorphism invariant theories of gravity non-minimally coupled to matter fields. We also study the Iyer-Wald ambiguities of the covariant phase formalism that generically plague the components of the entropy current.\] # Kazakov, Murali, Vieira ## Huge BPS Operators and Fluid Dynamics in $\mathcal{N}=4$ SYM \[Links: [arXiv](https://arxiv.org/abs/2406.01798), [PDF](https://arxiv.org/pdf/2406.01798)\] \[Abstract: In the bulk dual of holography, [[0645 Huge operators|huge operators]] correspond to sources so heavy that they fully backreact on the space-time geometry. Here we study the correlation function of three such huge operators when they are given by 1/2 [[0178 BPS|BPS]] operators in $\mathcal{N}=4$ SYM theory, dual to IIB Strings in $AdS_5 \times S^5$. We unveil simple matrix model representations for these correlators which we can sometimes solve analytically. For general huge operators, we translate these matrix model expressions into a 1+1 dimensional hydrodynamical fluid problem. This fluid is integrable thus unveiling a novel integrable sector of the [[0001 AdS-CFT|AdS/CFT]] duality in a full fledged gravitational regime, very far from the usual free string planar regime where integrability reigns supreme. We explain how an adiabatic deformation method can be developed to yield the solution to an integrable discrete formulation of these fluids -- the rational Calogero-Moser Model -- so we can access the general three point correlation functions of generic huge 1/2-BPS operators. Everything will be done on the gauge theory side of the duality. It would be fascinating to find the holographic dual of these [[0197 Matrix model|matrix models]] and fluids.\] # Kehle, Unger ## Extremal black hole formation as a critical phenomenon \[Links: [arXiv](https://arxiv.org/abs/2402.10190), [PDF](https://arxiv.org/pdf/2402.10190.pdf)\] \[Abstract: In this paper, we prove that extremal black holes arise on the threshold of gravitational collapse. More precisely, we construct smooth one-parameter families of smooth, spherically symmetric solutions to the Einstein-Maxwell-Vlasov system which interpolate between dispersion and collapse and for which the critical solution is an extremal black hole. Physically, these solutions can be understood as beams of gravitationally self-interacting collisionless charged particles fired into Minkowski space from past infinity. Depending on the precise value of the parameter, we show that the Vlasov matter either disperses due to the combined effects of angular momentum and electromagnetic repulsion, or undergoes gravitational collapse. At the critical value of the parameter, an extremal Reissner-Nordström black hole is formed. No naked singularities occur as the extremal threshold is crossed. We call this critical phenomenon extremal critical collapse and the present work constitutes the first rigorous result on the black hole formation threshold in general relativity.\] # Khuri, Kunduri ## The Spacetime Penrose Inequality for Cohomogeneity One Initial Data \[Links: [arXiv](https://arxiv.org/abs/2404.13247), [PDF](https://arxiv.org/pdf/2404.13247.pdf)\] \[Abstract: We prove the spacetime [[0476 Penrose inequality|Penrose inequality]] for asymptotically flat $2(n+1)$-dimensional initial data sets for the Einstein equations, which are invariant under a cohomogeneity one action of $\mathrm{SU}(n+1)$. Analogous results are obtained for asymptotically hyperbolic initial data that arise as spatial hypersurfaces in asymptotically Anti de-Sitter spacetimes. More precisely, it is shown that with the dominant [[0247 Energy conditions|energy condition]], the total mass is bounded below by an explicit function of the outermost [[0226 Apparent horizon|apparent horizon]] area. Furthermore, the inequality is saturated if and only if the initial data isometrically embed into a Schwarzschild(-AdS) spacetime. This generalizes the only previously known case of the conjectured spacetime Penrose inequality, established under the assumption of spherical symmetry. Additionally, in the time symmetric case, we observe that the inequality holds for $4(n+1)$-dimensional and 16-dimensional initial data invariant under cohomogeneity one actions of $\mathrm{Sp}(n+1)$ and $\mathrm{Spin}(9)$, respectively, thus treating the inequality for all cohomogeneity one actions in this regime.\] # Kirklin ## Generalised second law beyond the semiclassical regime \[Links: [arXiv](https://arxiv.org/abs/2412.01903), [PDF](https://arxiv.org/pdf/2412.01903)\] \[Abstract: We prove that the [[0082 Generalised second law|generalised second law]] (GSL), with an appropriate modification, holds in perturbative gravity to all orders beyond the semiclassical limit and without a UV cutoff imposed on the fields. Our proof uses algebraic techniques and builds on the recent work of Faulkner and Speranza, which combined Wall's proof of the GSL with the identification of generalised entropy as the von Neumann entropy of a boost-invariant crossed product algebra. The key additional step in our approach is to further impose invariance under null translations. Doing so requires one to describe horizon exterior regions in a relational manner, so we introduce 'dynamical cuts': quantum reference frames which give the location of a cut of the horizon. We use idealised dynamical cuts, but expect that our methods can be generalised to more realistic models. The modified GSL that we prove says that the difference in generalised entropies of the regions outside two dynamical cuts is bounded below by the free energy of the degrees of freedom giving the location of the later cut. If one takes a semiclassical limit, imposes a UV cutoff, and requires the cuts to obey certain [[0247 Energy conditions|energy conditions]], then our result reduces to the standard GSL.\] # Kmec, Mason, Ruzziconi, Srikant ## Celestial $Lw_{1+\infty}$ charges from a twistor action \[Links: [arXiv](https://arxiv.org/abs/2407.04028), [PDF](https://arxiv.org/pdf/2407.04028)\] \[Abstract: The celestial $Lw_{1+\infty}$ [[0328 w(1+infinity)|symmetries]] in asymptotically flat spacetimes have a natural geometric interpretation on [[0330 Twistor theory|twistor space]] in terms of Poisson diffeomorphisms. Using this framework, we provide a first-principle derivation of the canonical generators associated with these symmetries starting from the Poisson BF twistor action for self-dual gravity. We express these charges as surface integrals over the celestial sphere in terms of spacetime data at null infinity. The connection between twistor space and spacetime expressions at $\mathscr{I}$ is achieved via an integral formula for the asymptotic Bianchi identities due to Bramson and Tod. Finally, we clarify how $Lw_{1+\infty}$ transformations are symmetries of gravity from a phase space perspective by showing the invariance of the asymptotic Bianchi identities.\] # Knysh, Liu, Pinzani-Fokeeva ## New horizon symmetries, hydrodynamics, and quantum chaos \[Links: [arXiv](https://arxiv.org/abs/2405.17559), [PDF](https://arxiv.org/pdf/2405.17559)\] \[Abstract: We generalize the formulation of horizon symmetries presented in previous literature to include diffeomorphisms that can shift the location of the horizon. In the context of the [[0001 AdS-CFT|AdS/CFT]] duality, we show that horizon symmetries can be interpreted on the boundary as emergent low-energy gauge symmetries. In particular, we identify a new class of horizon symmetries that extend the so-called shift symmetry, which was previously postulated for effective field theories of maximally [[0008 Quantum chaos|chaotic]] systems. Additionally, we comment on the connections of horizon symmetries with bulk calculations of [[0482 Out-of-time-order correlator|out-of-time-ordered correlation functions]] and the phenomenon of [[0179 Pole skipping|pole-skipping]].\] # Kolanowski, Marolf, Rakic, Rangamani, Turiaci ## Looking at extremal black holes from very far away \[Links: [arXiv](https://arxiv.org/abs/2409.16248), [PDF](https://arxiv.org/pdf/2409.16248)\] \[Abstract: Near-extremal black holes are subject to large quantum effects, which modify their low-temperature thermodynamic behavior. Hitherto, these quantum effects were analyzed by separating the geometry into the near-horizon region and its exterior. It is desirable to understand and reproduce such corrections from the full higher-dimensional asymptotically flat or AdS geometry's perspective. We address this question in this article and fill this gap. Specifically, we find off-shell eigenmodes of the quadratic fluctuation operator of the Euclidean gravitational dynamics, with eigenvalues that vanish linearly with temperature. We illustrate this for BTZ and neutral black holes with hyperbolic horizons in AdS in Einstein-Hilbert theory, and for the charged black holes in Einstein-Maxwell theory. The linear scaling with Matsubara frequency, which is a distinctive feature of the modes, together with the fact that their wavefunctions localize close to the horizon as we approach extremality, identifies them as responsible for the aforementioned quantum effects. We provide a contour prescription to deal with the sign indefiniteness of the Euclidean Einstein-Maxwell action, which we derive to aid our analysis. We also resolve a technical puzzle regarding modes associated with rotational isometries in stationary black hole spacetimes.\] # Kolchmeyer, Liu ## Chaos and the Emergence of the Cosmological Horizon \[Links: [arXiv](https://arxiv.org/abs/2411.08090), [PDF](https://arxiv.org/pdf/2411.08090)\] \[Abstract: We construct algebras of diff-invariant observables in a global de Sitter universe with two observers and a free scalar QFT in two dimensions. We work in the strict $G_N \rightarrow 0$ limit, but allow the observers to have an order one mass in cosmic units. The observers are fully quantized. In the limit when the observers have infinite mass and are localized along geodesics at the North and South poles, it was shown in previous work [[2022#Chandrasekaran, Longo, Penington, Witten|CLPW]] that their algebras are mutually commuting type II$_1$ factors. Away from this limit, we show that the algebras fail to commute and that they are type I non-factors. Physically, this is because the observers' trajectories are uncertain and state-dependent, and they may come into causal contact. We compute [[0482 Out-of-time-order correlator|out-of-time-ordered correlators]] along an observer's worldline, and observe a [[0466 Lyapunov exponent|Lyapunov exponent]] given by $\frac{4 \pi}{\beta_{\text{dS}}}$, as a result of observer recoil and de Sitter expansion. This should be contrasted with results from AdS gravity, and exceeds the [[0474 Chaos bound|chaos bound]] associated with the de Sitter temperature by a factor of two. We also discuss how the cosmological horizon emerges in the large mass limit and comment on implications for [[0545 de Sitter quantum gravity|de Sitter holography]].\] # Kraus, Myers ## Carrollian Partition Functions and the Flat Limit of AdS \[Links: [arXiv](https://arxiv.org/abs/2407.13668), [PDF](https://arxiv.org/pdf/2407.13668)\] \[Abstract: The formulation of the S-matrix as a path integral with specified asymptotic boundary conditions naturally leads to the realization of a [[0419 Carrollian CFT|Carrollian]] partition function defined on the boundary of Minkowski space. This partition function, specified at past and future null infinity in the case of massless particles, generates Carrollian correlation functions that encode the S-matrix. We explore this connection, including the realization of symmetries, [[0009 Soft theorems|soft theorems]] arising from large gauge transformations, and the correspondence with standard momentum space amplitudes. This framework is also well-suited for embedding the Minkowski space S-matrix into the [[0001 AdS-CFT|AdS/CFT]] duality in the large radius limit. In particular, we identify the AdS and Carrollian partition functions through a simple map between their respective asymptotic data, establishing a direct correspondence between the actions of symmetries on both sides. Our approach thus provides a coherent framework that ties together various topics extensively studied in recent and past literature.\] # Kruthoff, Levine ## Semi-classical dilaton gravity and the very blunt defect expansion \[Links: [arXiv](https://arxiv.org/abs/2402.10162), [PDF](https://arxiv.org/pdf/2402.10162.pdf)\] \[Abstract: We explore [[0560 2d dilaton gravity|dilaton gravity]] with general dilaton potentials in the semi-classical limit viewed both as a gas of blunt defects and also as a semi-classical theory in its own right. We compare the exact defect gas picture with that obtained by naively canonically quantizing the theory in geodesic gauge. We find a subtlety in the canonical approach due to a non-perturbative ambiguity in geodesic gauge. Unlike in [[0050 JT gravity|JT gravity]], this ambiguity arises already at the disk level. This leads to a distinct mechanism from that in JT gravity by which the semi-classical approximation breaks down at low temperatures. Along the way, we propose that new, previously un-studied saddles contribute to the density of states of dilaton gravity. This in particular leads to a re-interpretation of the disk-level density of states in JT gravity in terms of two saddles with fixed energy boundary conditions: the disk, which caps off on the outer horizon, and another, sub-leading [[0335 Complex metrics|complex saddle]] which caps off on the inner horizon. When the theory is studied using a defect expansion, we show how the smooth classical geometries of dilaton gravity arise from a dense gas of very blunt defects in the $G_N \to 0$ limit. The classical saddle points arise from a balance between the attractive force on the defects toward negative dilaton and a statistical pressure from the entropy of the configuration. We end with speculations on the nature of the space-like singularity present inside black holes described by certain dilaton potentials.\] # Kusuki (Notes) ## Modern Approach to 2D Conformal Field Theory \[Links: [arXiv](https://arxiv.org/abs/2412.18307), [PDF](https://arxiv.org/pdf/2412.18307)\] \[Abstract: The primary aim of these lecture notes is to introduce the modern approach to [[0003 2D CFT|two-dimensional conformal field theory]] (2D CFT). The study of analytical methods in two-dimensional conformal field theory has developed over several decades, starting with BPZ. The development of analytical methods, particularly in rational conformal field theory (RCFT), has been remarkable, with complete classifications achieved for certain model groups. One motivation for studying CFT comes from its ability to describe quantum critical systems. Given that realistic quantum critical systems are fundamentally RCFTs, it is somewhat natural that the analytical methods of RCFT have evolved significantly. CFTs other than RCFTs are called irrational conformal field theories (ICFTs). Compared to RCFTs, the study of ICFTs has not progressed as much. Leaving aside whether there is physical motivation or not, ICFTs inherently possess a difficulty that makes them challenging to approach. However, with the development of quantum gravity, the advancement of analytical methods for ICFTs has become essential. The reason lies in the AdS/CFT correspondence. AdS/CFT refers to the relationship between d+1 dimensional quantum gravity and d dimensional CFT. Within this correspondence, the CFT appears as a non-perturbative formulation of quantum gravity. Except in special cases, this CFT belongs to ICFT. Against this backdrop, the methods for ICFTs have developed rapidly in recent years. Many of these ICFT methods are indispensable for modern quantum gravity research. Unfortunately, these cannot be learned from textbooks on 2D CFTs, such as Yellow book. These lecture notes aim to fill this gap. Specifically, we will cover techniques that have already been applied in many studies, such as HHLL block and monodromy method, and significant results that have become proper nouns, such as Hellerman bound and HKS bound.\] # Kusuki, Murciano, Ooguri, Pal ## Entanglement asymmetry and symmetry defects in boundary conformal field theory \[Links: [arXiv](https://arxiv.org/abs/2411.09792), [PDF](https://arxiv.org/pdf/2411.09792)\] \[Abstract: A state in a quantum system with a given global symmetry, $G$, can be sensitive to the presence of boundaries, which may either preserve or break this symmetry. In this work, we investigate how conformal invariant boundary conditions influence the $G$-symmetry breaking through the lens of the entanglement asymmetry, a quantifier of the "distance" between a symmetry-broken state and its symmetrized counterpart. By leveraging 2D [[0548 Boundary CFT|BCFT]], we investigate the symmetry breaking for both finite and compact Lie groups. Beyond the leading order term, we also compute the subleading corrections in the subsystem size, highlighting their dependence on the symmetry group $G$ and the BCFT operator content. We further explore the entanglement asymmetry following a global quantum quench, where a symmetry-broken state evolves under a symmetry-restoring Hamiltonian. In this dynamical setting, we compute the entanglement asymmetry by extending the method of images to a BCFT with non-local objects such as invertible symmetry defects.\] # Lai, Sun, Tian ## Holographic correlation functions from wedge \[Links: [arXiv](https://arxiv.org/abs/2411.12420), [PDF](https://arxiv.org/pdf/2411.12420)\] \[Abstract: In this work, we propose a novel holographic method for computing correlation functions of operators in conformal field theories. This method refines previous approaches and is specifically aimed at being applied to heavy operators. For operators that correspond to particles in the bulk, we show that the correlation functions can be derived from the on-shell actions of excised geometries for heavy operators, using numerical and perturbative calculations. These excised geometries are constructed from various background solutions such as Poincare AdS3, global AdS3, and [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] by cutting out a wedge bounded by two intersecting End-of-the-world branes and the AdS boundary. The wedge itself can be interpreted as a dual to a [[0548 Boundary CFT|BCFT]] with cusps in the [[0181 AdS-BCFT|AdS/BCFT]] framework. Additionally, we calculate the correlation functions for heavy operators directly by constructing backreacted bulk geometries for particle excitations through coordinate transformations from a conical solution. We find that the on-shell actions of these backreacted solutions accurately reproduce correlation functions, although they differ from those computed in [[0011 Fefferman-Graham expansion|Fefferman-Graham]] (FG) gauge. This discrepancy, previously noted and explained in our earlier work, is reinforced by additional examples presented here.\] ## Related - [[0660 Spacetime banana]] # Lee, Stanford ## Bulk thimbles dual to trace relations \[Links: [arXiv](https://arxiv.org/abs/2412.20769), [PDF](https://arxiv.org/pdf/2412.20769)\] \[Abstract: The maximal [[0662 Giant gravitons|giant graviton]] is a D-brane wrapping a maximal $S^3\subset S^5$ within $\text{AdS}_5\times S^5$. It represents an upper bound on the R charge that can be carried by certain bulk states. We study the maximal giant and its half-BPS fluctuations, motivated by a recent proposal [[2023#Lee]] connecting these fluctuations to trace relations in the boundary theory. In a computation of the partition function of half-BPS states, we find that the maximal giant is an unstable saddle point and that its Lefschetz thimble corresponds to the quantization of an imaginary phase space. The states resulting from the quantization of this phase space contribute negatively to the partition function and can be regarded as bulk duals of trace relations. Finally, we study a model for a path integral that would connect together components of the bulk half-BPS field space with different numbers of giants.\] # Leutheusser, Liu ## Superadditivity in large $N$ field theories and performance of quantum tasks \[Links: [arXiv](https://arxiv.org/abs/2411.04183), [PDF](https://arxiv.org/pdf/2411.04183)\] \[Abstract: Field theories exhibit dramatic changes in the structure of their operator algebras in the limit where the number of local degrees of freedom ($N$) becomes infinite. An important example of this is that the [[0415 Von Neumann algebra|algebras]] associated to local subregions may not be additively generated in the limit. We investigate examples and explore the consequences of this ''superadditivity'' phenomenon in large $N$ field theories and holographic systems. In holographic examples we find cases in which superadditive algebras can probe the black hole interior, while the additive algebra cannot. We also discuss how superaddivity explains the sucess of quantum error correction models of holography. Finally we demonstrate how superadditivity is intimately related to the ability of holographic field theories to perform quantum tasks that would naievely be impossible. We argue that the [[0656 Connected wedge theorem|connected wedge theorems]] (CWTs) of May, Penington, Sorce, and Yoshida, which characterize holographic protocols for quantum tasks, can be re-phrased in terms of superadditive algebras and use this re-phrasing to conjecture a generalization of the CWTs that is an equivalence statement.\] # Li (Z) ## Spinning Particle Geometries in AdS$_3$/CFT$_2$ \[Links: [arXiv](https://arxiv.org/abs/2403.05524), [PDF](https://arxiv.org/pdf/2403.05524.pdf)\] \[Abstract: We study spinning particle/defect geometries in the context of AdS$_3$/CFT$_2$. These solutions lie below the [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] threshold, and can be obtained from identifications of AdS$_3$. We construct the [[0103 Two-point functions|Feynman propagator]] by solving the bulk equation of motion in the spinning particle geometry, summing over the modes of the fields and passing to the boundary. The quantization of the scalar fields becomes challenging when confined to the regions that are causally well-behaved. If the region containing closed timelike curves (CTCs) is included, the normalization of the scalar fields enjoys an analytical simplification and the propagator can be expressed as an infinite sum over image geodesics. In the dual CFT$_2$, the propagator can be recast as the HHLL four-point function, where by taking into account the $PSL (2,\mathbb{Z})$ modular images, we recover the bulk computation. We comment on the casual behavior of bulk geometries associated with single-trace operators of spin scaling with the [[0033 Central charge|central charge]] below the BTZ threshold.\] # Li (P) ## Notes on the Factorisation of the Hilbert Space for Two-Sided Black Holes in Higher Dimensions \[Links: [arXiv](https://arxiv.org/abs/2410.23886), [PDF](https://arxiv.org/pdf/2410.23886)\] \[Abstract: In this paper, we investigate the [[0514 Lorentzian factorisation problem|Hilbert space factorisation problem]] of two-sided black holes in high dimensions. We demonstrate that the Hilbert space of two-sided black holes can be factorized into the tensor product of two one-sided bulk Hilbert spaces when the effect of non-perturbative replica wormholes is taken into account. We further interpret the one-sided bulk Hilbert space as the Hilbert space of a one-sided black hole. Therefore, since the Hilbert space of a two-sided black hole can be obtained from the tensor product of two single-sided black hole Hilbert spaces, we consider this as an embodiment of the [[0220 ER=EPR|ER=EPR]] conjecture, and we show when the entanglement between the two single-sided black holes is sufficiently strong, the (Lorentzian) geometry of a two-sided black hole will emerge.\] # Liu, Long, Ye ## Feynman rules and loop structure of Carrollian amplitude \[Links: [arXiv](https://arxiv.org/abs/2402.04120), [PDF](https://arxiv.org/pdf/2402.04120.pdf)\] \[Abstract: In this paper, we derive the [[0419 Carrollian CFT|Carrollian amplitude]] in the framework of bulk reduction. The Carrollian amplitude is shown to relate to the scattering amplitude by a Fourier transform in this method. We propose Feynman rules to calculate the Carrollian amplitude where the Fourier transforms emerge as the integral representation of the external lines in the Carrollian space. Then we study the four-point Carrollian amplitude at loop level in massless $\Phi^4$ theory. As a consequence of Poincaré invariance, the four-point Carrollian amplitude can be transformed to the amplitude that only depends on the cross ratio $z$ of the celestial sphere and a variable $\chi$ invariant under translation. The four-point Carrollian amplitude is a polynomial of the two-point Carrollian amplitude whose argument is replaced with $\chi$. The coefficients of the polynomial have branch cuts in the complex $z$ plane. We also show that the renormalized Carrollian amplitude obeys the Callan-Symanzik equation. Moreover, we initiate a generalized $\Phi^4$ theory by designing the Feynman rules for more general Carrollian amplitude.\] # Liu, Ma (Apr, a) ## Massive celestial amplitudes and celestial amplitudes beyond four points \[Links: [arXiv](https://arxiv.org/abs/2404.01920), [PDF](https://arxiv.org/pdf/2404.01920)\] \[Abstract: We compute scalar three-point celestial amplitudes involving two and three massive scalars. The three-point coefficient of celestial amplitudes with two massive scalars contains a hypergeometric function, and the one with three massive scalars can be represented as a triple Mellin-Barnes integral. Using these three-point [[0262 Celestial amplitude calculations|celestial amplitudes]], we investigate the [[0031 Conformal block|conformal block expansions]] of five- and six-point scalar celestial amplitudes in the comb channel. We observe the presence of two-particle operators in the conformal block expansion of five-point celestial amplitudes, which confirms the previous analysis by taking [[0077 Multi-collinear limit|multi-collinear limit]]. Moreover, we find that there are new three-particle operators in the conformal block expansion of six-point celestial amplitudes. Based on these findings, we conjecture that exchanges of $n$-particle operators can be observed by considering the comb channel conformal block expansion of $(n+3)$-point massless celestial amplitudes. Finally, we show that a new series of operators appears when turning on the mass of the first incoming particle. The leading operator in this series can be interpreted as a two-particle exchange in the [[0114 Celestial OPE|OPE]] of one massive and one massless scalars.\] # Liu, Ma (Apr, b) ## Celestial Optical Theorem \[Links: [arXiv](https://arxiv.org/abs/2404.18898), [PDF](https://arxiv.org/pdf/2404.18898.pdf)\] \[Abstract: We establish the nonperturbative celestial optical theorem from the unitarity of S-matrix. This theorem provides a set of nonperturbative bootstrap equations of the [[0020 Conformal partial wave decomposition|conformal partial wave]] (CPW) coefficients. The celestial optical theorem implies that the imaginary part of CPW coefficient with appropriate conformal dimensions is non-negative. By making certain assumptions and using the celestial optical theorem, we derive nonperturbative results concerning the analytic structure of CPW coefficients. We discover that the CPW coefficients of four massless particles must and only have simple poles located at specific positions. The CPW coefficients involving massive particles exhibit double-trace poles, indicating the existence of double-trace operators in nonperturbative [[0010 Celestial holography|CCFT]]. It is worth noting that, in contrast to [[0001 AdS-CFT|AdS/CFT]], the conformal dimensions of double-trace operators do not receive anomalous dimensions.\] # Liu, Nian, Zayas ## Quantum Corrections to Holographic Strange Metal at Low Temperature \[Links: [arXiv](https://arxiv.org/abs/2410.11487), [PDF](https://arxiv.org/pdf/2410.11487)\] \[Abstract: The holographic approach to the strange metal phase relies on near-extremal asymptotically AdS$_4$ electrically charged black branes with important input from their AdS$_2$ near-horizon throat geometry. Motivated by the current understanding of the role of [[0608 Quantum effects for near-extremal black holes|quantum fluctuations in the throat of near-extremal black holes]], we revisit some transport properties. We model quantum gravitational and gauge fluctuations in the throat region by adopting results in [[0050 JT gravity|Jackiw-Teitelboim gravity]], effectively leading to quantum corrections for the dual CFT$_1$ Green's function in the near-horizon infrared region. We use the quantum-corrected Green's function to compute the conductivity for (2+1)-dimensional holographic strange metals and obtain corrections for the DC resistivity and the optical conductivity. We also compare the quantum-corrected holographic approach with results from the complex [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] model and point out qualitative differences. Although experimental detection for the quantum-corrected holographic approach to the DC resistivity requires higher precision than current experimental accuracy, future experiments with improved technologies could detect these quantum corrections. Interestingly, including quantum corrections to the optical conductivity does provide a plausible explanation for the experimental anomalous power-law behavior detected in various strange metals.\] # Liu, Santos, Wiseman ## New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity \[Links: [arXiv](https://arxiv.org/abs/2402.04308), [PDF](https://arxiv.org/pdf/2402.04308.pdf); Talks: [Stony Brook](https://scgp.stonybrook.edu/video/video.php?id=6733)\] \[Abstract: We consider four-dimensional Euclidean [[0615 Gravity in a box|gravity in a finite cavity]]. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter family of boundary conditions, parameterized by a constant $p$, where a suitably Weyl rescaled boundary metric is fixed, and all give a well-posed elliptic system. Anderson and Dirichlet boundary conditions can be seen as the limits $p \to 0$ and $\infty$ of these. Focussing on static Euclidean solutions, we derive a thermodynamic first law. Restricting to a spherical spatial boundary, the infillings are flat space or the Schwarzschild solution, and have similar thermodynamics to the Dirichlet case. We consider smooth Euclidean fluctuations about the flat space saddle; for $p > 1/6$ the spectrum of the Lichnerowicz operator is stable -- its eigenvalues have positive real part. Thus we may regard large $p$ as a regularization of the ill-posed Dirichlet boundary conditions. However for $p < 1/6$ there are unstable modes, even in the spherically symmetric and static sector. We then turn to Lorentzian signature. For $p < 1/6$ we may understand this spherical Euclidean instability as being paired with a Lorentzian instability associated with the dynamics of the boundary itself. However, a mystery emerges when we consider perturbations that break spherical symmetry. Here we find a plethora of dynamically unstable modes even for $p > 1/6$, contrasting starkly with the Euclidean stability we found. Thus we seemingly obtain a system with stable thermodynamics, but unstable dynamics, calling into question the standard assumption of smoothness that we have implemented when discussing the Euclidean theory.\] ## Two families - Generalised Dirichlet: $\delta\left(\gamma^p K\right)=0$ and $\delta \tilde{\gamma}_{\mu \nu}=0$ - Generalised Neumann: $\delta\left(\gamma^p K\right)=0$ and $\tilde{K}^{\mu \nu}=0$ # Lowe, Wang, Yang ## Holographic Reconstruction of Gravitational Perturbations in AdS/CFT and Implications for Celestial Conformal Field Theory \[Links: [arXiv](https://arxiv.org/abs/2411.02364), [PDF](https://arxiv.org/pdf/2411.02364)\] \[Abstract: We begin by reexamining the [[0026 Bulk reconstruction|holographic reconstruction]] of scalar fields in four-dimensional anti-de Sitter spacetime, adopting a purely Lorentzian signature derivation, reproducing earlier results of [[0016 HKLL|HKLL]] and generalizing to arbitrary boundary metrics. The approach is extended to gravitational perturbations, focussing on perturbations around AdS$_{4}$ and show that the mapping can be formulated as a purely light-like integral of the conformal field theory stress energy tensor. An example is considered of relevance to the [[0454 Flat holography from AdS-CFT|flat spacetime limit]] with nontrivial BMS charges turned on, potentially providing a quantum field theory definition of [[0010 Celestial holography|celestial CFT]] as a large [[0033 Central charge|central charge]] limit of a [[0634 3d CFT|3d CFT]].\] # Macedo, Zenginoglu (Review) ## Hyperboloidal Approach to Quasinormal Modes \[Links: [arXiv](https://arxiv.org/abs/2409.11478), [PDF](https://arxiv.org/pdf/2409.11478)\] \[Abstract: Oscillations of black hole spacetimes exhibit divergent behavior toward the bifurcation sphere and spatial infinity. This divergence can be understood as a consequence of the geometry in these spacetime regions. In contrast, black-hole oscillations are regular when evaluated toward the event horizon and null infinity. Hyperboloidal surfaces naturally connect these regions, providing a geometric regularization of time-harmonic oscillations called [[0325 Quasi-normal modes|quasinormal modes]] (QNMs). This review traces the historical development of the hyperboloidal approach to QNMs. We discuss the physical motivation for the hyperboloidal approach and highlight current developments in the field.\] # Maldacena ## Real observers solving imaginary problems \[Links: [arXiv](https://arxiv.org/abs/2412.14014), [PDF](https://arxiv.org/pdf/2412.14014)\] \[Abstract: The sphere partition function is one of the simplest euclidean gravity computations. It is usually interpreted as count of states. However, the one loop gravity correction contains a dimension dependent phase factor, $i^{D+2}$, which seems confusing for such an interpretation. We show that, after including an observer, this phase gets mostly cancelled for the quantity that should correspond to a count of states. However, an overall minus sign remains.\] # Marolf ## On the nature of ensembles from gravitational path integrals \[Links: [arXiv](https://arxiv.org/abs/2407.04625), [PDF](https://arxiv.org/pdf/2407.04625)\] \[Abstract: Spacetime wormholes in [[0555 Gravitational path integral|gravitational path integrals]] have long been interpreted in terms of ensembles of theories. Here we probe what sort of theories such ensembles might contain. Careful consideration of a simple $d=2$ topological model indicates that the Hilbert space structure of a general ensemble element fails to factorize over disconnected Cauchy-surface boundaries, and in particular that its Hilbert space ${\cal H}_{N_{CS\partial}}$ for $N_{CS\partial}$ Cauchy-surface boundaries fails to be positive definite when the number $N_{CS\partial}$ of disconnected such boundaries is large. This suggests a generalization of the AdS/CFT correspondence in which a bulk theory is dual to an ensemble of theories that deviate from standard CFTs by violating both locality and positivity (at least under certain circumstances). Since violations of positivity are undesirable, we propose that positivity-violating elements of the ensemble be removed when studying physics in asymptotically AdS spacetimes (or in other contexts in which Cauchy surfaces have asymptotic boundaries), perhaps reducing the ensemble to a single standard CFT. Nevertheless, properties of any remaining CFTs that are uncorrelated with positivity of ${\cal H}_{N_{CS\partial}}$ at large $N_{CS\partial}$ will agree with those of typical elements of the full ensemble and may be computed using the ensemble average. On the other hand, elements that violate positivity at large $N_{CS\partial}$ can still have a positive-definite cosmological sector with $N_{CS\partial}=0$. Such elements then define a basis for a Hilbert space describing such cosmologies. In contrast to the cases in which Cauchy-surfaces are allowed to have boundaries, we argue that the resulting Hilbert space need not decohere into single-state theories. As a result, familiar physics might be more easily recovered from this new scenario.\] # Matsuo ## Universal structure of islands in evaporating black holes \[Links: [arXiv](https://arxiv.org/abs/2407.20921), [PDF](https://arxiv.org/pdf/2407.20921)\] \[Abstract: The [[0301 Entanglement entropy|entanglement entropy]] of the [[0304 Hawking radiation|Hawking radiation]] contains contributions from a region inside the black hole, which is called islands, implying that the Hawking radiation contains the information of [[0213 Islands|islands]]. The boundary of the island is given by the [[0212 Quantum extremal surface|quantum extremal surface]], whose position is determined so that the entanglement entropy is extremized. In many cases of stationary black holes and a few cases of evaporating black holes, it was already confirmed that the quantum extremal surface is located outside the horizon for stationary black holes and is inside the horizon for evaporating black holes. In this paper, we calculate islands in general black holes and show that the island extends to the outside of the horizon for stationary black holes but is hidden inside the horizon for evaporating black holes independent of details of the black hole.\] # Mei, Mo ## On-shell Bootstrap for n-gluons and gravitons scattering in (A)dS, Unitarity and Soft limit \[Links: [arXiv](https://arxiv.org/abs/2402.09111), [PDF](https://arxiv.org/pdf/2402.09111.pdf)\] \[Abstract: We propose an algorithm to recursively bootstrap $n$-point gluon and graviton Mellin-Momentum [[0105 AdS amplitudes|amplitudes in (A)dS spacetime]] using only three-point amplitude. We discover that gluon amplitudes are simply determined by factorization for $n\geq 5$. The same principle applies to $n$-point graviton amplitudes, but additional constraints such as flat space and [[0009 Soft theorems|soft]] limits are needed to fix contact terms. Furthermore, we establish a mapping from $n$-point Mellin-Momentum amplitudes to $n$-point cosmological correlators. We efficiently compute explicit examples up to five points. This leads to the first five-graviton amplitude in AdS$_{d+1}$.\] # Melton, Sharma, Strominger ## Soft Algebras for Leaf Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2402.04150), [PDF](https://arxiv.org/pdf/2402.04150.pdf)\] \[Abstract: Celestial [[0061 Maximally helicity violating amplitudes|MHV]] amplitudes are comprised of non-distributional leaf amplitudes associated to an AdS$_3$ leaf of a foliation of flat spacetime. It is shown here that the leaf amplitudes are governed by the same infinite-dimensional soft 'S-algebra' as their [[0010 Celestial holography|celestial]] counterparts. Moreover, taking the soft limit of the smooth three-point MHV leaf amplitude yields a nondegenerate minus-minus two-point [[0613 Leaf amplitudes|leaf amplitude]]. The two- and three-point MHV leaf amplitudes are used to compute the plus-minus-minus leaf operator product coefficients.\] # Melton, Sharma, Strominger, Wang ## A Celestial Dual for MHV Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2403.18896), [PDF](https://arxiv.org/pdf/2403.18896)\] \[Abstract: It is shown that a 2D CFT consisting of a [[0033 Central charge|central charge]] $c$ [[0562 Liouville theory|Liouville theory]], a chiral level one, rank $N$ [[0069 Kac-Moody algebra|Kac-Moody algebra]] and a weight -3/2 free fermion holographically generate 4D [[0061 Maximally helicity violating amplitudes|MHV]] tree-level scattering amplitudes. The correlators of this 2D CFT give directly the 4D [[0613 Leaf amplitudes|leaf amplitudes]] associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large-$N$ and semiclassical large-$c$ limit, according to the holographic dictionary, as a translationally-invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact AdS$_3$ [[0109 Witten diagrams|Witten diagrams]].\] # Miao, Xie ## Holographic Entanglement Entropy for Brane-World Higher Derivative Gravity \[Links: [arXiv](https://arxiv.org/abs/2410.18314), [PDF](https://arxiv.org/pdf/2410.18314)\] \[Abstract: Due to the splitting problem, it is difficult to derive the [[0007 RT surface|holographic entanglement entropy]] for general [[0006 Higher-derivative gravity|higher derivative gravity]]. Inspired by double holography and renormalized entanglement entropy, we develop a method to derive the generalized gravitational entropy for the brane-world higher derivative (BWHD) gravity. Remarkably, this approach is independent of the splitting problem. The so-called BWHD gravity is an effective theory on the brane, given by the counter terms of holographic renormalization. Interestingly, all solutions to Einstein gravity are also solutions to BWHD gravity. We first verify our approach can derive the correct results for curvature-squared gravity and then derive the holographic entanglement entropy for cubic BWHD gravity, which is the main result of this paper. We also derive the entropy of quartic BWHD gravity in flat space with constant extrinsic curvatures and perform several tests on our results. Finally, we briefly comment on our results.\] # Mitra ## Celestial Conformal Primaries in Effective Field Theories \[Links: [arXiv](https://arxiv.org/abs/2402.09256), [PDF](https://arxiv.org/pdf/2402.09256.pdf)\] \[Abstract: Scattering amplitudes in $d+2$ dimensions can be recast as correlators of conformal primary operators in a putative [[0010 Celestial holography|holographic CFT]]$_d$ by working in a basis of boost eigenstates instead of momentum eigenstates. It has been shown previously that conformal primary operators with $\Delta \in \frac{d}{2} + i {\mathbb R}$ form a basis for massless one-particle representations. In this paper, we consider more general conformal primary operators with $\Delta \in {\mathbb C}$ and show that completeness, normalizability, and consistency with CPT implies that we must restrict the scaling dimensions to either $\Delta \in \frac{d}{2} + i {\mathbb R}$ or $\Delta \in {\mathbb R}$. Unlike those with $\Delta \in \frac{d}{2} + i {\mathbb R}$, the conformal primaries with $\Delta \in {\mathbb R}$ can be constructed without knowledge of the UV and can therefore be defined in effective field theories. With additional analyticity assumptions, we can restrict $\Delta \in 2 - {\mathbb Z}_{\geq0}$ or $\Delta \in \frac{1}{2}-{\mathbb Z}_{\geq0}$ for bosonic or fermionic operators, respectively.\] # Miyashita ## Thermodynamics of the Einstein-Maxwell system \[Links: [arXiv](https://arxiv.org/abs/2402.16113), [PDF](https://arxiv.org/pdf/2402.16113.pdf)\] \[Abstract: At first glance, thermodynamic properties of gravity with asymptotically AdS conditions and those with [[0615 Gravity in a box|box]] boundary conditions, where the spatial section of the boundary is a sphere of finite radius, appear similar. Both exhibit a similar phase structure and [[0012 Hawking-Page transition|Hawking-Page phase transition]]. However, when we introduce a $U(1)$ gauge field to the system, discrepancies in thermodynamic properties between the two cases has been reported in [7] (JHEP 11 (2016) 041). In this paper, by accepting the assumption that all Euclidean saddles contribute to the partition function, I found that these discrepancies are resolved due to the contribution from the "[[0281 Bag-of-gold spacetime|bag of gold]] (BG)," which is the class of Euclidean geometries whose area of bolt is bigger than that of the boundary. As a result, the Hawking-Page phase structure is restored, with the unexpected properties that the upper bound of thermodynamic entropy is always larger than the boundary area divided by $4G$ when the chemical potential is non-zero, and that such high entropy states are realized at sufficiently high temperature.\] # Naskar, Samal ## Topological entanglement entropy meets holographic entropy inequalities \[Links: [arXiv](https://arxiv.org/abs/2412.05484), [PDF](https://arxiv.org/pdf/2412.05484)\] \[Abstract: Topological entanglement entropy (TEE) is an efficient way to detect topological order in the ground state of gapped Hamiltonians. The seminal work of Kitaev and Preskill and simultaneously by Levin and Wen proposed information quantities that can probe the TEE. In the present work, we explain why the subtraction schemes in the proposed information quantities work for the computation of TEE and generalize them for arbitrary number of subregions by explicitly noting the necessary conditions for an information quantity to capture TEE. Our conditions differentiate the probes defined by Kitaev-Preskill and Levin-Wen into separate classes. While there are infinitely many possible probes of TEE, we focus particularly on the cyclic quantities $Q_{2n+1}$ and multi-information $I_n$. We also show that the [[0259 Holographic entropy cone|holographic entropy inequalities]] are satisfied by the quantum entanglement entropy of the non-degenerate ground state of a topologically ordered two-dimensional medium with a mass gap.\] # Neiman, O'Connell ## Topology Change from Pointlike Sources \[Links: [arXiv](https://arxiv.org/abs/2403.04281), [PDF](https://arxiv.org/pdf/2403.04281.pdf)\] \[Abstract: In this paper we study [[0420 Topology change in gravity|topology-changing]] spacetimes occurring from pointlike sources. Following an old idea of Penrose, we will opt for a non-Hausdorff model of topology change in which an initial pointlike source is "doubled" and allowed to propagate along null rays into an eventual cobordism. By appealing to recent developments in non-Hausdorff differential geometry, we will describe and evaluate gravitational actions on these pointlike topology-changing spacetimes. Motivated by analogous results for the Trousers space, we describe a sign convention for Lorentzian angles that will ensure the dampening of our non-Hausdorff topology-changing spacetimes within a two-dimensional [[0555 Gravitational path integral|path integral for gravity]].\] # Okuyama ## Baby universe operators in double-scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2408.03726), [PDF](https://arxiv.org/pdf/2408.03726)\] \[Abstract: We consider the baby universe operator $\mathcal{B}_a$ in the [[0503 Double-scaled SYK|double-scaled SYK]] (DSSYK) model, which creates a [[0051 Baby universes|baby universe]] of size $a$. We find that $\mathcal{B}_a$ is written in terms of the transfer matrix $T$, and vice versa. In particular, the identity operator on the chord Hilbert space is expanded as a linear combination of $\mathcal{B}_a$, which implies that the disk partition function of DSSYK is written as a linear combination of trumpets. We also find that the thermofield double state of DSSYK is generated by a pair of baby universe operators, which corresponds to a double trumpet. This can be thought of as a concrete realization of the idea of [[0220 ER=EPR|ER=EPR]].\] # Ogawa, Takahashi, Tsuda, Waki ## Celestial CFT from $H_3^+$-WZW Model \[Links: [arXiv](https://arxiv.org/abs/2404.12049), [PDF](https://arxiv.org/pdf/2404.12049)\] \[Abstract: Recently, there has been a growing interest in [[0010 Celestial holography|celestial holography]], which is holography in asymptotically flat spacetimes. This holographic duality exhibits numerous mysterious and fruitful features, particularly on the dual CFT side. In this paper, we present the candidate of dual CFT for Minkowski spacetime extracted from $SL(2,\mathbb{C})/SU(2)\cong H^+_3$ [[0601 Weiss-Zumino-Witten models|Wess-Zumino-Witten]] (WZW) model, the simplest non-compact CFT. We demonstrate that it reproduces the well-known principal series and [[0516 Celestial correlators|correlation functions]] dual to the bulk scattering amplitudes.\] # Ookouchi, Sato, Tsukahara ## Decay of Kaluza-Klein Vacuum via Singular Instanton \[Links: [arXiv](https://arxiv.org/abs/2404.13917), [PDF](https://arxiv.org/pdf/2404.13917.pdf)\] \[Abstract: In the decay process of metastable vacua in quantum field theories, the bounce solution, a classical solution in Euclideanized theories, is helpful in calculating the decay rate. Recently, the bounce solution with a conical singularity has attracted wide attention and revealed physical importance. In this paper, we discuss the [[0168 Bubble of nothing|bubble of nothing]] solution, which describes the decay process of a five-dimensional [[0169 Kaluza-Klein|Kaluza-Klein]] vacuum, and study the consequence of including conical singularity. We found that the bounce solution with singularities has a higher decay rate than those without. This effect suggests that a singular solution can play a dominant role in vacuum decay of theories with compact internal space. We also discuss the enhanced decay rate from a thermodynamic perspective.\] # Ozaki, Katsura ## Disorder-Free Sachdev-Ye-Kitaev models: Integrability and Quantum Chaos \[Links: [arXiv](https://arxiv.org/abs/2402.13154), [PDF](https://arxiv.org/pdf/2402.13154.pdf)\] \[Abstract: We introduce two disorder-free variants of the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] (SYK) model, demonstrate their integrability, and study their static and dynamical properties. Unlike diagrammatic techniques, the integrability of these models allows us to obtain dynamical correlation functions even when the number of Majorana fermions is finite. From the solutions, we find that [[0482 Out-of-time-order correlator|out-of-time-order correlators]] (OTOCs) in these models exhibit exponential growth at early times, resembling that of quantum chaotic systems such as those with disorder or external kick terms. Conversely, our analysis shows no evidence of [[0579 Random matrix theory|random-matrix]] behavior in level statistics or the [[0062 Spectral form factor|spectral form factor]]. Our findings illustrate that the clean versions of the SYK models represent simple but nontrivial examples of disorder-free quantum many-body systems displaying [[0008 Quantum chaos|chaos]]-like behavior of OTOCs.\] # Ozkan, Pang, Sezgin (Review) ## Higher Derivative Supergravities in Diverse Dimensions \[Links: [arXiv](https://arxiv.org/abs/2401.08945), [PDF](https://arxiv.org/pdf/2401.08945.pdf)\] \[Abstract: We survey on-shell and off-shell [[0385 Supergravity corrections|higher derivative supergravities]] in dimensions $1\le D\le 11$. Various approaches to their construction, including the Noether procedure, (harmonic) superspace, superform method, superconformal tensor calculus, S-matrix and dimensional reduction, are summarized. Primarily the bosonic parts of the invariants and the supertransformations of the fermionic fields are provided. The process of going on-shell, solutions to the Killing spinor equations, typical supersymmetric solutions, and the role of duality symmetries in the context of $R^4$, $D^4 R^4$ and $D^6 R^4$ invariants are reviewed.\] # Pano, Borji ## Distributional Celestial Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2401.08877), [PDF](https://arxiv.org/pdf/2401.08877.pdf)\] \[Abstract: Scattering amplitudes are tempered distributions, which are defined through their action on functions in the Schwartz space $S(\mathbb{R})$ by duality. For massless particles, their conformal properties become manifest when considering their [[0079 Mellin transform|Mellin transform]]. Therefore we need to mathematically well-define the Mellin transform of distributions in the dual space $S'(\mathbb{R}^+)$. In this paper, we investigate this problem by characterizing the Mellin transform of the Schwartz space $S(\mathbb{R}^+)$. This allows us to rigorously define the Mellin transform of tempered distributions through a Parseval-type relation. Massless celestial amplitudes are then properly defined by taking the Mellin transform of elements in the topological dual of the Schwartz space $S(\mathbb{R}^+)$. We conclude the paper with applications to tree-level graviton [[0516 Celestial correlators|celestial amplitudes]].\] # Parrikar, Rajgadia, Singh, Sorce ## Relational bulk reconstruction from modular flow \[Links: [arXiv](https://arxiv.org/abs/2403.02377), [PDF](https://arxiv.org/pdf/2403.02377.pdf)\] \[Abstract: The [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]] paradigm in [[0001 AdS-CFT|AdS/CFT]] states that for a bulk qudit within the entanglement wedge of a boundary subregion $\bar{A}$, operators acting on the bulk qudit can be reconstructed as CFT operators on $\bar{A}$. This naturally fits within the framework of [[0146 Quantum error correction|quantum error correction]], with the CFT states containing the bulk qudit forming a code protected against the erasure of the boundary subregion $A$. In this paper, we set up and study a framework for relational [[0026 Bulk reconstruction|bulk reconstruction]] in holography: given two code subspaces both protected against erasure of the boundary region $A$, the goal is to relate the operator reconstructions between the two spaces. To accomplish this, we assume that the two code subspaces are smoothly connected by a one-parameter family of codes all protected against the erasure of $A$, and that the maximally-entangled states on these codes are all full-rank. We argue that such code subspaces can naturally be constructed in holography in a "measurement-based" setting. In this setting, we derive a flow equation for the operator reconstruction of a fixed code subspace operator using modular theory which can, in principle, be integrated to relate the reconstructed operators all along the flow. We observe a striking resemblance between our formulas for relational bulk reconstruction and the infinite-time limit of Connes cocycle flow, and take some steps towards making this connection more rigorous. We also provide alternative derivations of our reconstruction formulas in terms of a canonical reconstruction map we call the modular reflection operator.\] # Passegger, Verch ## Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization \[Links: [arXiv](https://arxiv.org/abs/2402.14794), [PDF](https://arxiv.org/pdf/2402.14794.pdf)\] \[Abstract: For any local, translation-covariant quantum field theory on Minkowski spacetime we prove that two distinct primary states that are invariant under the inertial time evolutions in different inertial reference frames and satisfy a timelike cluster property called the mixing property are disjoint, i.e. each state is not a perturbation of the other. These conditions are fulfilled by the inertial KMS states of the free scalar field, thus showing that a state satisfying the [[0521 KMS condition|KMS condition]] relative to one reference frame is far from thermal equilibrium relative to other frames. We review the property of return to equilibrium in open quantum systems theory and discuss the implications of disjointness on the asymptotic behavior of detector systems coupled to states of a free massless scalar field. We argue that a coupled system consisting of an Unruh-DeWitt detector moving with constant velocity relative to the field in a thermal state, or an excitation thereof, cannot approach a KMS state at late times under generic conditions. This leads to an illustration of the physical differences between heat baths in inertial systems and the apparent "heat bath" of the Unruh effect from the viewpoint of moving detectors. The article also reviews, from a quantum field theoretical perspective, the quantum dynamical system of an Unruh-DeWitt detector coupled to a massless scalar field in a KMS state relative to the rest frame of the detector.\] # Pelliconi, Sonner, Verlinde ## Gravity as a mesoscopic system \[Links: [arXiv](https://arxiv.org/abs/2409.13808), [PDF](https://arxiv.org/pdf/2409.13808)\] \[Abstract: We employ a probabilistic mesoscopic description to draw conceptual and quantitative analogies between Brownian motion and late-time fluctuations of thermal correlation functions in generic chaotic systems respecting [[0040 Eigenstate thermalisation hypothesis|ETH]]. In this framework, thermal correlation functions of 'simple' operators are described by stochastic processes, which are able to probe features of the microscopic theory only in a probabilistic sense. We apply this formalism to the case of semiclassical gravity in AdS$_3$, showing that wormhole contributions can be naturally identified as moments of stochastic processes. We also point out a 'Matryoshka doll' recursive structure in which information is hidden in higher and higher moments, and which can be naturally justified within the stochastic framework. We then re-interpret the gravitational results from the boundary perspective, promoting the OPE data of the CFT to probability distributions. The outcome of this study shows that semiclassical gravity in AdS can be naturally interpreted as a mesoscopic description of quantum gravity, and a mesoscopic holographic duality can be framed as a moment-vs-probability-distribution duality.\] ## Topics - [[0002 3D gravity]] # Penington, Rath ## The Diagonal Approximation for Holographic Rényi Entropies \[Links: [arXiv](https://arxiv.org/abs/2412.03670), [PDF](https://arxiv.org/pdf/2412.03670)\] \[Abstract: Recently [[2023#Dong, Kudler-Flam, Rath|Dong, Rath and Kudler-Flam]] proposed a modified cosmic brane prescription for computing the [[0293 Renyi entropy|Rényi entropy]] $S_\alpha$ of a holographic system in the presence of multiple extremal surfaces. This prescription was found by assuming a diagonal approximation, where the Rényi entropy is computed after first measuring the areas of all extremal surfaces. We derive this diagonal approximation and show that it accurately computes Rényi entropies up to $O(\log G)$ corrections. For $\alpha<1$, this allows us to derive the modified cosmic brane prescription, which differs from the original cosmic brane prescription at leading order in $G$. For $\alpha>1$, it leads to the original cosmic brane prescription without needing to assume that replica symmetry is unbroken in the bulk.\] # Penington, Witten ## Algebras and states in super-JT gravity \[Links: [arXiv](https://arxiv.org/abs/2412.15549), [PDF](https://arxiv.org/pdf/2412.15549)\] \[Abstract: In bosonic [[0050 JT gravity|JT gravity]], minimally coupled to bulk matter, there exists a single, delta-function-normalisable state in each $SL(2,R)$ representation of the matter QFT for any pair of positive energies $E_L$, $E_R$ at the left and right boundaries. In $\mathcal{N} = 2$ super-JT gravity coupled to matter, we show that there exists a single normalisable state in each $SU(1,1|1)$ matter representation (given appropriate R-charges) that has exactly zero energy at both boundaries. For non-BPS representations, these states have the peculiar property that they break all supersymmetry in the bulk, while preserving supersymmetry at both boundaries. Projecting the algebras of boundary observables onto these zero-energy states leads to a Type II$_1$ [[0415 Von Neumann algebra|von Neumann]] factor at each boundary that contains a single operator for each supersymmetric matter boundary primary with sufficiently small R-charge. For neutral boundary primaries, the Type II_1 factor has a natural action on the matter QFT Hilbert space (with no additional gravitational degrees of freedom) such that the QFT vacuum is the unique tracial state. Moreover, the product of neutral matter operators can be found very explicitly and has a remarkably simple form. When primaries with nonzero matter R-charge are included, the trace can be written as a sum over matter vacuum expectation values associated to each allowed boundary R-charge $J_R$, with the terms in the sum weighted by $\mathrm{cos}(\pi J_R)$. In this way, the ground state algebras encode the ratios of the number of [[0178 BPS|BPS]] microstates within each R-charge sector. In addition to the results on super-JT gravity described above, we provide a purely Lorentzian derivation of the algebraic structure of canonically quantised (bosonic) JT gravity plus matter, without appeal to the [[0555 Gravitational path integral|Euclidean gravitational path integrals]] used in previous work.\] # Post, Tsiares ## A non-rational Verlinde formula from Virasoro TQFT \[Links: [arXiv](https://arxiv.org/abs/2411.07285), [PDF](https://arxiv.org/pdf/2411.07285)\] \[Abstract: We use the [[0596 Virasoro TQFT|Virasoro TQFT]] to derive an integral identity that we view as a non-rational generalization of the Verlinde formula for the Virasoro algebra with central charge $c\geq 25$. The identity expresses the Virasoro fusion kernel as an integral over a ratio of modular S-kernels on the (punctured) torus. In particular, it shows that the one-point S-kernel diagonalizes the Virasoro [[0597 6j symbol|6j symbol]]. After carefully studying the analytic properties of this 'Virasoro-Verlinde formula', we present three applications. In [[0642 Boundary Liouville CFT|boundary Liouville CFT]], the formula ensures the open-closed duality of the boundary one-point function on the annulus. In pure [[0002 3D gravity|3d gravity]], it provides an essential step in computing the partition function on hyperbolic 3-manifolds that fiber over the circle. Lastly, in AdS$_3$/CFT$_2$, the formula computes a three-boundary torus wormhole, which leads to a prediction for the statistical correlation between the density of states and two OPE coefficients in the dual large-$c$ CFT ensemble. We conclude by discussing the implications of our result for the fusion rules in generic non-rational [[0003 2D CFT|2d CFTs]].\] # Prabhu, Satishchandran ## Infrared finite scattering theory: Amplitudes and soft theorems \[Links: [arXiv](https://arxiv.org/abs/2402.18637), [PDF](https://arxiv.org/pdf/2402.18637.pdf)\] \[Abstract: Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an out-state with [[0287 Memory effect|memory]]. Scattering with any massless fields violates the standard assumption of asymptotic completeness -- that all "in" and "out" states lie in the standard (zero memory) Fock space -- and therefore leads to infrared divergences in the standard S-matrix amplitudes. We define an infrared finite scattering theory valid for general quantum field theories and quantum gravity. The (infrared finite) "superscattering" map $\$ is defined as a map between "in" and "out" states which does not require any a priori choice of a preferred Hilbert space. We define a "generalized asymptotic completeness" which accommodates states with memory in the space of asymptotic states. We define a complete basis of improper states on any memory Fock space (called "BMS particle" states) which are eigenstates of the energy-momentum -- or, more generally, the BMS supermomentum -- that generalize the usual $n$-particle momentum basis to account for states with memory. We then obtain infrared finite $\$-amplitudes defined as matrix elements of $\$ in the BMS particle basis. This formulation of the scattering theory is a key step towards analyzing fine-grained details of the [[0295 Infrared divergences in scattering amplitude|infrared finite]] scattering theory. In quantum gravity, invariance of $\$ under BMS supertranslations implies factorization of $\$-amplitudes as the frequency of one of the BMS particles vanishes. This proves an infrared finite analog of the [[0009 Soft theorems|soft graviton theorem]]. Similarly, an infrared finite soft photon theorem in QED follows from invariance of $\$ under [[0060 Asymptotic symmetry|large gauge transformations]]. We comment on how one must generalize this framework to consider $\$-amplitudes for theories with [[0078 Collinear limit|collinear divergences]] (e.g., massless QED and Yang-Mills theories).\] # Qu ## P-adic AdS/CFT on subspaces of the Bruhat-Tits tree \[Links: [arXiv](https://arxiv.org/abs/2402.03730), [PDF](https://arxiv.org/pdf/2402.03730.pdf)\] \[Abstract: On two different subspaces of Bruhat-Tits tree, the exact effective actions and two-point functions of deformed CFTs are calculated according to the [[0084 p-adic holography|p-adic]] version of [[0001 AdS-CFT|AdS/CFT]]. These subspaces are specially chosen such that in the case of $p\equiv3\pmod4$, they can be viewed as a circle and a hyperbola over p-adic numbers when taken to infinities. It is found that two-point functions of CFTs depend on chordal distances of the circle and the hyperbola.\] # Ribault (Review) ## Exactly solvable conformal field theories \[Links: [arXiv](https://arxiv.org/abs/2411.17262), [PDF](https://arxiv.org/pdf/2411.17262)\] \[Abstract: We review [[0003 2D CFT|2d CFT]] in the [[0036 Conformal bootstrap|bootstrap]] approach, and sketch the known exactly solvable CFTs with no extended chiral symmetry: [[0562 Liouville theory|Liouville theory]], (generalized) minimal models, limits thereof, and loop CFTs, including the $O(n)$, Potts and $PSU(n)$ CFTs. Exact solvability relies on local conformal symmetry, and on the existence of degenerate fields. We show how these assumptions constrain the spectrum and correlation functions. We discuss how crossing symmetry equations can be solved analytically and/or numerically, leading to analytic expressions for structure constants in terms of the double Gamma function. In the case of loop CFTs, we sketch the corresponding statistical models, and derive the relation between statistical and CFT variables. We review the resulting combinatorial description of correlation functions, and discuss what remains to be done for solving the CFTs.\] # Riddell, von Keyserlingk, Prosen, Bertini ## Structural Stability Hypothesis of Dual Unitary Quantum Chaos \[Links: [arXiv](https://arxiv.org/abs/2402.19096), [PDF](https://arxiv.org/pdf/2402.19096.pdf)\] \[Abstract: Having spectral correlations that, over small enough energy scales, are described by [[0579 Random matrix theory|random matrix theory]] is regarded as the most general defining feature of [[0008 Quantum chaos|quantum chaotic]] systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits -- a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focussing on the *[[0062 Spectral form factor|spectral form factor]]*, i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions.\] # Roussillon ## On the Virasoro fusion and modular kernels at any irrational central charge \[Links: [arXiv](https://arxiv.org/abs/2405.09325), [PDF](https://arxiv.org/pdf/2405.09325)\] \[Abstract: We propose a series representation for the Virasoro [[0573 Crossing kernel|fusion and modular kernels]] at any irrational [[0033 Central charge|central charge]]. Two distinct, yet closely related formulas are needed for the cases $c\in \mathbb C \backslash (-\infty,1]$ and $c <1$. We also conjecture that the formulas have a well-defined limit as the central charge approaches rational values. Our proposal for $c <1$ agrees numerically with the fusion transformation of the four-point spherical conformal blocks, whereas our proposal for $c\in \mathbb C \backslash (-\infty,1]$ agrees numerically with Ponsot and Teschner's integral formula for the fusion kernel. The case of the modular kernel is studied as a special case of the fusion kernel.\] # Ruzziconi, Stieberger, Taylor, Zhu ## Differential Equations for Carrollian Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2407.04789), [PDF](https://arxiv.org/pdf/2407.04789)\] \[Abstract: Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of [[0419 Carrollian CFT|Carrollian CFT]] that holographically describes asymptotically flat spacetime. We derive linear differential equations satisfied by Carrollian [[0061 Maximally helicity violating amplitudes|MHV]] gluon and graviton amplitudes. We obtain non-distributional solutions for both the gluon and graviton cases. We perform various consistency checks for these differential equations, including compatibility with conformal Carrollian symmetries.\] # Saha, Kulkarni, Dhar ## Generalised Hydrodynamics description of the Page curve-like dynamics of a freely expanding fermionic gas \[Links: [arXiv](https://arxiv.org/abs/2402.18422), [PDF](https://arxiv.org/pdf/2402.18422.pdf)\] \[Abstract: We consider an analytically tractable model that exhibits the main features of the Page curve characterizing the evolution of [[0301 Entanglement entropy|entanglement entropy]] during evaporation of a black hole. Our model is a gas of non-interacting fermions on a lattice that is released from a box into the vacuum. More precisely, our Hamiltonian is a tight-binding model with a defect at the junction between the filled box and the vacuum. In addition to the entanglement entropy we consider several other observables, such as the spatial density profile and current, and show that the semiclassical approach of generalized hydrodynamics provides a remarkably accurate description of the quantum dynamics including that of the entanglement entropy at all times. Our hydrodynamic results agree closely with those obtained via exact microscopic numerics. We find that the growth of entanglement is linear and universal, i.e, independent of the details of the defect. The decay shows $1/t$ scaling for conformal defect while for non-conformal defects, it is slower. Our study shows the power of the semiclassical approach and could be relevant for discussions on the resolution of the [[0131 Information paradox|black hole information paradox]].\] # Santos, Boschi-Filho ## Geometric Josephson junction \[Links: [arXiv](https://arxiv.org/abs/2407.10008), [PDF](https://arxiv.org/pdf/2407.10008)\] \[Abstract: In this work, we present a gravitational dual of a Josephson junction constructed from the [[0181 AdS-BCFT|AdS/BCFT]] correspondence. On the gravity side, we consider a planar AdS-Schwarzschild black hole. Our junction is connected by the boundary $Q$ with tension $\Sigma$ of the boundary CFT. Our computations on the gravity side reproduce the standard relation between the current across the junction and the phase difference of the condensate controlled by the tension $\Sigma$. We also study the maximum current's dependence on the junction's tension and size and reproduce familiar results.\] # Sathiapalan ## Mapping from Exact RG to Holographic RG in Flat Space \[Links: [arXiv](https://arxiv.org/abs/2408.00628), [PDF](https://arxiv.org/pdf/2408.00628)\] \[Abstract: In earlier papers a method was given for constructing from first principles a [[0257 Holographic RG flow|holographic bulk dual action]] in Euclidean AdS space for a Euclidean CFT on the boundary. The starting point was an Exact RG for the boundary theory. The bulk action is obtained from the evolution operator for this ERG followed by a field redefinition. This procedure guarantees that the boundary correlators are all recovered correctly. In this paper we use the same method in an attempt to construct a holographic dual action for the free $O(N)$ model where the bulk is flat Euclidean space with a plane boundary wall. The scalar cubic interaction is found to be local (in $D=3$) but depends on the distance from the boundary - which can be interpreted as a non constant background dilaton field. The spin 2 - scalar - scalar interaction is found to be non local - in contrast to the AdS case. A field redefinition that makes the kinetic term quartic in derivatives can be done to mitigate (but not eliminate) this non locality. It is shown that, in spite of the non locality, the action can be obtained by gauge fixing an action that has the linearized gauge invariance associated with general coordinate invariance. Boundary correlators (two point and three point) are shown to be reproduced by bulk calculations - as expected in this approach to holography.\] # Sharapov, Skvortsov, Sukhanov ## Matter-coupled higher spin gravities in 3d: no- and yes-go results \[Links: [arXiv](https://arxiv.org/abs/2409.12830), [PDF](https://arxiv.org/pdf/2409.12830)\] \[Abstract: Massless [[0588 Higher-spin fields|higher-spin fields]] show no preference for any value of the cosmological constant in 3d. All matter-free higher-spin gravities in 3d are equivalent to [[0089 Chern-Simons theory|Chern-Simons theories]] with an appropriate choice of gauge algebra. For various reasons, including holography, it is important to enrich them with matter fields. In (A)dS$_3$, the coupling of matter fields to higher-spin fields is well-known to the leading order and is determined by the representation theory. We extend this result to flat space, where the relevant higher-spin algebra is the Poisson algebra, aka $w_{1+\infty}$. However, we show that both in flat and (A)dS$_3$ spaces there are no nontrivial higher order deformations/interactions. Nevertheless, by enlarging the field content with some auxiliary fields and taking advantage of the chiral higher-spin gravity's vertices, it is possible to construct an exotic matter-coupled theory on (A)dS$_3$. It also admits a flat limit. The equations of motion have the form of a Poisson sigma-model and a meaningful action has the form of a Courant sigma-model. We also explore the potential for embedding this theory into a holographic duality.\] # Sharma, Ghosh, Sarkar ## Symmetries of Love: Ladder Structure of Static and Rotating Black Holes \[Links: [arXiv](https://arxiv.org/abs/2401.00703), [PDF](https://arxiv.org/pdf/2401.00703.pdf)\] \[Abstract: Black hole solutions of [[0554 Einstein gravity|general relativity]] exhibit a symmetry for the static perturbations around these spacetimes, known as ''ladder symmetry''. This symmetry proves useful in constructing a tower of solutions for perturbations and elucidating their general properties. Specifically, the presence of this symmetry leads to vanishing of the [[0581 Tidal Love numbers|tidal love number]] associated with black holes. In this work, we find the most general spherical symmetric and static black hole spacetime that accommodates this ladder symmetry for scalar perturbation. Furthermore, we extend our calculations beyond spherical symmetry to find the class of stationary Konoplya-Rezzola-Zhidenko black holes, which also possess a similar ladder structure.\] # Shekar, Taylor ## Replica analysis of entanglement properties \[Links: [arXiv](https://arxiv.org/abs/2410.07312), [PDF](https://arxiv.org/pdf/2410.07312)\] \[Abstract: In this paper we develop a systematic analysis of the properties of [[0301 Entanglement entropy|entanglement entropy]] in curved backgrounds using the replica approach. We explore the analytic $(q-1)$ expansion of [[0293 Renyi entropy|Rényi entropy]] $S_q$ and its variations; our setup applies to generic variations, from symmetry transformations to variations of the background metric or entangling region. Our methodology elegantly reproduces and generalises results from the literature on entanglement entropy in different dimensions, backgrounds, and states. We use our analytic expansions to explore the behaviour of entanglement entropy in static black hole backgrounds under specific scaling transformations, and we explain why this behaviour is key to determining whether there are islands of entanglement.\] # Shi, Zhang ## A universal approach to Renyi entropy of multiple disjoint intervals \[Links: [arXiv](https://arxiv.org/abs/2411.18353), [PDF](https://arxiv.org/pdf/2411.18353)\] \[Abstract: We develop a general theory for computing the [[0293 Renyi entropy|Renyi entropy]] with general multiple disjoint intervals from the swapping operations. Our theory is proposed based on the fact that we have observed the resemblance between the replica trick in quantum field theory and the swapping operation. Consequently, the Renyi entropy can be obtained by evaluating the expectation values of the swapping operator. As an application, we study the Renyi entropy of a one-dimensional transverse-field Ising model for two, three and four disjoint intervals. As the system is at the critical point, our computations of the Renyi entropy are consistent with the analytical results from the conformal field theory. Moreover, our methods can go beyond the critical regime of the Ising model.\] # Sivakumar ## Real Time Correlations and Complexified Horizons \[Links: [arXiv](https://arxiv.org/abs/2410.18188), [PDF](https://arxiv.org/pdf/2410.18188)\] \[Abstract: We construct black hole saddles dual to real-time/[[0042 Schwinger-Keldysh techniques|Schwinger-Keldysh]] (SK) path integrals with arbitrary splits of the thermal density matrix generalizing the holographic SK prescription in [[2018#Glorioso, Crossley, Liu]]. Using a scalar probe on the AdS Schwarzschild black brane as an example, we demonstrate how [[0521 KMS condition|KMS]] properties of the boundary correlators naturally derive from these geometries. As deforming the boundary time contour is equivalent to the action of half sided modular transformation, these saddles can be used to compute higher point modular transformed correlators using a well controlled bulk perturbation theory. An interesting relation between these saddles and the more familiar eternal geometries, and the respective generators of time translation on them is described. Inspired from recent discussions on algebras of observables in gravity, we motivate that classical ensembles of such geometries with different amount of modular transformations should be promoted to genuine configurations of the bulk geometry. In particular, this is argued to imply the existence of additional classical moduli in the boundary open EFT dual to the exterior dynamics, and via [[0228 Fluid-gravity correspondence|fluid gravity correspondence]], in the fluctuating hydrodynamics of the boundary. Finally, a Lorentzian version of the [[0335 Complex metrics|Kontsevich-Segal conditions]] is verified for all these geometries.\] # Sonner, Strittmatter ## Quantum Chaos in Liouville CFT \[Links: [arXiv](https://arxiv.org/abs/2407.11124), [PDF](https://arxiv.org/pdf/2407.11124)\] \[Abstract: Fast scrambling is a distinctive feature of quantum gravity, which by means of holography is closely tied to the behaviour of large-$c$ conformal field theories. We study this phenomenon in the context of semiclassical [[0562 Liouville theory|Liouville theory]], providing both insights into the mechanism of scrambling in CFTs and into the structure of Liouville theory, finding that it exhibits a maximal [[0466 Lyapunov exponent|Lyapunov exponent]] despite not featuring the identity in its spectrum. However, as we show, the states contributing to the relevant correlation function can be thought of as dressed scramblons. At a technical level we we first use the path integral picture in order to derive the Euclidean four-point function in an explicit compact form. Next, we demonstrate its equivalence to a conformal block expansion, revealing an explicit but non-local map between path integral saddles and conformal blocks. By analytically continuing both expressions to Lorentzian times, we obtain two equivalent formulations of the [[0482 Out-of-time-order correlator|OTOC]], which we use to study the onset of chaos in Liouville theory. We take advantage of the compact form in order to extract a Lyapunov exponent and a scrambling time. From the conformal block expansion formulation of the OTOC we learn that scrambling shifts the dominance of conformal blocks from heavy primaries at early times to the lightest primary at late times. Finally, we discuss our results in the context of holography.\] # Tang ## Entanglement entropy in type II$_1$ von Neumann algebra: examples in Double-Scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2404.02449), [PDF](https://arxiv.org/pdf/2404.02449)\] \[Abstract: An intriguing feature of type II$_1$ [[0415 Von Neumann algebra|von Neumann algebra]] is that the entropy of the mixed states is negative. Although the type classification of von Neumann algebra and its consequence in holography have been extensively explored recently, there has not been an explicit calculation of entropy in some physically interesting models with type II$_1$ algebra. In this paper, we study the entanglement entropy $S_n$ of the fixed length state $\{|n\rangle\}$ in [[0503 Double-scaled SYK|Double-Scaled Sachdev-Ye-Kitaev]] model, which has been recently shown to exhibit type II$_1$ von Neumann algebra. These states furnish an orthogonal basis for 0-particle chord Hilbert space. We systematically study $S_n$ and its Rényi generalizations $S_n^{(m)}$ in various limit of DSSYK model, ranging $q\in[0,1]$. We obtain exotic analytical expressions for the scaling behavior of $S_n^{(m)}$ at large $n$ for [[0579 Random matrix theory|random matrix theory]] limit ($q=0$) and SYK$_2$ limit ($q=1$), for the former we observe highly non-flat entanglement spectrum. We then dive into triple scaling limits where the fixed chord number states become the geodesic wormholes with definite length connecting left/right AdS$_2$ boundary in [[0050 JT gravity|Jackiw-Teitelboim gravity]]. In semi-classical regime, we match the boundary calculation of [[0301 Entanglement entropy|entanglement entropy]] with the dilaton value at the center of geodesic, as a nontrivial check of the [[0007 RT surface|Ryu-Takayanagi formula]].\] # Tao ## The Aharony-Bergman-Jafferis-Maldacena theory on a circle \[Links: [arXiv](https://arxiv.org/abs/2406.02680), [PDF](https://arxiv.org/pdf/2406.02680)\] \[Abstract: In this letter, we bootstrapped the 4-point correlators on the 1D celestial circle using 3D symmetries in the [[0137 ABJM|Aharony-Bergman-Jafferis-Maldacena]] theory as constraints. We find that the dual inversion property is strong enough to replace the crossing symmetry condition when bootstrapping. We also give some results about the [[0031 Conformal block|conformal block expansion]] coefficients which contain the spectrum and the leading multi-OPE of this [[0010 Celestial holography|celestial CFT]]. Finally, we find a non-local 2-particle operator from the multi-OPE at the leading OPE. Although we studied a specific theory, the methods used are valid for general cases.\] # Tian, Lai ## Aspects of three-dimensional C-metric \[Links: [arXiv](https://arxiv.org/abs/2401.04457), [PDF](https://arxiv.org/pdf/2401.04457.pdf)\] \[Abstract: In this work, we present an extensive analysis of the thermodynamics and holographic properties of three-dimensional [[0336 C-metric|C-metrics]] in the FG gauge, where we find that the free energy is equal to the Euclidean on-shell action with a generic conformal factor. For the black hole solutions we find that Smarr relation and the first law of [[0127 Black hole thermodynamics|thermodynamics]] can be formulated when the contributions of the boundary entropy are considered . We also compute [[0007 RT surface|holographic entanglement entropy]] following the [[0181 AdS-BCFT|AdS/BCFT]] formalism. By comparing the free energies of different bulk solutions with a fixed flat torus boundary geometry, we find that a specific type of accelerating black hole is dominant in the high temperature regime.\] # Tian, Lai, Omidi ## Spacetime Bananas with EOW Branes and Spins \[Links: [arXiv](https://arxiv.org/abs/2410.18729), [PDF](https://arxiv.org/pdf/2410.18729)\] \[Abstract: In this work, we study and generalize the spacetime banana proposal for computing correlation functions of [[0645 Huge operators|huge operators]]. First, we introduce time-like and space-like EOW branes into the proposal and demonstrate that: 1) a holographic dual of the one-point function in a [[0548 Boundary CFT|BCFT]] can be obtained and its modified on-shell action reproduces the expected BCFT result; and 2) the [[0138 Variational principle|GHY term]] on the stretched horizon can be replaced by the action of an EOW brane which wraps the horizon. Next, we discuss the two (one)-point function of huge spinning operators described by a rotating black hole in the bulk. We show that simply adding a GHY term on the stretched horizon is insufficient to reproduce the CFT results; instead, the appropriate modified action should be the micro-canonical action. Finally. we revisit the existing approaches for computing correlation functions using the gravity on-shell action of conical geometry or Banados geometries. Surprisingly, we find that the on-shells actions of the Banados geometries or the gravity solutions in the [[0011 Fefferman-Graham expansion|Fefferman-Graham]] gauge yield unexpected incorrect results.\] # Tropper ## Supersymmetric Soft Theorems \[Links: [arXiv](https://arxiv.org/abs/2404.03717), [PDF](https://arxiv.org/pdf/2404.03717)\] \[Abstract: We show that in supersymmetric theories, knowing the [[0009 Soft theorems|soft theorem]] for a single particle in a supermultiplet allows one to immediately determine soft theorems for the remainder of the supermultiplet. While soft theorems in supersymmetric theories have a rich history, they have only been chronicled for specific examples due to the fact that they are usually derived with technical Feynman diagrammatics or amplitudes methods. By contrast, we show that one can compute soft theorems non-perturbatively for entire supermultiplets in one line of algebra. This formalism is directly applicable to the most general supersymmetric theory: one with an arbitrary matter content, number of supercharges, and spacetime dimension. We give many explicit examples illustrating the scope and dexterity of this framework.\] # Usatyuk, Wang, Zhao ## Closed universes in two dimensional gravity \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: We study closed universes in simple models of two dimensional gravity, such as [[0050 JT gravity|Jackiw-Teiteilboim]] (JT) gravity coupled to matter, and a toy topological model that captures the key features of the former. We find there is a stark contrast, as well as some connections, between the perturbative and non-perturbative aspects of the theory. We find rich semi-classical physics. However, when non-perturbative effects are included there is a unique closed universe state in each theory. We discuss possible meanings and interpretations of this observation.\] # Usatyuk, Zhao ## Closed universes, factorization, and ensemble averaging \[Links: [arXiv](https://arxiv.org/abs/2403.13047), [PDF](https://arxiv.org/pdf/2403.13047)\] \[Abstract: We study closed universes in holographic theories of quantum gravity. We argue that within any fixed theory, [[0249 Factorisation problem|factorization]] implies there is one unique closed universe state. The wave function of any state that can be prepared by the path integral is proportional to the [[0162 No-boundary wavefunction|Hartle-Hawking wave function]]. This unique wave function depends on the properties of the underlying holographic theory such as the energy spectrum. We show these properties explicitly in [[0050 JT gravity|JT gravity]], which is known to be dual to an [[0154 Ensemble averaging|ensemble]] of random Hamiltonians. For each member of the ensemble, the corresponding wave function is erratic as a result of the spectrum being chaotic. After ensemble averaging, we obtain smooth semi-classical wave functions as well as different closed universe states.\] # van der Heijden, Verlinde ## An Operator Algebraic Approach To Black Hole Information \[Links: [arXiv](https://arxiv.org/abs/2408.00071), [PDF](https://arxiv.org/pdf/2408.00071)\] \[Abstract: We present an operator algebraic perspective on the black hole information problem. For a black hole after Page time that is entangled with the early radiation we formulate a version of the [[0131 Information paradox|information puzzle]] that is well-posed in the $G\to 0$ limit. We then give a description of the information recovery protocol in terms of [[0415 Von Neumann algebra|von Neumann algebras]] using elements of the Jones index theory of type II$_1$ subfactors. The subsequent evaporation and recovery steps are represented by Jones's basic construction, and an operation called the canonical shift. A central element in our description is the Jones projection, which leads to an entanglement swap and implements an operator algebraic version of a quantum teleportation protocol. These aspects are further elaborated on in a microscopic model based on type I algebras. Finally, we argue that in the emergent type III algebra the canonical shift may be interpreted as a spacetime translation and, hence, that at the microscopic level "translation = teleportation".\] # Vardhan, Moudgalya ## Entanglement dynamics from universal low-lying modes \[Links: [arXiv](https://arxiv.org/abs/2407.16763), [PDF](https://arxiv.org/pdf/2407.16763)\] \[Abstract: Information-theoretic quantities such as [[0293 Renyi entropy|Renyi entropies]] show a remarkable universality in their late-time behaviour across a variety of [[0008 Quantum chaos|chaotic quantum]] many-body systems. Understanding how such common features emerge from very different microscopic dynamics remains an important challenge. In this work, we address this question in a class of Brownian models with random time-dependent Hamiltonians and a variety of different microscopic couplings. In any such model, the Lorentzian time-evolution of the $n$-th Renyi entropy can be mapped to evolution by a Euclidean Hamiltonian on $2n$ copies of the system. We provide evidence that in systems with no symmetries, the low-energy excitations of the Euclidean Hamiltonian are universally given by a gapped quasiparticle-like band. The eigenstates in this band are plane waves of locally dressed domain walls between ferromagnetic ground states associated with two permutations in the symmetric group $S_n$. These excitations give rise to the [[0433 Membrane theory of entanglement dynamics|membrane picture]] of [[0522 Entanglement dynamics|entanglement growth]], with the membrane tension determined by their dispersion relation. We establish this structure in a variety of cases using analytical perturbative methods and numerical variational techniques, and extract the associated dispersion relations and membrane tensions for the second and third Renyi entropies. For the third Renyi entropy, we argue that phase transitions in the membrane tension as a function of velocity are needed to ensure that physical constraints on the membrane tension are satisfied. Overall, this structure provides an understanding of entanglement dynamics in terms of a universal set of gapped low-lying modes, which may also apply to systems with time-independent Hamiltonians.\] # Verlinde ## Double-scaled SYK, Chords and de Sitter Gravity \[Links: [arXiv](https://arxiv.org/abs/2402.00635), [PDF](https://arxiv.org/pdf/2402.00635.pdf)\] \[Abstract: We study the partition function of 3D de Sitter gravity defined as the trace over the Hilbert space obtained by quantizing the phase space of non-rotating Schwarzschild-de Sitter spacetime. Motivated by the correspondence with [[0503 Double-scaled SYK|double scaled SYK]], we identify the Hamiltonian with the gravitational Wilson-line that measures the conical deficit angle. We express the Hamiltonian in terms of canonical variables and find that it leads to the exact same chord rules and energy spectrum as the double scaled SYK model. We use the obtained match to compute the partition function and scalar two-point function in 3D de Sitter gravity.\] # Verlinde, Zhang ## SYK Correlators from 2D Liouville-de Sitter Gravity \[Links: [arXiv](https://arxiv.org/abs/2402.02584), [PDF](https://arxiv.org/pdf/2402.02584.pdf)\] \[Abstract: We introduce and study a candidate gravity dual to the [[0503 Double-scaled SYK|double scaled SYK]] model in the form of an exactly soluble 2D de Sitter gravity model consisting of two spacelike [[0562 Liouville theory|Liouville CFTs]] with complex central charge adding up to $c_+ + c_- = 26$. In [1] it was shown that the two-point function of physical operators in a doubled SYK model matches in the semi-classical limit with the Green's function of a massive scalar field in 3D de Sitter space. As further evidence of the duality, we adapt a result from Zamolodchikov to compute the boundary two-point function of the 2D Liouville-de Sitter gravity model on a disk and find that it reproduces the exact DSSYK two-point function to all orders in $\lambda=p^2/N$. We describe how the 2D Liouville-de Sitter gravity model arises from quantizing 3D de Sitter gravity.\] # Visser, Yan ## Properties of Dynamical Black Hole Entropy \[Links: [arXiv](https://arxiv.org/abs/2403.07140), [PDF](https://arxiv.org/pdf/2403.07140)\] \[Abstract: We study the first law for non-stationary perturbations of a stationary black hole whose event horizon is a Killing horizon, that relates the first-order change in the mass and angular momentum to the change in the entropy of an arbitrary horizon cross-section. Recently, Hollands, Wald and Zhang [1] have shown that the [[0005 Black hole second law|dynamical black hole entropy]] that satisfies this first law, for general relativity, is $S_{\text{dyn}}=(1-v\partial_v)S_{\text{BH}}$, where $v$ is the affine parameter of the null horizon generators and $S_{\text{BH}}$ is the Bekenstein-Hawking entropy, and for general diffeomorphism covariant theories of gravity $S_{\text{dyn}}=(1-v\partial_v)S_{\text{Wall}}$, where $S_{\text{Wall}}$ is the Wall entropy. They obtained the first law by applying the Noether charge method to non-stationary perturbations and arbitrary cross-sections. In this formalism, the dynamical black hole entropy is defined as an ''improved'' Noether charge, which is unambiguous to first order in the perturbation. In the present article we provide a pedagogical derivation of the physical process version of the non-stationary first law for general relativity by integrating the linearised Raychaudhuri equation between two arbitrary horizon cross-sections. Moreover, we generalise the derivation of the first law in [1] to non-minimally coupled matter fields that are smooth on the horizon, using boost weight arguments rather than Killing field arguments, and we relax some of the gauge conditions on the perturbations by allowing for non-zero variations of the horizon Killing field and surface gravity. Finally, for $f(\text{Riemann})$ theories of gravity we show explicitly using Gaussian null coordinates that the improved Noether charge is $S_{\text{dyn}}=(1-v\partial_v)S_{\text{Wall}}$, which is a non-trivial check of [1].\] # Wall, Yan ## Linearised Second Law for Higher Curvature Gravity and Non-Minimally Coupled Vector Fields \[Links: [arXiv](https://arxiv.org/abs/2402.05411), [PDF](https://arxiv.org/pdf/2402.05411.pdf)\] \[Abstract: Expanding the work of [[2015#Wall (Essay)]], we show that black holes obey a [[0005 Black hole second law|second law]] for linear perturbations to bifurcate Killing horizons, in any covariant [[0006 Higher-derivative gravity|higher curvature gravity]] coupled to scalar and vector fields. The vector fields do not need to be gauged, and (like the scalars) can have arbitrary non-minimal couplings to the metric. The increasing entropy has a natural expression in covariant phase space language, which makes it manifestly invariant under [[0018 JKM ambiguity|JKM ambiguities]]. An explicit entropy formula is given for f(Riemann) gravity coupled to vectors, where at most one derivative acts on each vector. Besides the previously known curvature terms, there are three extra terms involving differentiating the Lagrangian by the symmetric vector derivative (which therefore vanish for gauge fields).\] ## Zero-boost terms using the [[0019 Covariant phase space|CPS]] formalism - varying the Lagrangian - $\delta \boldsymbol{L}=\frac{1}{2} \boldsymbol{E}_{a b} \delta g^{a b}+\mathcal{E}^a \delta V_a+\mathrm{d} \boldsymbol{\Theta}[g, V, \delta g, \delta V]$ - specialise to the variation along a vector field $\zeta$ - $£_\zeta \boldsymbol{L}=\frac{1}{2} \boldsymbol{E}_{a b} £_\zeta g^{a b}+\mathcal{E}^a £_\zeta V_a+\mathrm{d} \boldsymbol{\Theta}_\zeta$ - define off-shell Noether current - $\boldsymbol{J}_\zeta=\boldsymbol{\Theta}_\zeta-\iota_\zeta \boldsymbol{L}$ - check conservation of current - by taking $\mathrm{d}$ of $£_\zeta \boldsymbol{L}$ - and using the Cartan-Killing equation ($£_\zeta=\iota_\zeta \mathrm{d}+\mathrm{d} \iota_\zeta$) - get: $\mathrm{d} \boldsymbol{J}_\zeta=\left(E_{a b} \nabla^a \zeta^b-\mathcal{E}^a\left(\zeta^b \nabla_b V_a+V_b \nabla_a \zeta^b\right)\right) \boldsymbol{\epsilon}$ - take Hodge dual of $\mathrm{d} \boldsymbol{J}_\zeta$ - and rearrange - $\nabla^a\left(\left(\star J_\zeta\right)_a+E_{a b} \zeta^b-\mathcal{E}_a V_b \zeta^b\right)=\zeta^b\left(\nabla^a E_{a b}-\mathcal{E}^a F_{a b}-V_b \nabla_a \mathcal{E}^a\right)$ - here $F_{a b}=\nabla_a V_b-\nabla_b V_a$ - get generalised Bianchi identity - by integrating and choosing arbitrary $\zeta$ - get $\nabla^a E_{a b}=\mathcal{E}^a F_{a b}+V_b \nabla_a \mathcal{E}^a$ - using generalised Bianchi to get the other side to zero - write $\mathrm{d}\left(\boldsymbol{J}_\zeta+\boldsymbol{C}_\zeta\right)=0$ - where $\left(\star C_\zeta\right)_a=E_{a b} \zeta^b-\mathcal{E}_a V_b \zeta^b$ - define off-shell Noether charge - $\boldsymbol{J}_\zeta+\boldsymbol{C}_\zeta=\mathrm{d} \boldsymbol{Q}_\zeta$ - vary a constraint, $\boldsymbol{C}_\zeta$ - using earlier definition $\boldsymbol{J}_\zeta=\boldsymbol{\Theta}_\zeta-\iota_\zeta \boldsymbol{L}$ - defining $\boldsymbol{\omega}\left[\delta g, \delta V ; £_\zeta g, £_\zeta V\right]=\delta \boldsymbol{\Theta}_\zeta\left[£_\zeta g, £_\zeta V\right]-£_\zeta \boldsymbol{\Theta}[\delta g, \delta V]$ - $\delta \boldsymbol{C}_\zeta=\mathrm{d}\left(\delta \boldsymbol{Q}_\zeta-\iota_\zeta \boldsymbol{\Theta}[\delta g, \delta V]\right)-\boldsymbol{\omega}\left[\delta g, \delta V ; £_\zeta g, £_\zeta V\right]+\iota_\zeta\left(\frac{1}{2} \boldsymbol{E}_{a b} \delta g^{a b}+\mathcal{E}^a \delta V_a\right)$ - now specialise to $\zeta$ to the boost generator $\xi$ - $\boldsymbol{\omega}\left[\delta g, \delta V ; £_\xi g, £_\xi V\right]=0$ on the stationary background: as $£_\xi g= £_\xi V=0$ - $\iota_\xi(\cdots)=0$ on the horizon: $\xi$ is tangent to the horizon - integrate over the horizon and integrate by parts - $\int_{\frac{1}{2} \mathcal{H}} \delta \boldsymbol{C}_{\xi}=\left(\int_{\mathcal{C}(+\infty)}-\int_{\mathcal{C}(0)}\right)\left(\delta \boldsymbol{Q}_{\xi}-\iota_{\xi} \boldsymbol{\Theta}[\delta g, \delta V]\right)$ - n.b. 2nd term now vanishes as $\iota_\xi (\cdots)=0$ as before - assume compact support with at delta function at $v=0$ - write down surviving terms from both sides - get $\int_{\mathcal{C}(0)} \mathrm{d}^{D-2} x \sqrt{h} \sum_I A_{(0)}^I \delta B_{(0)}^I=\int_{\mathcal{C}(0)} \delta \boldsymbol{Q}_{\zeta}=\left.\delta S_{\mathrm{IW}}\right|_{v=0}$ - i.e. zero-boost terms sum to an exact differential form - related $v=0$ and a finite $v$ using a clever argument - draw conclusion - zero-boost terms sum to an exact differential # Wang, He, Li ## Shear transport in far-from-equilibrium isotropization of supersymmetric Yang-Mills plasma \[Links: [arXiv](https://arxiv.org/abs/2411.10706), [PDF](https://arxiv.org/pdf/2411.10706)\] \[Abstract: We holographically study the far-from-equilibrium isotropization dynamics of the strongly coupled [[0155 N=4 SYM|N=4 SYM]]. The dual gravitational background is driven to be out of equilibrium and anisotropic by a time-dependent change in boundary conditions. At late times, the system relaxes and asymptotically approaches a static configuration. The large initial energy densities accelerate the isotropization significantly compared to the initial geometry corresponding to the supersymmetric Yang-Mills vacuum. We analyze shear transport during isotropization by directly computing the time-dependent stress tensor, which is now a nonlinear function of the shear rate. The shear viscosity far from equilibrium displays much richer dynamics than its near-equilibrium counterpart. Moreover, we uncover that the equilibrium [[0430 Holographic shear viscosity|viscosity-to-entropy ratio]] at late times depends on the details of the quench function and the initial data, which could be due to a resummation of the hydrodynamic description. In particular, this ratio can be parametrically smaller than the Kovtun-Son-Starinets bound calculated from linear response theory.\] # Wang, Wang ## Higher-spin localized shocks \[Links: [arXiv](https://arxiv.org/abs/2409.19785), [PDF](https://arxiv.org/pdf/2409.19785)\] \[Abstract: In the context of AdS/CFT, gravitational shockwaves serve as a geometric manifestation of boundary quantum chaos. We study this connection in general diffeomorphism-invariant theories involving an arbitrary number of bosonic fields. Specifically, we demonstrate that theories containing spin-2 or higher-spin fields generally admit classical localized shockwave solutions on black hole backgrounds, whereas spin-0 and spin-1 theories do not. As in the gravitational case, these higher-spin shockwaves provide a means to compute the out-of-time-order correlator. Both the Lyapunov exponent and the butterfly velocity are found to universally agree with predictions from pole skipping. In particular, higher-spin fields lead to a Lyapunov exponent that violates the chaos bound and a butterfly velocity that may exceed the speed of light.\] # Wang, Yao ## Quantum Energy Teleportation versus Information Teleportation \[Links: [arXiv](https://arxiv.org/abs/2405.13886), [PDF](https://arxiv.org/pdf/2405.13886)\] \[Abstract: [[0628 Quantum energy teleportation|Quantum energy teleportation]] (QET) is the phenomenon in which locally inaccessible energy is activated as extractable work through collaborative local operations and classical communication (LOCC) with an entangled partner. It closely resembles the more well-known quantum information teleportation (QIT) where quantum information can be sent through an entangled pair with LOCC. It is tempting to ask how QET is related to QIT. Here we report a first study of this connection. Despite the apparent similarity, we show that these two phenomena are not only distinct but moreover are mutually exclusive to each other. We show a perturbative trade-off relation between their performance in a thermal entangled chaotic many-body system, in which both QET and QIT are simultaneously implemented through a traversable wormhole in an emergent spacetime. To better understand their competition, we study the finite-dimensional counterpart of two entangled qudits and prove a universal non-perturbative trade-off bound. It shows that for any teleportation scheme, the overall performance of QET and QIT together is constrained by the amount of the entanglement resource. We discuss some explanations of our results.\] # Weber, Tall, Haneder, Urbina, Richter ## Unorientable topological gravity and orthogonal random matrix universality \[Links: [arXiv](https://arxiv.org/abs/2405.17177), [PDF](https://arxiv.org/pdf/2405.17177)\] \[Abstract: The duality of [[0050 JT gravity|Jackiw-Teitelboim]] (JT) gravity and a double scaled [[0197 Matrix model|matrix integral]] has led to studies of the canonical [[0062 Spectral form factor|spectral form factor]] (SFF) in the so called $\tau$-scaled limit of large times, $t \to \infty$, and fixed temperature in order to demonstrate agreement with universal [[0579 Random matrix theory|random matrix theory]] (RMT). Though this has been established for the unitary case, extensions to other symmetry classes requires the inclusion of [[0624 Unorientable manifold|unorientable manifolds]] in the sum over geometries, necessary to address time reversal invariance, and regularization of the corresponding prime geometrical objects, the [[0617 Weil-Petersson volume|Weil-Petersson]] (WP) volumes. We report here how universal signatures of [[0008 Quantum chaos|quantum chaos]], witnessed by the fidelity to the Gaussian orthogonal ensemble, emerge for the low-energy limit of unorientable JT gravity, i.e. the Airy model/topological gravity. To this end, we implement the loop equations for the corresponding dual (double-scaled) matrix model and find the generic form of the Airy WP volumes, supported by calculations using unorientable Kontsevich graphs. In an apparent violation of the gravity/chaos duality, the $\tau$-scaled SFF on the gravity side acquires both logarithmic and power law contributions in $t$, not manifestly present on the RMT side. We show the expressions can be made to agree by means of [[0036 Conformal bootstrap|bootstrapping]]-like relations hidden in the asymptotic expansions of generalized hypergeometric functions. Thus, we are able to establish strong evidence of the quantum chaotic nature of unorientable topological gravity.\] # Wei (F-S) ## Soft theorems based on differential operators from gravity to Yang-Mills and BAS \[Links: [arXiv](https://arxiv.org/abs/2407.16429), [PDF](https://arxiv.org/pdf/2407.16429)\] \[Abstract: This note study the [[0009 Soft theorems|soft behavior]] of Yang-Mills (YM) and bi-adjoint scalar (BAS) amplitudes at tree level, by using transmutation operators proposed by Cheung, Shen and Wen. By acting such transmutation operators to gravity amplitudes in the soft limit, we reproduce universal soft factors of YM amplitudes at the leading and sub-leading orders, and explain that the analogous universal soft behavior does not exist at the sub-sub-leading order. Subsequently, by acting the same operators on YM amplitudes, we obtain the universal soft factor of BAS amplitudes at the leading order. Furthermore, we find that a "weaker" version of universal soft behavior of BAS amplitudes holds at the sub-leading order, if we exclude the special 4-point case.\] # Wei (Z) ## Holographic Dual of Crosscap Conformal Field Theory \[Links: [arXiv](https://arxiv.org/abs/2405.03755), [PDF](https://arxiv.org/pdf/2405.03755)\] \[Abstract: We propose a holographic dual for [[0003 2D CFT|2D CFT]] defined on closed [[0620 Non-orientable CFT|non-orientable]] manifolds, such as the real projective plane $\mathbb{RP}^2$ and the Klein bottle $\mathbb{K}^2$. Such CFT can be constructed by introducing antipodally identified cuttings, i.e. crosscaps, to a sphere and hence called crosscap CFT (XCFT). The gravity dual is AdS$_3$ spacetime with dS$_2$ end-of-the-world branes. In particular, the Lorentzian spacetime with a global dS$_2$ brane is dual to the unitary time evolution of a crosscap state in CFT, post-selected on the CFT ground state. We compute the holographic $\mathbb{RP}^2$ partition function (or the $p$-function), one-point function, and $\mathbb{K}^2$ partition function, and see that they successfully reproduce the XCFT results. We also show a holographic $p$-theorem as an application.\] # Wen, Xu, Zhong ## Partial entanglement entropy threads in island phase \[Links: [arXiv](https://arxiv.org/abs/2408.13535), [PDF](https://arxiv.org/pdf/2408.13535)\] \[Abstract: In the context of [[0001 AdS-CFT|AdS/CFT]], it was recently proposed that the boundary [[0292 Partial entanglement entropy|partial entanglement entropy]] structure can be represented by the so-called partial entanglement entropy (PEE) threads in the AdS bulk, which are bulk geodesics with the density determined by the boundary PEE structure. In Poincaré AdS space, it was shown that the PEE threads cover the AdS space uniformly, such that the number of intersections between any bulk surface and the bulk PEE threads is always given by the area of the surface divided by 4G. In this paper, we investigate the configurations of PEE threads when the boundary state is in island phase. The island phase was studied in the context of the holographic Weyl transformed CFT$_2$, which has been shown to capture all the main features of [[0181 AdS-BCFT|AdS/BCFT]]. Compared with AdS$_3$/CFT$_2$, in [[0213 Islands|island]] phase instead of modifying the distribution of the bulk PEE threads, we should replace the boundary points with the corresponding cutoff spheres. Then the two-point and four-point functions of twist operators can be reproduced by identifying the bulk homologous surfaces anchored on the corresponding cutoff spheres that has the minimal number of intersections with the bulk PEE threads. This gives us a better understanding about the PEE structure in island phase and reproduces the island formula for [[0301 Entanglement entropy|entanglement entropy]] by allowing homologous surfaces to anchor on any cutoff surfaces. Furthermore, it gives a demonstration for the two basic proposals and a better understanding for the entanglement contribution that makes the foundation to compute the balanced partial entanglement entropy (BPE) which reproduces the [[0319 Entanglement wedge cross-section|entanglement wedge cross-section]] in island phase.\] # Witten (Notes) ## Introduction to Black Hole Thermodynamics \[Links: [arXiv](https://arxiv.org/abs/2412.16795), [PDF](https://arxiv.org/pdf/2412.16795)\] \[Abstract: These notes aim to provide an introduction to the basics of [[0127 Black hole thermodynamics|black hole thermodynamics]]. After explaining Bekenstein's original proposal that black holes have [[0004 Black hole entropy|entropy]], we discuss Hawking's discovery of [[0304 Hawking radiation|black hole radiation]], its analog for Rindler space in the Unruh effect, the Euclidean approach to black hole thermodynamics, some basics about [[0301 Entanglement entropy|von Neumann entropy]] and its applications, the [[0007 RT surface|Ryu-Takayanagi formula]], and the nature of a white hole.\] # Xu ## Von Neumann Algebras in Double-Scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2403.09021), [PDF](https://arxiv.org/pdf/2403.09021.pdf)\] \[Abstract: It's been argued that a finite effective temperature emerges and characterizes the thermal property of [[0503 Double-scaled SYK|double-scaled SYK]] model in the infinite temperature limit. On the other hand, in static patch of de Sitter, the maximally entangled state exhibits [[0521 KMS condition|KMS condition]] of infinite temperature, suggesting the Type II$_1$ nature of the algebra formed by operators that are gravitationally dressed to the static patch observer. In the current work we study the double-scaled algebra generated by chord operators in double-scaled SYK model. We show that the algebra exhibits a behavior reminiscent of both perspectives. In particular, we prove that it's a Type II$_1$ factor, and the empty state with no chords satisfies the tracial property, thus aligning with the expectation in previous work. Furthermore, we show it's a cyclic separating state by exploring the modular structure of the algebra. We then study various limits of the theory and explore corresponding relations to [[0050 JT gravity|JT gravity]], theory of [[0051 Baby universes|baby universe]], and Brownian double-scaled SYK. We also present a full solution to the energy spectrum of 0- and 1- particle irreducible representations.\] # Yan ## Gravitational focusing and horizon entropy for higher-spin fields \[Links: [arXiv](https://arxiv.org/abs/2412.07107), [PDF](https://arxiv.org/pdf/2412.07107)\] \[Abstract: Previously, the [[0408 Raychaudhuri equation|Raychaudhuri equation]] and the focusing theorem in General Relativity were generalised to diffeomorphism-invariant theories of gravity coupled to scalar and vector fields on linearly perturbed Killing horizons. The Wall entropy can be extracted from the generalised focusing equation and it satisfies the first and the [[0005 Black hole second law|second laws]] of thermodynamics. In this paper, we further extend the discussion of gravitational focusing on the horizon to include arbitrary bosonic fields with spin $s \geq 2$. These higher-spin fields introduce indefinite terms into the generalised focusing equation, obstructing the proof of the focusing theorem and the existence of an increasing horizon entropy. To resolve this issue, we propose a higher-spin focusing condition that eliminates these indefinite terms, thereby restoring the focusing theorem and the associated thermodynamic laws. We speculate that the focusing condition could be a necessary condition for the physical consistency of higher-spin theories.\] # Yuan, Ge, Kim ## Pole-skipping in two-dimensional de Sitter spacetime and double-scaled SYK model \[Links: [arXiv](https://arxiv.org/abs/2408.12330), [PDF](https://arxiv.org/pdf/2408.12330)\] \[Abstract: We develop the [[0179 Pole skipping|pole-skipping]] structure in de Sitter (dS) spacetime and find that their leading frequencies satisfy the relation $\omega_{dS}=i2\pi T_{dS}(1-s)$ with $T_{dS}$ denotes $T_{dS}=1/2\pi L$ and $s$ spin. In the two-dimensional dS spacetime, the pole-skipping points near the cosmic horizon $r=L$ for the scalar field of spin-0 and the fermionic field of spin-$\frac{1}{2}$ correspond one-to-one with those in the infinite temperature limit of [[0503 Double-scaled SYK|double-scaled Sachdev-Ye-Kitaev model]] (DSSYK$_\infty$). The retarded Green's functions of these two systems also have similar forms at the pole-skipping positions. This provides a numerical correspondence between the static patch of dS$_2$ spacetime and the DSSYK$_\infty$ model.\] # Zhou ## Constructing tree amplitudes of scalar EFT from double soft theorem \[Links: [arXiv](https://arxiv.org/abs/2406.03784), [PDF](https://arxiv.org/pdf/2406.03784)\] \[Abstract: The well known Adler zero can fully determine tree amplitudes of non-linear sigma model (NLSM), but fails to fix tree pion amplitudes with higher-derivative interactions. To fill this gap, in this paper we propose a new method based on exploiting the double soft theorem for scalars, which can be applied to a wider range. A remarkable feature of this method is, we only assume the universality of soft behavior at the beginning, and determine the explicit form of [[0504 Double soft limits|double soft]] factor in the process of constructing amplitudes. To test the applicability, we use this method to construct tree NLSM amplitudes and tree amplitudes those pions in NLSM couple to bi-adjoint scalars. We also construct the simplest pion amplitudes which receive leading higher-derivative correction, with arbitrary number of external legs. All resulted amplitudes are formulated as universal expansions to appropriate basis.\] # Zolfi ## Firewalls from wormholes in higher genus \[Links: [arXiv](https://arxiv.org/abs/2401.04476), [PDF](https://arxiv.org/pdf/2401.04476.pdf)\] \[Abstract: An old black hole can tunnel into a white hole/ [[0195 Firewall|firewall]] by emitting large [[0051 Baby universes|baby universes]]. This phenomenon was investigated in [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] for genus one. In this paper, the focus is on higher genus corresponding to emitting more than one baby universe ($n > 1$). The probability of encountering a firewall or tunneling into a white hole after emitting $n$ baby universes is proportional to $e^{-2nS(E)}e^{4 \pi \sqrt{E}(n-1)}E^{2n^2-n-9/2}t^{4n^2-2n-5}$, where $t$ is the age of the black hole, and $S$ and $E$ represent the entropy and energy of the black hole, respectively.\]