# Abajian, Aprile, Myers, Vieira (Jun) ## Holography and Correlation Functions of Huge Operators: Spacetime Bananas \[Links: [arXiv](https://arxiv.org/abs/2306.15105), [PDF](https://arxiv.org/pdf/2306.15105)\] \[Abstract: We initiate the study of holographic correlators for [[0645 Huge operators|operators whose dimension scales with the central charge of the CFT]]. Differently from light correlators or probes, the insertion of any such maximally heavy operator changes the AdS metric, so that the correlator itself is dual to a backreacted geometry with marked points at the Poincaré boundary. We illustrate this new physics for two-point functions. Whereas the bulk description of light or probe operators involves Witten diagrams or extremal surfaces in an AdS background, the maximally heavy two-point functions are described by nontrivial new geometries which we refer to as "spacetime bananas". As a universal example, we discuss the two-point function of maximally heavy scalar operators described by the Schwarzschild black hole in the bulk and we show that its onshell action reproduces the expected CFT result. This computation is nonstandard, and adding boundary terms to the action on the stretched horizon is crucial. Then, we verify the conformal Ward Identity from the holographic stress tensor and discuss important aspects of the Fefferman-Graham patch. Finally we study a Heavy-Heavy-Light-Light correlator by using geodesics propagating in the banana background. Our main motivation here is to set up the formalism to explore possible universal results for three- and higher-point functions of maximally heavy operators.\] # Abajian, Aprile, Myers, Vieira (Jul) ## Correlation Functions of Huge Operators in AdS$_3$/CFT$_2$: Domes, Doors and Book Pages \[Links: [arXiv](https://arxiv.org/abs/2307.13188), [PDF](https://arxiv.org/pdf/2307.13188)\] \[Abstract: We describe solutions of asymptotically AdS$_3$ Einstein gravity that are sourced by the insertion of operators in the boundary CFT$_2$, whose [[0645 Huge operators|dimension scales with the central charge]] of the theory. Previously, we found that the geometry corresponding to a black hole two-point function is simply related to an infinite covering of the Euclidean BTZ black hole. However, here we find that the geometry sourced by the presence of a third black hole operator turns out to be a Euclidean wormhole with two asymptotic boundaries. We construct this new geometry as a quotient of empty AdS${}_3$ realized by domes and doors. The doors give access to the infinite covers that are needed to describe the insertion of the operators, while the domes describe the fundamental domains of the quotient on each cover. In particular, despite the standard fact that the [[0011 Fefferman-Graham expansion|Fefferman-Graham]] expansion is single-sided, the extended bulk geometry contains a wormhole that connects two asymptotic boundaries. We observe that the two-sided wormhole can be made single-sided by cutting off the wormhole and gluing on a "Lorentzian cap". In this way, the geometry gives the holographic description of a three-point function, up to phases. By rewriting the metric in terms of a Liouville field, we compute the on-shell action and find that the result matches with the Heavy-Heavy-Heavy three-point function predicted by the modular [[0036 Conformal bootstrap|bootstrap]]. Finally, we describe the geometric transition between doors and defects, that is, when one or more dual operators describe a conical defect insertion, rather than a black hole insertion.\] # Abbasi, Landsteiner Pole-skipping as order parameter to probe a quantum critical point \[Links: [arXiv](https://arxiv.org/abs/2307.16716), [PDF](https://arxiv.org/pdf/2307.16716.pdf)\] \[Abstract: The holographic system described by Einstein-Maxwell-Chern-Simons dynamics in the bulk of AdS exhibits a chiral magnetic effect and a quantum critical point. Through numerical calculations, we find that the [[0167 Butterfly velocity|butterfly velocity]] can serve as a new identifier for the quantum critical point in this system. We show that the critical point is the point at which the butterfly velocity is equal to the speed of light in the direction of the magnetic field, while in the opposite direction the butterfly propagation vanishes. Furthermore, by studying the [[0179 Pole skipping|pole-skipping]] points of the response function of the operator dual to the tensor part of the metric perturbation in the bulk, we discover a set of order parameters that distinguish the two states of the system near the quantum critical point. Each of these order parameters is the sum of the absolute values of the real parts of momentum at all pole-skipping points associated with a particular frequency. This quantity vanishes in the disordered state while taking a positive value in the ordered state. In addition, our results confirm the idea that the chiral magnetic effect can manifest macroscopically through [[0008 Quantum chaos|quantum chaos]].\] # Adamo, Bogna, Mason, Sharma ## Scattering on self-dual Taub-NUT \[Links: [arXiv](https://arxiv.org/abs/2309.03834), [PDF](https://arxiv.org/pdf/2309.03834.pdf)\] \[Abstract: We derive exact solutions of massless free field equations and tree-level two-point amplitudes up to spin 2 on self-dual Taub-NUT space-time, as well as on its single copy, the self-dual dyon. We use Killing spinors to build analogues of momentum eigenstates, finding that, in the spirit of [[0152 Colour-kinematics duality|color-kinematics duality]], those for the self-dual dyon lift directly to provide states on the self-dual Taub-NUT background if one replaces charge with energy. We discover that they are forced to have faster growth at infinity than in flat space due to the topological non-triviality of these backgrounds. The amplitudes for massless scalars and spinning particles in the $(+\,+)$ and $(+\,-)$ helicity configurations vanish for generic kinematics as a consequence of the integrability of the self-dual sector. The $(-\,-)$ amplitudes are non-vanishing and we compute them exactly in the backgrounds, which are treated non-perturbatively. It is explained how spin is easily introduced via a Newman-Janis imaginary shift along the spin-vector leading directly to the additional well-known exponential factor in the dot product of the spin with the momenta. We also observe a double copy relation between the gluon amplitude on a self-dual dyon and graviton amplitude on a self-dual Taub-NUT space-time.\] # Adamo, Bu, Zhu ## Infrared structures of scattering on self-dual radiative backgrounds \[Links: [arXiv](https://arxiv.org/abs/2309.01810), [PDF](https://arxiv.org/pdf/2309.01810.pdf)\] \[Abstract: The scattering of gluons and gravitons in trivial backgrounds is endowed with many surprising infrared features which have interesting conformal interpretations on the two-dimensional [[0022 Celestial sphere|celestial sphere]]. However, the fate of these structures in more general asymptotically flat backgrounds is far from clear. In this paper, we consider holomorphic infrared structures in the presence of non-perturbative, self-dual background gauge and gravitational fields which are determined by freely specified radiative data. We make use of explicit formulae for tree-level gluon and graviton scattering in these self-dual radiative backgrounds, as well as chiral twistor sigma model descriptions of the classical dynamics. Remarkably, we find that the leading holomorphic part of tree-level [[0078 Collinear limit|collinear splitting functions]] -- or [[0114 Celestial OPE|celestial OPEs]] -- and infinite-dimensional chiral [[0009 Soft theorems|soft]] algebras are undeformed by the background. We also compute all-order holomorphic celestial OPEs in the [[0061 Maximally helicity violating amplitudes|MHV]] sectors of gauge theory and gravity.\] ## Celestial OPE - the collinear splitting function is undeformed - the regular terms now depend on the background data - the definition of descendants also need to be modified # Adhikari, Rijal, Aryal, Ghimire, Singh, Deppe ## Krylov Complexity of Fermionic and Bosonic Gaussian States \[Links: [arXiv](https://arxiv.org/abs/2309.10382), [PDF](https://arxiv.org/pdf/2309.10382.pdf)\] \[Abstract: The concept of [[0204 Quantum complexity|complexity]] has become pivotal in multiple disciplines, including quantum information, where it serves as an alternative metric for gauging the chaotic evolution of a quantum state. This paper focuses on [[0564 Krylov complexity|Krylov complexity]], a specialized form of quantum complexity that offers an unambiguous and intrinsically meaningful assessment of the spread of a quantum state over all possible orthogonal bases. Our study is situated in the context of Gaussian quantum states, which are fundamental to both Bosonic and Fermionic systems and can be fully described by a covariance matrix. We show that while the covariance matrix is essential, it is insufficient alone for calculating Krylov complexity due to its lack of relative phase information. Our findings suggest that the relative covariance matrix can provide an upper bound for Krylov complexity for Gaussian quantum states. We also explore the implications of Krylov complexity for theories proposing complexity as a candidate for holographic duality by computing Krylov complexity for the [[0574 Thermofield double|thermofield double States]] (TFD) and Dirac field.\] # Agia, Jafferis ## AdS$_3$ String Stars at Pure NSNS Flux \[Links: [arXiv](https://arxiv.org/abs/2311.04956), [PDF](https://arxiv.org/pdf/2311.04956.pdf)\] \[Abstract: We study [[0323 Horowitz-Polchinski solution|Horowitz-Polchinski string stars]] in pure AdS$_3$ near the [[0439 Hagedorn transition|Hagedorn]] temperature using the technique of worldsheet conformal perturbation theory. Since the worldsheet CFT for pure AdS$_3$ is known exactly, our methodology provides a systematic way to construct Horowitz-Polchinski backgrounds to all orders in $\alpha'$. We explicitly construct the leading string star equations in a double expansion in temperature and WZW level $k$ which we then solve numerically.\] # Agriela, Campiglia ## Fermionic asymptotic symmetries in massless QED \[Links: [arXiv](https://arxiv.org/abs/2307.11171), [PDF](https://arxiv.org/pdf/2307.11171.pdf)\] \[Abstract: We consider soft electrons in massless QED at tree-level. The emission amplitude at leading order in the soft electron energy factorizes in a way similar to the soft photon case. We recast the soft electron factorization formula as a [[0106 Ward identity|Ward identity]] of an [[0060 Asymptotic symmetry|asymptotic charge]]. This leads to the first example of an [[0060 Asymptotic symmetry|asymptotic fermionic symmetry]] in a theory with no conventional supersymmetry, suggesting that tree-level massless QED may posses an asymptotic supersymmetry algebra. Although our approach does not yet allow us to completely characterize the algebra, it suggests that subleading soft photons should feature in the anticommutator of two fermionic symmetry generators.\] # Ahmad, Jefferson ## Crossed product algebras and generalized entropy for subregions \[Links: [arXiv](https://arxiv.org/abs/2306.07323), [PDF](https://arxiv.org/pdf/2306.07323.pdf)\] \[Abstract: An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a [[0415 Von Neumann algebra|von Neumann]] factor of type III$_1$, in which entropy cannot be well-defined because such algebras do not admit a trace or density states. However, associated to the algebra is a modular group of automorphisms characterizing the local dynamics of degrees of freedom in the region, and the crossed product of the algebra with its modular group yields a type II$_\infty$ factor, in which traces and hence [[0301 Entanglement entropy|von Neumann entropy]] can be well-defined. In this work, we generalize recent constructions of the crossed product algebra for the TFD to, in principle, arbitrary spacetime regions in arbitrary QFTs, paving the way to the study of entanglement entropy without UV divergences. In this sense, the crossed product construction represents a refinement of Haag's assignment of nets of observable algebras to spacetime regions by providing a natural construction of a type II factor. We present several concrete examples: a QFT in Rindler space, a CFT in an open ball of Minkowski space, and arbitrary boundary subregions in AdS/CFT. In the holographic setting, we provide a novel argument for why the bulk dual must be the entanglement wedge, and discuss the distinction arising from boundary modular flow between causal and entanglement wedges for excited states and disjoint regions.\] # Ahmed, Cong, Kubiznak, Mann, Visser (Feb) ## Holographic dual of extended black hole thermodynamics \[Links: [arXiv](https://arxiv.org/abs/2302.08163), [PDF](https://arxiv.org/pdf/2302.08163.pdf)\] \[Abstract: By respecting the conformal symmetry of the dual CFT, and treating the conformal factor of the AdS boundary as a dynamical variable, we formulate the holographic first law that is exactly dual to the first law of [[0525 Black hole chemistry|extended black hole thermodynamics]] with variable cosmological constant but fixed Newton’s constant.\] ## Refs - [[0525 Black hole chemistry]] # Ahmed, Cong, Kubiznak, Mann, Visser (May) ## Holographic CFT Phase Transitions and Criticality for Rotating AdS Black Holes \[Links: [arXiv](https://arxiv.org/abs/2305.03161), [PDF](https://arxiv.org/pdf/2305.03161.pdf)\] \[Abstract: Employing the novel exact dictionary between the laws of [[0525 Black hole chemistry|extended black hole thermodynamics]] and the laws of the dual CFT, we study the extended thermodynamics for CFT states that are dual to neutral singly-spinning asymptotically AdS black holes in d bulk spacetime dimensions. On the field theory side we include two independent pairs of thermodynamic conjugate variables: the central charge-chemical potential term and the pressure-volume term. In this setting we uncover various phase transitions and critical behaviour in the CFT, focusing on three different thermodynamic ensembles. Namely, for fixed angular momentum and central charge, we show there is a Van der Waals-like criticality for $d=4,5$ and reentrant phase transitions for $d\ge 6$. At fixed angular velocity and central charge, there is a first-order (de)confinement phase transition in all dimensions $d \ge 3$. Finally, at fixed angular momentum and chemical potential we find a plethora of zero-order phase transitions and unstable phases in both $d=4$ and $d=6$.\] ## Refs - earlier work [[2023#Ahmed, Cong, Kubiznak, Mann, Visser (Feb)]] # Akers, Faulkner, Lin, Rath ## Entanglement of Purification in Random Tensor Networks \[Links: [arXiv](https://arxiv.org/abs/2306.06163), [PDF](https://arxiv.org/pdf/2306.06163.pdf)\] \[Abstract: The [[0258 Entanglement of purification|entanglement of purification]] $E_P(A\colon B)$ is a powerful correlation measure, but it is notoriously difficult to compute because it involves an optimization over all possible purifications. In this paper, we prove a new inequality: $E_P(A\colon B)\geq \frac{1}{2}S_R^{(2)}(A\colon B)$, where $S_R^{(n)}(A\colon B)$ is the Renyi reflected entropy. Using this, we compute $E_P(A\colon B)$ for a large class of [[0368 Random tensor network|random tensor networks]] at large bond dimension and show that it is equal to the entanglement wedge cross section $EW(A\colon B)$, proving a previous conjecture motivated from [[0001 AdS-CFT|AdS/CFT]].\] # Akers, Levine, Penington, Wildenhain ## One-shot holography \[Links: [arXiv](https://arxiv.org/abs/2307.13032), [PDF](https://arxiv.org/pdf/2307.13032.pdf)\] \[Abstract: Following the work of [[2020#Akers, Penington]], we define a generally covariant max-entanglement wedge of a boundary region $B$, which we conjecture to be the bulk region reconstructible from $B$. We similarly define a covariant min-entanglement wedge, which we conjecture to be the bulk region that can influence the boundary state on B. We prove that the min- and max-entanglement wedges obey various properties necessary for this conjecture, such as nesting, inclusion of the causal wedge, and a reduction to the usual quantum extremal surface prescription in the appropriate special cases. These proofs rely on one-shot versions of the (restricted) [[0243 Quantum focusing conjecture|quantum focusing conjecture]] (QFC) that we conjecture to hold. We argue that this QFC implies a one-shot [[0082 Generalised second law|generalized second law]] (GSL) and quantum [[0171 Covariant entropy bound|Bousso bound]]. Moreover, in a particular semiclassical limit we prove this one-shot GSL directly using algebraic techniques. Finally, in order to derive our results, we extend both the frameworks of one-shot quantum Shannon theory and state-specific reconstruction to finite-dimensional [[0415 Von Neumann algebra|von Neumann algebras]], allowing nontrivial centers.\] # Ali, Suneeta ## Generalized Entropy in Higher Curvature Gravity And Entropy of Algebra of Observables \[Links: [arXiv](https://arxiv.org/abs/2307.00241), [PDF](https://arxiv.org/pdf/2307.00241.pdf)\] \[Abstract: Recently, [[2022#Chandrasekaran, Penington, Witten|Chandrasekaran, Penington and Witten]] (CPW) have shown that the generalized entropy of the Schwarzschild black hole at the bifurcation surface equals the entropy of an extended [[0415 Von Neumann algebra|von Neumann algebra]] of quantum observables in the black hole exterior, in semiclassical Einstein gravity. They also derive a version of the [[0082 Generalised second law|Generalized Second law]]. We generalize these results to a static black hole in an arbitrary diffeomorphism invariant theory of gravity. Thus, a version of the Generalized second law for an arbitrary diffeomorphism invariant theory of gravity follows.\] # Anand ## Island in Warped AdS Black Holes \[Links: [arXiv](https://arxiv.org/abs/2308.05432), [PDF](https://arxiv.org/pdf/2308.05432.pdf)\] \[Abstract: This paper investigates the Page curve in Warped Anti-de Sitter black holes using the [[0212 Quantum extremal surface|quantum extremal surface]] prescription. The findings reveal that in the absence of an [[0213 Islands|island]], the [[0301 Entanglement entropy|entanglement entropy]] of [[0304 Hawking radiation|Hawking radiation]] grows proportionally with time and becomes divergent at later times. However, when considering the island's emergence, which extends slightly beyond the event horizon, the growth of the entanglement entropy of Hawking radiation comes to a constant value. Eventually, the constant value is precisely twice the [[0004 Black hole entropy|Bekenstein-Hawking entropy]]. We have also discussed the Page time as well as the Scrambling time.\] # Ananth, Bhave, Pandey, Pant ## Deriving interaction vertices in higher derivative theories \[Links: [arXiv](https://arxiv.org/abs/2306.05074), [PDF](https://arxiv.org/pdf/2306.05074.pdf)\] \[Abstract: We derive cubic interaction vertices for a class of [[0593 Amplitudes for higher-dimensional operators|higher-derivative theories]] involving three arbitrary integer spin fields. This derivation uses the requirement of closure of the Poincarè algebra in four-dimensional flat spacetime. We find two varieties of permitted structures at the cubic level and eliminate one variety, which is proportional to the equations of motion, using suitable field redefinitions. We then consider [[0009 Soft theorems|soft theorems]] for field theories with higher-derivative interactions and construct amplitudes in these theories using the [[0515 Inverse soft construction|inverse-soft approach]].\] ## $F^3$ theory - MHV inverse recursion: - $A_{n+1}(\phi, 1,2, \ldots \ldots n)=\frac{\langle n-1,1\rangle}{\langle n-1, n\rangle\langle n 1\rangle} A_n\left(\phi, 1^{\prime}, 2, \ldots \ldots n-1^{\prime}\right)$ - same as for YM - result for holomorphic MHV (3 negative) - $A_n^{F_{+}}\left(1^{-}, 2^{-}, 3^{-}, 4^{+}, \ldots \ldots, n^{+}\right)=\frac{\langle 12\rangle^2\langle 23\rangle^2\langle 31\rangle^2}{\langle 12\rangle\langle 23\rangle\langle 34\rangle \ldots\langle n 1\rangle}$ ## $R^3$ theory - MHV inverse recursion: - $M_{M H V}\left(1, \ldots , n^{+}\right)=\sum_{i=3}^{n-1} \frac{[i n]\langle 1 i\rangle\langle 2 i\rangle}{\langle n i\rangle\langle 1 n\rangle\langle 2 n\rangle} M_{M H V}\left(1^{\prime}, \ldots , i^{\prime}, \ldots ,(n-1)\right)$ - same as for pure gravity - result for holomorphic MHV (3 negative) - $M_n^{R_{+}}\left(1^{-}, 2^{-}, 3^{-}, 4^{+}, \ldots , n^{+}\right)=\frac{\langle 12\rangle^4\langle 23\rangle^4\langle 31\rangle^4}{\langle 12\rangle^8} M_n^R\left(1^{-}, 2^{-}, 3^{+}, \ldots , n^{+}\right)$ - where $M_n^R$ is for pure gravity # Ang, Remy, Sun, Zhu ## Derivation of all structure constants for boundary Liouville CFT \[Links: [arXiv](https://arxiv.org/abs/2305.18266), [PDF](https://arxiv.org/pdf/2305.18266)\] \[Abstract: We prove that the probabilistic definition of the most general boundary three-point and bulk-boundary structure constants in [[0562 Liouville theory|Liouville conformal field theory]] (LCFT) agree respectively with the formula proposed by Ponsot-Techsner (2002) and by Hosomichi (2001). These formulas also respectively describe the [[0573 Crossing kernel|fusion kernel and modular kernel]] of the Virasoro conformal blocks, which are important functions in various contexts of mathematical physics. As an intermediate step, we obtain the formula for the boundary reflection coefficient of LCFT proposed by Fateev-Zamolodchikov-Zamolodchikov (2000). Our proof relies on the boundary Belavin-Polyakov-Zamolodchikov differential equation recently proved by the first named author, and inputs from the coupling theory of Liouville quantum gravity (LQG) and Schramm Loewner evolution. Our results supply all the structure constants needed to perform the conformal bootstrap for boundary LCFT. They also yield exact descriptions for the joint law of the area and boundary lengths of basic LQG surfaces, including quantum triangles and two-pointed quantum disks.\] # Antonini, Grado-White, Jian, Swingle ## Holographic measurement in CFT thermofield doubles \[Links: [arXiv](https://arxiv.org/abs/2304.06743), [PDF](https://arxiv.org/pdf/2304.06743.pdf)\] \[Abstract: We extend the results of [[2022#Antonini, Bentsen, Cao, Harper, Jian, Swingle|arXiv:2209.12903]] by studying local projective measurements performed on subregions of two copies of a CFT${}_2$ in the thermofield double state and investigating their consequences on the bulk double-sided black hole holographic dual. We focus on CFTs defined on an infinite line and consider measurements of both finite and semi-infinite subregions. In the former case, the connectivity of the bulk spacetime is preserved after the measurement. In the latter case, the measurement of two semi-infinite intervals in one CFT or of one semi-infinite interval in each CFT can destroy the Einstein-Rosen bridge and disconnect the bulk dual spacetime. In particular, we find that a transition between a connected and disconnected phase occurs depending on the relative size of the measured and unmeasured subregions and on the specific Cardy state the measured subregions are projected on. We identify this phase transition as an entangled/disentangled phase transition of the dual CFT system by computing the post-measurement holographic entanglement entropy between the two CFTs. We also find that bulk information encoded in one CFT in the absence of measurement can sometimes be reconstructed from the other CFT when a measurement is performed, or can be erased by the measurement. Finally, we show that a purely CFT calculation of the [[0293 Renyi entropy|Renyi entropy]] using the replica trick yields results compatible with those obtained in our bulk analysis.\] # Anupam, Athira, Chowdhury, Sen ## Logarithmic Correction to BPS Black Hole Entropy from Supersymmetric Index at Finite Temperature \[Links: [arXiv](https://arxiv.org/abs/2306.07322), [PDF](https://arxiv.org/pdf/2306.07322.pdf)\] \[Abstract: It has been argued by [[2021#Iliesiu, Kologlu, Turiaci|Iliesiu, Kologlu and Turiaci]] in [arXiv:2107.09062](https://arxiv.org/abs/2107.09062) that one can compute the supersymmetric index of black holes using black hole geometry carrying finite temperature but a specific complex angular velocity. We follow their prescription to compute the logarithmic correction to the entropy of BPS states in four dimensions, defined as the log of the index of supersymmetric black holes, and find perfect agreement with the previous results for the same quantity computed using the near horizon AdS$_2 \times S^2$ geometry of zero temperature black holes. Besides giving an independent computation of supersymmetric black hole entropy, this analysis also provides a test of the procedure used previously for computing logarithmic corrections to Schwarzschild and other non-extremal black hole entropy.\] # Aretakis, Khanna, Sabharwal ## An observational signature for extremal black holes \[Links: [arXiv](https://arxiv.org/abs/2307.03963), [PDF](https://arxiv.org/pdf/2307.03963.pdf)\] \[Abstract: We consider scalar perturbations of the Reissner--Nordström family and the Kerr family. We derive a characteristic expression of the radiation field, at any given unit solid angle of future null infinity, and numerically show that its amplitude gets excited only in the extremal case. Our work, therefore, identifies an observational signature for extremal black holes. Moreover, we show that the source of the excitation is the [[0340 Aretakis instability|extremal horizon instability]] and its magnitude is exactly equal to the conserved horizon charge.\] # Artemev ## $p \to \infty$ limit of tachyon correlators in $(2,2p+1)$ minimal Liouville gravity from classical Liouville theory \[Links: [arXiv](https://arxiv.org/abs/2305.08118), [PDF](https://arxiv.org/pdf/2305.08118)\] \[Abstract: Previously it was suggested, motivated by correspondence with [[0050 JT gravity|JT gravity]], that tachyon correlators in $(2,2p+1)$ minimal Liouville gravity (MLG) in the $p\to \infty$ (semiclassical) limit should be interpreted as moduli space volumes for constant curvature surfaces with conical defects. In this work we propose that these volumes are associated with Kahler metrics on moduli spaces introduced by Zograf and Takhtajan, for which the classical Liouville action is a Kahler potential. We check this proposal by numerical calculation of these Kahler metrics and associated volumes for the simplest example of genus 0 surface with 4 conical defects, using conformal field theory. A peculiar property of MLG correlators is proportionality to number of conformal blocks in a certain region of parameter space; in a particular limiting case, we check this property for the volumes following from classical Liouville action and thus provide an analytic confirmation of our proposal.\] # Baggioli, Cremonini, Early, Li, Sun ## Breaking rotations without violating the KSS viscosity bound \[Links: [arXiv](https://arxiv.org/abs/2304.01807), [PDF](https://arxiv.org/pdf/2304.01807.pdf)\] \[Abstract: We revisit the computation of the [[0430 Holographic shear viscosity|shear viscosity]] to entropy ratio in a holographic p-wave superfluid model, focusing on the role of ==rotational symmetry breaking==. We study the interplay between explicit and spontaneous symmetry breaking and derive a simple horizon formula for $\eta/s$, which is valid also in the presence of explicit breaking of rotations and is in perfect agreement with the numerical data. We observe that a source which explicitly breaks rotational invariance suppresses the value of $\eta/s$ in the broken phase, competing against the effects of spontaneous symmetry breaking. However, $\eta/s$ always reaches a constant value in the limit of zero temperature, which is never smaller than the Kovtun-Son-Starinets (KSS) bound, $1/4\pi$. This behavior appears to be in contrast with previous holographic anisotropic models which found a power-law vanishing of $\eta/s$ at small temperature. This difference is shown to arise from the properties of the near-horizon geometry in the extremal limit. Thus, our construction shows that the breaking of rotations itself does not necessarily imply a violation of the KSS bound.\] ## Conclusion - breaking rotation alone does not violate KSS, but breaking rotation plus translation invariance could violate KSS # Bahiru, Belin, Papadodimas, Sarosi, Vardian ## Holography and Localization of Information in Quantum Gravity \[Links: [arXiv](https://arxiv.org/abs/2301.08753), [PDF](https://arxiv.org/pdf/2301.08753.pdf)\] \[Abstract: Within the [[0001 AdS-CFT|AdS/CFT]] correspondence, we identify a class of CFT operators which represent diff-invariant and approximately local observables in the gravitational dual. Provided that the bulk state breaks all [[0060 Asymptotic symmetry|asymptotic symmetries]], we show that these operators commute to all orders in $1/N$ with asymptotic charges, thus resolving an apparent tension between locality in perturbative quantum gravity and the gravitational Gauss law. The interpretation of these observables is that they are not gravitationally dressed with respect to the boundary, but instead to features of the state. We also provide evidence that there are bulk observables whose commutator vanishes to all orders in $1/N$ with the entire algebra of single-trace operators defined in a space-like separated time-band. This implies that in a large $N$ [[0122 Holographic CFT|holographic CFT]], the algebra generated by single-trace operators in a short-enough time-band has a non-trivial commutant when acting on states which break the symmetries. It also implies that information deep in the interior of the bulk is invisible to single-trace correlators in the time-band and hence that it is possible to localize information in perturbative quantum gravity.\] # Balasubramanian, Cummings ## The entropy of finite gravitating regions \[Links: [arXiv](https://arxiv.org/abs/2312.08434), [PDF](https://arxiv.org/pdf/2312.08434.pdf)\] \[Abstract: We develop a formalism for calculating the [[0301 Entanglement entropy|entanglement entropy]] of an arbitrary spatial region of a gravitating spacetime at a moment of time symmetry. The crucial ingredient is a path integral over embeddings of the region in the overall spacetime, interpretable as a sum over the [[0556 Edge mode|edge modes]] associated with the region. We find that the entanglement entropy of a gravitating region equals the minimal surface area among all regions that enclose it. This suggests a notion of "terrestrial holography" where regions of space can encode larger ones, in contrast to the standard form of holography, in which degrees of freedom on the [[0022 Celestial sphere|celestial sphere]] at the boundary of the universe encodes the interior.\] # Bagchi, Dhivakar, Dutta ## Holography in Flat Spacetimes: the case for Carroll \[Links: [arXiv](https://arxiv.org/abs/2311.11246), [PDF](https://arxiv.org/pdf/2311.11246.pdf)\] \[Abstract: We compare and contrast the two approaches of holography in asymptotically flat spacetimes, viz. the co-dimension two [[0010 Celestial holography|Celestial]] approach based on the Mellin transformation and the co-dimension one [[0419 Carrollian CFT|Carrollian]] approach based on the modified Mellin and elucidate how some of the problems of the Celestial approach can be rectified by the Carrollian one. Considering flat holography as a limit from [[0001 AdS-CFT|AdS/CFT]] makes a co-dimension one dual more plausible, and our previous construction of Carrollian correlations from AdS Witten diagrams is testimony to this. In this paper, we show how to generalize our earlier analysis for operators with spin. We work out a large number of explicit non-trivial examples (eleven) and show matching between the limit of AdS$_4$ Witten diagrams and 3d boundary symmetry considerations, thus making the case for the Carrollian dual even stronger.\] # Baishya, Chakrabarti, Maity ## Effect of scalar condensation on fermionic Pole-Skipping \[Links: [arXiv](https://arxiv.org/abs/2311.05314), [PDF](https://arxiv.org/pdf/2311.05314.pdf)\] \[Abstract: In this paper, we have studied the holographic fermionic [[0179 Pole skipping|Pole-Skipping]] phenomena for a class of interacting theory in a charged AdS black hole background. We have studied two types of fermion-scalar interactions in the bulk: Dipole and Yukawa type interaction. Depending upon the interaction we introduced both real and charged scalar fields. We have particularly analyzed the effect of scalar condensation on the fermionic Pole-Skipping points and discussed their behaviour near critical temperatures.\] # Ball, De, Srikant, Volovich ## Scalar-Graviton Amplitudes and Celestial Holography \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: We compute scattering amplitudes involving one massive scalar and two, three, or four gravitons. We show that when the conformal dimension of the massive scalar is set to zero, the resulting [[0516 Celestial correlators|celestial correlators]] depend *only* on the coordinates of the gravitons. Such correlators of gravitons are well-defined and do not suffer from divergences associated with the [[0079 Mellin transform|Mellin transform]] of usual graviton amplitudes. Moreover, they are non-distributional and take the form of standard CFT correlators. We show that they are consistent with the usual OPEs but the statement of the soft theorem is modified.\] # Ball, Hu, Pasterski ## Multicollinear Singularities in Celestial CFT \[Links: [arXiv](https://arxiv.org/abs/2309.16602), [PDF](https://arxiv.org/pdf/2309.16602.pdf)\] \[Abstract: The purpose of this paper is to study the holomorphic [[0077 Multi-collinear limit|multicollinear limit]] of (celestial) amplitudes and use it to further investigate the double residue condition for (hard celestial) amplitudes and the celestial operator product expansion. We first set up the notion of holomorphic multicollinear limits of amplitudes and derive the 3-collinear splitting functions for [[0071 Yang-Mills|Yang-Mills]] theory, [[0554 Einstein gravity|Einstein gravity]], and massless $\phi^3$ theory. In particular, we find that in $\phi^3$ theory the celestial 3-[[0030 Operator product expansion|OPE]] contains a term with a branch cut. This explicit example confirms that branch cuts can obstruct the double residue condition for hard celestial amplitudes, which is the underlying cause of the celestial [[0453 Jacobi identity or associativity of celestial OPE|Jacobi identities]] not holding for certain theories. This addresses an ongoing debate in the literature about [[0453 Jacobi identity or associativity of celestial OPE|associativity of the celestial OPEs]] and concretely demonstrates a new (multi-particle) term in the [[0114 Celestial OPE|celestial OPE]] coming from the multi-particle channel in the amplitudes.\] ## Comments - the multi-collinear factorisation channel is generic in EFTs, and YM for example is special in that something in the numerator cancels with the denominator ## New term in OPE - a naive addition to the OPE between 2 and 3 would involve the conformal dimension of 1, which is non-local - to not depend on $\Delta_1$, the new term would take the form of an integral over $\Delta$ # Banerjee, Kulkarni, Paul (Jan) ## An infinite family of $w_{1+\infty}$ invariant theories on the celestial sphere \[Links: [arXiv](https://arxiv.org/abs/2301.13225), [PDF](https://arxiv.org/pdf/2301.13225.pdf)\] \[Abstract: In this note we determine the graviton-graviton [[0114 Celestial OPE|OPE]] and the null states in any [[0328 w(1+infinity)|w(1+infinity) symmetric]] theory on the [[0022 Celestial sphere|celestial sphere]]. Our analysis shows that there exists a discrete infinite family of such theories. The [[0061 Maximally helicity violating amplitudes|MHV]]-sector and the quantum [[0234 Self-dual gravity|self dual gravity]] are two members of this infinite family. However, the bulk description of other theories are not known to us.\] ## Setup and assumptions - assume $\overline{\rm{Vir}}$ is not part of the symmetry (see [[2022#Banerjee, Pasterski]]) - leading term in OPE is $\mathcal{O}\left(\frac{\bar{z}}{z}\right)$ (from collinear graviton scattering) - explicit results at $\mathcal{O}\left(z_{12}^0 \bar{z}_{12}^0\right)$ and $\mathcal{O}\left(z_{12}^0 \bar{z}_{12}^1\right)$ ## Null states - two theories $A$ and $B$, both invariant under $w$ symmetry and same operator content - then there is a universal part of the OPE (OPE$_w$) such that - $\mathrm{OPE}_w=\mathrm{OPE}_A+$ Linear combination of Null-States of theory $\mathrm{A}$ - $\mathrm{OPE}_w=\mathrm{OPE}_B+$ Linear combination of Null-States of theory $\mathrm{B}$ - now if we can choose $A$ such that null states of $A$ form a basis for null states of theory $B$, then - $\mathrm{OPE}_B=\mathrm{OPE}_A+$ Linear combination of Null-States of theory $\mathrm{A}$ - choice of $A$: [[0061 Maximally helicity violating amplitudes|MHV]] sector - because it has the maximal number of null states ## What is special about MHV - simplest: max number of null states - => OPE contains least number of types of descendants (it only has supertranslation and $\overline{sl_2}$ current algebra descendants) ## $w$ invariance - supertranslations are generated by the soft graviton $H^1(z,\bar z)$ - $\overline{sl_2(R)}$ is generated by the soft graviton $H^0(z,\bar z)$ - $\bar L_1$ relates different orders: see eq. (5.7) - => same $n$ in equations (6.1) and (6.2) - $s l_2(R)_V$: $\left\{H_{-1 / 2,-1 / 2}^1, H_{0,0}^0, H_{1 / 2,1 / 2}^{-1}\right\}$ - $s l_2(R)_V$ constrains the OPE at each order in $z$ and $\bar z$ - they not mix terms of different orders in $z$ and $\bar z$ - therefore terms in each order in $z$ and $\bar z$ transform in some representation of this algebra - $\overline{s l_2(R)}$ and $s l_2(R)_V$ generates the full tower, so only need to check invariance under these two symmetry algebras ## Allowed theories with $w$ invariance - MHV null results that can appear at $\mathcal{O}\left(z_{12}^0 \bar{z}_{12}^0\right)$ - $\Phi_k(\Delta)=\left[H_{\frac{k-3}{2}, \frac{k+1}{2}}^{1-k}\left(-H_{-\frac{1}{2},-\frac{1}{2}}^1\right)^k-\frac{(-1)^k}{k !} \frac{\Gamma(\Delta+k-2)}{\Gamma(\Delta-2)} H_{-\frac{3}{2}, \frac{1}{2}}^1\right] G_{\Delta-1}^{+}$ - MHV null results that can appear at $\mathcal{O}\left(z_{12}^0 \bar{z}_{12}^1\right)$ - $\Psi_k(\Delta)=\dots$(long equation) - denote - $\Omega_k(\Delta)=\sum_{n=1}^k \frac{1}{(k-n) !} \frac{\Gamma(\Delta+k-2)}{\Gamma(\Delta+n-2)} \Phi_n(\Delta)$ - $\Pi_k(\Delta)=\sum_{n=1}^k \frac{1}{(k-n) !} \frac{\Gamma(\Delta+k-2)}{\Gamma(\Delta+n-2)} \Psi_n(\Delta)$ - $w$ invariance requires - $\Omega_{k+1}(\Delta)=0, k \geq n \geq 0$, at $\mathcal{O}\left(z^0 \bar{z}^0\right)$ - $\Pi_{k+1}(\Delta)=0, k \geq n \geq 0$, at $\mathcal{O}\left(z^0 \bar{z}^1\right)$ - can have $w$ invariant OPE at $\mathcal{O}\left(z^0 \bar{z}^0\right)$ and $\mathcal{O}\left(z^0 \bar{z}^1\right)$ determined by - $\left\{\Omega_1(\Delta), \ldots, \Omega_n(\Delta)\right\}$ and $\left\{\Pi_1(\Delta), \cdots, \Pi_n(\Delta)\right\}$ - but $n$ is free! - so we have infinitely many theories - examples - $n=0$: [[0061 Maximally helicity violating amplitudes|MHV amplitudes]] - $n=4$: [[0234 Self-dual gravity|self-dual gravity]] ## Future - higher orders in $z$: different orders seem independent, unlike with $\bar z$ --- \[*I thank Shamik Banerjee for correspondence.*\] # Banerjee, Kulkarni, Paul (Nov) ## Celestial OPE in Self Dual Gravity \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: In this paper we compute the [[0114 Celestial OPE|celestial operator product expansion]] between two outgoing positive helicity gravitons in the [[0234 Self-dual gravity|self dual gravity]]. It has been shown that the self dual gravity is a w$_{1+\infty}$-invariant theory whose scattering amplitudes are one loop exact with all positive helicity gravitons. Celestial [[0328 w(1+infinity)|w]]$_{1+\infty}$ symmetry is generated by an infinite tower of (conformally soft) gravitons which are holomorphic conserved currents. We find that at any given order only a *finite* number of w$_{1+\infty}$ descendants contribute to the OPE. This is somewhat surprising because the spectrum of conformal dimensions in celestial CFT is not bounded from below. However, this is consistent with our earlier analysis based on the representation theory of w$_{1+\infty}$. The phenomenon of truncation suggests that in some (unknown) formulation the spectrum of conformal dimensions in the dual two dimensional theory can be bounded from below.\] # Banerjee, Mandal, Manu, Paul ## MHV Gluon Scattering in the Massive Scalar Background and Celestial OPE \[Links: [arXiv](https://arxiv.org/abs/2302.10245), [PDF](https://arxiv.org/pdf/2302.10245.pdf)\] \[Abstract: In this paper we study the [[0114 Celestial OPE|OPE]] between two positive helicity outgoing gluons in the celestial CFT for the Yang-Mills theory chirally coupled to a massive scalar background. This theory breaks the translation as well as scale invariance. We compute the subleading terms in the OPE expansion and show that they are same as the subleading terms of the OPE expansions in the [[0061 Maximally helicity violating amplitudes|MHV]] sector. As a result the amplitudes of this theory also satisfy the set of differential equations obtained previously for MHV amplitudes in pure YM theory. This is not surprising because the symmetries coming from the leading and subleading [[0009 Soft theorems|soft gluon theorems]] do not change in the presence of a massive scalar background.\] ## Refs - [[0114 Celestial OPE]] # Banerjee, Mandal, Misra, Panda, Paul ## All S invariant gluon OPEs on the celestial sphere \[Links: [arXiv](https://arxiv.org/abs/2311.16796), [PDF](https://arxiv.org/pdf/2311.16796.pdf)\] \[Abstract: S algebra is an infinite dimensional Lie algebra which is known to be the symmetry algebra of some gauge theories. It is a "coloured version" of the [[0328 w(1+infinity)|w]]$_{1+\infty}$. In this paper we write down all possible S invariant [[0114 Celestial OPE|(celestial) OPEs]] between two positive helicity outgoing gluons and also find the Knizhnik-Zamolodchikov type null states for these theories. Our analysis hints at the existence of an infinite number of S invariant gauge theories which include the (tree-level) [[0061 Maximally helicity violating amplitudes|MHV]]-sector and the [[0136 Self-dual Yang-Mills|self-dual Yang-Mills]] theory.\] ## Summary - twin paper of [[2023#Banerjee, Kulkarni, Paul (Jan)]] # Banks ## Holography for Small Values of the Cosmological Constant \[Links: [arXiv](https://arxiv.org/abs/2308.13360), [PDF](https://arxiv.org/pdf/2308.13360.pdf)\] \[Abstract: We review recent work on holography for finite area causal diamonds and explore its implications for the description of such diamonds in the Anti-deSitter space Conformal Field Theory correspondence. We argue that the algebra of operators in a finite area diamond is well defined in a UV cutoff [[0054 Tensor network|tensor network]] construction, but is not related in any simple way to any infinite [[0415 Von Neumann algebra|von Neumann sub-algebra]] of the boundary algebra or its cross product. Our argument relies on a novel construction of tensor networks that preserves rotation invariance.\] # Belaey, Mariani, Mertens ## Branes in JT (super)gravity from group theory \[Links: [arXiv](https://arxiv.org/abs/2310.04245), [PDF](https://arxiv.org/pdf/2310.04245.pdf)\] \[Abstract: In this work, we revisit the end-of-the-world (EOW) brane amplitudes in [[0050 JT gravity|JT gravity]] from a [[0557 BF theory|BF gauge theoretic]] perspective. Observing and identifying the correct group theoretic ingredient for a closed EOW brane as a discrete series character, we use the group theory framework as a guide towards formulating the analogous supersymmetric problem. We compute these amplitudes explicitly in the supersymmetric generalizations of JT gravity ($\mathcal{N}=1,2,4$), motivated by the prospective of possibly finite amplitudes. In the process, we develop some of the representation theory of OSp$(2\vert 2,\mathbb{R})$ and PSU$(1,1\vert 2)$, relevant for the $\mathcal{N}=2$ and $\mathcal{N}=4$ cases.\] # Belin, de Boer, Jafferis, Nayak, Sonner ## Approximate CFTs and Random Tensor Models \[Links: [arXiv](https://arxiv.org/abs/2308.03829), [PDF](https://arxiv.org/pdf/2308.03829.pdf), [Talk at strings](https://pirsa.org/23070030)\] \[Abstract: A key issue in both the field of [[0008 Quantum chaos|quantum chaos]] and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of 'CFT data'. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the [[0154 Ensemble averaging|ensembles]], we introduce the notion of approximate CFT, defined as a collection of 'CFT data' satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS$_3$ as a [[0600 A tensor model for AdS3|random matrix/tensor model]] implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a [[0197 Matrix model|random matrix/tensor model]] governed by the Virasoro 6j-symbol.\] ## Three directions of approach - by starting with an individual element of the ensemble - by studying moments of the ensemble - (tensor model for [[0002 3D gravity|AdS3]]) by explicitly constructing the probability distribution over structure constants ## Comments - conformal symmetry is exact (so the CFT data specify the theory) but locality is approximate ## Conventions - eq.(4.9) uses $\mathbb{F}_{P_s P_t}$ whereas some other papers use $\mathbb{F}_{P_t P_s}$ # Berenstein, Yan ## The endpoint of partial deconfinement \[Links: [arXiv](https://arxiv.org/abs/2307.06122), [PDF](https://arxiv.org/pdf/2307.06122.pdf)\] \[Abstract: We study the matrix quantum mechanics of two free hermitian $N\times N$ matrices subject to a singlet constraint in the microcanonical ensemble. This is the simplest example of a theory that at large $N$ has a [[0441 Confinement-deconfinement transition|confinement/deconfinement transition]]. In the microcanonical ensemble, it also exhibits partial confinement with a Hagedorn density of states. We argue that the entropy of these configurations, calculated by a counting of states based on the fact that Young diagrams are dominated by Young diagrams that have the VKLS shape. When the shape gets to the maximal depth allowed for a Young diagram of $SU(N)$, namely $N$, we argue that the system stops exhibiting the Hagedorn behavior. The number of boxes (energy) at the transition is $N^2/4$, independent of the charge of the state.\] # Bhatta, Chakrabortty, Mandal, Maurya ## Holographic Thermal Correlators for Hyperbolic CFTs \[Links: [arXiv](https://arxiv.org/abs/2308.14704), [PDF](https://arxiv.org/pdf/2308.14704.pdf)\] \[Abstract: We use holography to compute the exact form of [[0473 Retarded Green's function|retarded Green's functions]] for a scalar operator with conformal dimension $\Delta$ in a thermal CFT and in its related counterpart with chemical potential in $R^1 \times H^3$. In our analysis, we recast the wave equation of a scalar field in the normal form of Heun's equation in the dual gravity theories described by the AdS hyperbolic blackhole and its charged version. Heun's equation is identified to the semiclassical limit of the BPZ equation for a five-point correlator with one degenerate field insertion in the Liouville theory on the Riemann sphere. The crossing symmetry of conformal block in the Liouville theory eventually gives rise to a set of connection formulas among the solutions of Heun's equation evaluated at different regular singularities. We use the connection formula to reproduce the leading order behaviors of the scalar field near the horizon as well as near the boundary and achieve the exact form of the retarded thermal Green's function. We show a recipe to obtain the exact retarded Green's function for a thermal CFT dual to AdS blackbrane from a high-temperature limit accompanied by a complex mapping on AdS hyperbolic blackhole. Moreover, we show the retarded Green's function for the boundary CFT of Rindler AdS spacetime admits a free integer parameter.\] # Bhattacharjee, Mukherjee ## Bulk reconstruction for normalizable and non-normalizable modes: p-forms and the graviton \[Links: [arXiv](https://arxiv.org/abs/2307.02710), [PDF](https://arxiv.org/pdf/2307.02710.pdf)\] \[Abstract: In this paper, we consider the [[0016 HKLL|HKLL bulk reconstruction]] procedure for $p$-form fields and graviton in empty AdS$_{d + 1}$. We derive spacelike HKLL bulk reconstruction kernels for the normalizable and non-normalizable modes of $p$-forms and graviton in the Poincaré patch of AdS$_{d + 1}$. The kernels are first derived via a mode-sum approach in arbitrary even dimensions. The appropriate AdS-covariant fields are identified and corresponding kernels obtained via the mode-sum approach for these fields. We present arguments for casting these kernels in terms of the AdS chordal distance. Introducing an antipodal-like mapping, the kernels are cast in a spacelike form. An alternative derivation is presented for these kernels, by using a chordal Green's function approach. A derivation of the normalizable mode Green's function is discussed and a natural choice of the non-normalizable Green's function is proposed. From the asymptotic expansion of the bulk fields and using Green's theorem, we read off the spacelike kernels for both modes of $p$-forms and graviton, which agree with the kernels obtained by the mode-sum approach. Part of the Appendix is devoted to extending the massless $p$-form field reconstruction to the massive field, along with comments on the Brietenlohner-Freedman bound, while part of it is devoted to discussion on the $p$-form and graviton bulk reconstruction in arbitrary odd dimensional AdS. The manuscript is concluded with a summary of the main results and some future directions.\] # Bhattacharya, Bhattacharyya, Patra ## Holographic complexity of Jackiw-Teitelboim gravity from Karch-Randall braneworld \[Links: [arXiv](https://arxiv.org/abs/2304.09909), [PDF](https://arxiv.org/pdf/2304.09909.pdf)\] \[Abstract: Recently, it has been argued in \cite{Geng:2022slq} that [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] can be naturally realized in the [[0452 Karch-Randall braneworld|Karch-Randall braneworld]] in (2+1) dimensions. Using the '[[0204 Quantum complexity|complexity]]=volume' proposal, we studied this model and computed the holographic complexity of the JT gravity from the bulk perspective. We find that the complexity grows linearly with boundary time at late times, and the leading order contribution is proportional to the $\varphi_0$, similar to the answer found in [[2018#Brown, Gharibyan, Lin, Susskind, Thorlacius, Zhao]]. However, in addition, we find subleading corrections to the complexity solely arising from the fluctuations of these Karch-Randall branes.\] # Bhattacharya, Ghosh ## Gravitational wave memory for a class of static and spherically symmetric spacetimes \[Links: [arXiv](https://arxiv.org/abs/2309.04130), [PDF](https://arxiv.org/pdf/2309.04130.pdf)\] \[Abstract: This article aims at comparing gravitational wave [[0287 Memory effect|memory effect]] in a Schwarzschild spacetime with that of other compact objects with static and spherically symmetric spacetime, with the purpose of proposing a procedure for differentiating between various compact object geometries. We do this by considering the relative evolution of two nearby test geodesics with in different backgrounds in the presence and absence of a gravitational wave pulse and comparing them. Memory effect due to a gravitational wave would ensure that there is a permanent effect on each spacetime and the corresponding geodesic evolution, being metric dependent, would display distinct results in each case. For a complete picture, we have considered both displacement and velocity memory effect in each geometry.\] # Bianchi, Firrotta, Sonnenschein, Weissman ## Measuring chaos in string scattering processes \[Links: [arXiv](https://arxiv.org/abs/2303.17233), [PDF](https://arxiv.org/pdf/2303.17233.pdf)\] \[Abstract: We analyze the amplitudes of one highly excited string (HES) state with two or three tachyons in open bosonic string theory. We argue that these processes are [[0008 Quantum chaos|chaotic]] by showing that the spacing ratios of successive peaks in the angular dependence of the amplitudes are distributed as predicted by the $\beta$-ensemble of [[0579 Random matrix theory|random matrix theory]] (RMT). We show how the continuous parameter $\beta$ depends on the level and helicity of the scattered HES state. We derive the scattering amplitude of an HES and three tachyons and show that it takes the form of the Veneziano amplitude times a dressing factor, and that the dressing is chaotic as a function of the scattering angle, in the sense that its spacing ratios match with RMT predictions.\] # Bigazzi, Canneti, Cotrone ## Higher Order Corrections to the Hagedorn Temperature at Strong Coupling \[Links: [arXiv](https://arxiv.org/abs/2306.17126), [PDF](https://arxiv.org/pdf/2306.17126.pdf)\] \[Abstract: We propose a general formula for higher order corrections to the value of the [[0439 Hagedorn transition|Hagedorn]] temperature of a class of holographic confining gauge theories in the strong coupling expansion. Inspired by recent proposals in the literature, the formula combines the sigma-model string expansion with an effective approach. In particular, it includes the sigma-model contributions to the Hagedorn temperature at next-to-next-to leading order, which are computed in full generality. For ${\cal N}=4$ [[0155 N=4 SYM|SYM]] on $S^3$ our result agrees with numerical field theory estimates with excellent precision. We use the general formula to predict the value of the Hagedorn temperature for [[0137 ABJM|ABJM]] on $S^2$ and for the dual of purely RR global AdS$_3$.\] # Biggs, Maldacena ## Scaling similarities and quasinormal modes of D0 black hole solutions \[Links: [arXiv](https://arxiv.org/abs/2303.09974), [PDF](https://arxiv.org/pdf/2303.09974.pdf)\] \[Abstract: We study the gravity solution dual to the D0 brane quantum mechanics, or [[0479 BFSS matrix model|BFSS matrix model]], in the 't Hooft limit. The classical physics described by this gravity solution is invariant under a scaling transformation, which changes the action with a specific critical exponent, sometimes called the hyperscaling violating exponent. We present an argument for this critical exponent from the matrix model side, which leads to an explanation for the peculiar temperature dependence of the entropy in this theory, $S \propto T^{9/5}$. We also present a similar argument for all other D$p$-brane geometries. We then compute the black hole [[0325 Quasi-normal modes|quasinormal modes]]. This involves perturbing the finite temperature geometry. These perturbations can be easily obtained by a mathematical trick where we view the solution as the dimensional reduction of an AdS$_{ 2 + 9/5 } \times S^8$ geometry.\] ## Similarity v.s. symmetry - a similarity is a transformation that rescales the action rather than leaving it invariant - if we only care about the classical solution, it is a symmetry of the equations of motion, which is all that matters ## Critical exponent from the matrix model - the key idea is that, a similarity of the full action is also a similarity of any effective action - here they take the effective action for the vev of a bosonic matrix after Higgsing and write down the general form of the effective action allowed by the scaling similarity - finally they use supersymmetry to constrain the unknowns in the general effective action, which turns out enough to find the critical exponent # Biggs, Maldacena, Narovlansky ## A supersymmetric SYK model with a curious low energy behavior \[Links: [arXiv](https://arxiv.org/abs/2309.08818), [PDF](https://arxiv.org/pdf/2309.08818.pdf)\] \[Abstract: We consider $\mathcal{N} = 2, 4$ supersymmetric [[0201 Sachdev-Ye-Kitaev model|SYK]] models that have a peculiar low energy behavior, with the entropy going like $S = S_{0} + \text{(constant)}T^{a}$, where $a \neq 1$. The large $N$ equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the [[0479 BFSS matrix model|BFSS]] matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions.\] # Bilotta ## A Traversable Wormhole from the Kerr Black Hole \[Links: [arXiv](https://arxiv.org/abs/2304.07356), [PDF](https://arxiv.org/pdf/2304.07356.pdf)\] \[Abstract: The approach of [[2016#Gao, Jafferis, Wall]] to perturbatively construct [[0083 Traversable wormhole|traversable wormholes]] has seen success in a number of black hole backgrounds, particularly [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] and AdS$_2$, whereas historically most wormhole solutions have been either found to violate the achronal [[0417 Averaged null energy condition|ANEC]], violate a classical no-go theorem, or exist only in astrophysically irrelevant spacetimes. In this work, we show that a double-trace deformation to the near-horizon, near-extremal region of Kerr yields a traversable wormhole. We also comment on the potential for a fully nonperturbative approach to a four-dimensional rotating traversable wormhole in asymptotically flat space.\] # Bittleston, Heuveline, Skinner ## The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space \[Links: [arXiv](https://arxiv.org/abs/2305.09451), [PDF](https://arxiv.org/pdf/2305.09451.pdf)\] \[Abstract: We consider the twistor description of classical [[0234 Self-dual gravity|self-dual Einstein gravity]] in the presence of a defect operator wrapping a certain $\mathbb{CP}^1$. The backreaction of this defect deforms the flat twistor space to that of Eguchi-Hanson space. We show that the celestial chiral algebra of self-dual gravity on the Eguchi-Hanson background is likewise deformed to become the loop algebra of a certain scaling limit of the family of $W(\mu)$-algebras, where the scaling limit is controlled by the radius of the Eguchi-Hanson core. We construct this algebra by computing the Poisson algebra of holomorphic functions on the deformed [[0330 Twistor theory|twistor space]], and check this result with a space-time calculation of the leading contribution to the gravitational [[0078 Collinear limit|splitting function]]. The loop algebra of a general $W(\mu)$-algebra (away from the scaling limit) similarly arises as the celestial chiral algebra of Moyal-deformed self-dual gravity on Eguchi-Hanson space. We also obtain corresponding results for [[0136 Self-dual Yang-Mills|self-dual Yang-Mills]].\] # Blake, Thompson ## The Page curve from the entanglement membrane \[Links: [arXiv](https://arxiv.org/abs/2306.13140), [PDF](https://arxiv.org/pdf/2306.13140.pdf)\] \[Abstract: We study [[0522 Entanglement dynamics|entanglement dynamics]] in toy models of black hole information built out of chaotic many-body quantum systems, by utilising a coarse-grained description of entanglement dynamics in such systems known as the '[[0433 Membrane theory of entanglement dynamics|entanglement membrane]]'. We show that in these models the Page curve associated to the entropy of Hawking radiation arises from a transition in the entanglement membrane around the Page time, in an analogous manner to the change in [[0212 Quantum extremal surface|quantum extremal surfaces]] that leads to the Page curve in semi-classical gravity. We also use the entanglement membrane prescription to study the [[0217 Hayden-Preskill decoding criterion|Hayden-Preskill protocol]], and demonstrate how information initially encoded in the black hole is rapidly transferred to the radiation around the Page time. Our results relate recent developments in black hole information to generic features of entanglement dynamics in chaotic many-body quantum systems.\] # Blommaert, Mertens, Yao ## The q-Schwarzian and Liouville gravity \[Links: [arXiv](https://arxiv.org/abs/2312.00871), [PDF](https://arxiv.org/pdf/2312.00871.pdf)\] \[Abstract: We present a new holographic duality between $q$-Schwarzian quantum mechanics and [[0562 Liouville theory|Liouville gravity]]. The $q$-Schwarzian is a one parameter deformation of the Schwarzian, which is dual to [[0050 JT gravity|JT gravity]] and describes the low energy sector of [[0201 Sachdev-Ye-Kitaev model|SYK]]. We show that the $q$-Schwarzian in turn is dual to sinh dilaton gravity. This one parameter deformation of JT gravity can be rewritten as Liouville gravity. We match the thermodynamics and classical two point function between $q$-Schwarzian and Liouville gravity. We further prove the duality on the quantum level by rewriting sinh dilaton gravity as a topological gauge theory, and showing that the latter equals the q-Schwarzian. As the $q$-Schwarzian can be quantized exactly, this duality can be viewed as an exact solution of sinh dilaton gravity on the disk topology. For real $q$, this $q$-Schwarzian corresponds to [[0503 Double-scaled SYK|double-scaled SYK]] and is dual to a sine dilaton gravity.\] # Bogna, Mason ## Yang-Mills form factors on self-dual backgrounds \[Links: [arXiv](https://arxiv.org/abs/2305.07542), [PDF](https://arxiv.org/pdf/2305.07542.pdf)\] \[Abstract: The construction of perturbative quantities on non-linear backgrounds leads to the possibility of incorporating strong field effects in perturbation theory. We continue a programme to construct QFT observables on self-dual backgrounds. The approach works with asymptotic data for fields defined at null infinity $\mathscr{I}$, extending earlier work on Yang-Mills amplitudes on self-dual backgrounds to form factors and incorporating supersymmetry. Since our analysis is based on reconstruction from data at null infinity, it naturally ties into work on [[0010 Celestial holography|celestial]] and [[0130 Twisted holography|twisted holography]]. We study form factors both in pure Yang-Mills and their supersymmetric counterparts in $\mathcal{N}=4$ SYM, giving a full treatment of $\mathcal{N}=4$ super-Yang-Mills at null infinity and their self-dual nonlinear backgrounds. We obtain tree-level [[0061 Maximally helicity violating amplitudes|MHV]] form factors around these backgrounds using new formulae for lifting operators to [[0330 Twistor theory|twistor space]] leading to simple dressings of the corresponding form factors around the vacuum. We give brief indications on how to go beyond the MHV sector by introducing dressed versions of the MHV diagram propagator. We discuss generating functionals of the MHV all plus 1-loop amplitude in this context together with its various dual conformal representations.\] # Bonifacio, Hinterbichler ## Fermionic Shift Symmetries in (Anti) de Sitter Space \[Links: [arXiv](https://arxiv.org/abs/2312.06743), [PDF](https://arxiv.org/pdf/2312.06743.pdf)\] \[Abstract: We study extended [[0500 Shift symmetry|shift symmetries]] that arise for fermionic fields on anti-de Sitter (AdS) space and de Sitter (dS) space for particular values of the mass relative to the curvature scale. We classify these symmetries for general mixed-symmetry fermionic fields in arbitrary dimension and describe how fields with these symmetries arise as the decoupled longitudinal modes of massive fermions as they approach partially massless points. For the particular case of AdS$_4$, we look for non-trivial Lie superalgebras that can underly interacting theories that involve these fields. We study from this perspective the minimal such theory, the Akulov--Volkov theory on AdS$_4$, which is a non-linear theory of a spin-1/2 Goldstino field that describes the spontaneous breaking of ${\cal N}=1$ supersymmetry on AdS$_4$ down to the isometries of AdS$_4$. We show how to write the nonlinear supersymmetry transformation for this theory using the fermionic ambient space formalism. We also study the Lie superalgebras of candidate multi-field examples and rule out the existence of a supersymmetric special galileon on AdS$_4$.\] # Bonnefoy, Durieux, Nepveu ## Higher-derivative relations between scalars and gluons \[Links: [arXiv](https://arxiv.org/abs/2310.13041), [PDF](https://arxiv.org/pdf/2310.13041.pdf)\] \[Abstract: We extend the covariant [[0152 Colour-kinematics duality|color-kinematics duality]] introduced by Cheung and Mangan to effective field theories. We focus in particular on relations between the effective field theories of gluons only and of gluons coupled to bi-adjoint scalars. Maps are established between their respective equations of motion and between their tree-level scattering amplitudes. An additional rule for the replacement of flavor structures by kinematic factors realizes the map between higher-derivative amplitudes. As an example of new relations, the pure-gluon amplitudes of mass dimension up to eight, featuring insertions of the $F^3$ and $F^4$ operators which satisfy the traditional color-kinematics duality, can be generated at all multiplicities from just renormalizable amplitudes of gluons and bi-adjoint scalars. We also obtain closed-form expressions for the kinematic numerators of the dimension-six gluon effective field theory, which are valid in $D$ space-time dimensions. Finally, we find strong evidence that this extended covariant color-kinematics duality relates the $(DF)^2+$YM$(+\phi^3)$ theories which, at low energies, generate infinite towers of operators satisfying the traditional color-kinematics duality, beyond aforementioned $F^3$ and $F^4$ ones.\] # Boruch, Iliesiu, Yan ## Constructing all BPS black hole microstates from the gravitational path integral \[Links: [arXiv](https://arxiv.org/abs/2307.13051), [PDF](https://arxiv.org/pdf/2307.13051.pdf)\] \[Abstract: Understanding how to prepare and count black hole micro-states by using the [[0555 Gravitational path integral|gravitational path integral]] is one of the most important problems in quantum gravity. Nevertheless, a state-by-state count of [[0248 Black hole microstates|black hole microstates]] is difficult because the apparent number of degrees of freedom available in the gravitational effective theory can vastly exceed the entropy of the black hole, even in the special case of [[0178 BPS|BPS]] black holes. In this paper, we show that we can use the gravitational path integral to prepare a basis for the Hilbert space of all BPS black hole microstates. We find that the dimension of this Hilbert space computed by an explicit state count is in complete agreement with the degeneracy obtained from the Gibbons-Hawking prescription. Specifically, this match includes all non-perturbative corrections in $1/G_N$. Such corrections are, in turn, necessary in order for this degeneracy of BPS states to match the non-perturbative terms in the $1/G_N$ expansion in the string theory count of such microstates.\] # Boruch, Lin, Yan ## Exploring supersymmetric wormholes in $\cal{N} = 2$ SYK with chords \[Links: [arXiv](https://arxiv.org/abs/2308.16283), [PDF](https://arxiv.org/pdf/2308.16283.pdf)\] \[Abstract: A feature the $\mathcal{N}=2$ supersymmetric [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] (SYK) model shares with extremal black holes is an exponentially large number of ground states that preserve supersymmetry. In fact, the dimension of the ground state subsector is a finite fraction of the total dimension of the SYK Hilbert space. This fraction has a remarkably simple bulk interpretation as the probability that the zero-temperature wormhole -- a supersymmetric Einstein-Rosen bridge -- has vanishing length. Using chord techniques, we compute the zero-temperature Hartle-Hawking wavefunction; the results reproduce the ground state count obtained from boundary index computations, including non-perturbative corrections. Along the way, we improve the construction [arXiv:2003.04405](https://arxiv.org/abs/2003.04405) of the super-chord Hilbert space and show that the transfer matrix of the empty wormhole enjoys an enhanced $\mathcal{N} = 4$ supersymmetry. We also obtain expressions for various two point functions at zero temperature. Finally, we find the expressions for the supercharges acting on more general wormholes with matter and present the superchord algebra.\] # Bousso, Miyaji ## Fluctuations in the Entropy of Hawking Radiation \[Links: [arXiv](https://arxiv.org/abs/2307.13920), [PDF](https://arxiv.org/pdf/2307.13920.pdf)\] \[Abstract: We use the [[0555 Gravitational path integral|gravitational path integral]] (GPI) to compute the fluctuations of the Hawking radiation entropy around the Page curve, in a two-dimensional model introduced by Penington *et al*. Before the Page time, we find that \delta $S = e^{-S}/\sqrt{2}$, where $S$ is the black hole entropy. This result agrees with the Haar-averaged entropy fluctuations of a bipartite system, which we also compute at leading order. After the Page time, we find that $\delta S \sim e^{-S}$, up to a prefactor that depends logarithmically on the width of the microcanonical energy window. This is not symmetric under exchange of subsystem sizes and so does not agree with the Haar average for a subsystem of fixed Hilbert space dimension. The discrepancy can be attributed to the fact that the black hole Hilbert space dimension is not fixed by the state preparation: even in a microcanonical ensemble with a top-hat smearing function, the GPI yields an additive fluctuation in the number of black hole states. This result, and the fact that the Page curve computed by the GPI is smooth, all point towards an [[0154 Ensemble averaging|ensemble]] interpretation of the GPI.\] # Bousso, Penington ## Holograms In Our World \[Links: [arXiv](https://arxiv.org/abs/2302.07892), [PDF](https://arxiv.org/pdf/2302.07892.pdf)\] \[Abstract: In [[0001 AdS-CFT|AdS/CFT]], the entanglement wedge EW$(B)$ is the portion of the bulk geometry that can be [[0219 Entanglement wedge reconstruction|reconstructed]] from a boundary region $B$; in other words, EW$(B)$ is the hologram of $B$. We extend this notion to arbitrary spacetimes. Given any gravitating region a, we define a max- and a min-entanglement wedge, $e_{\rm max}(a)$ and $e_{\rm min}(a)$, such that $e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$. Unlike their analogues in AdS/CFT, these two spacetime regions can differ already at the classical level, when the [[0212 Quantum extremal surface|generalized entropy]] is approximated by the area. All information outside $a$ in $e_{\rm max}(a)$ can flow inwards towards $a$, through quantum channels whose capacity is controlled by the areas of intermediate homology surfaces. In contrast, all information outside $e_{\rm min}(a)$ can flow outwards. The generalized entropies of appropriate entanglement wedges obey [[0218 Strong subadditivity|strong subadditivity]], suggesting that they represent the [[0301 Entanglement entropy|von Neumann entropies]] of ordinary quantum systems. The entanglement wedges of suitably independent regions satisfy a no-cloning relation. This suggests that it may be possible for an observer in $a$ to summon information from spacelike related points in $e_{\rm max}(a)$, using resources that transcend the semiclassical description of $a$.\] # Brown, Kampf, Oktem, Paranjape, Trnka ## Scalar BCJ Bootstrap \[Links: [arXiv](https://arxiv.org/abs/2305.05688), [PDF](https://arxiv.org/pdf/2305.05688.pdf)\] \[Abstract: In this letter, we study tree-level scattering amplitudes of scalar particles in the context of effective field theories. We use tools similar to the soft bootstrap to build an ansatz for cyclically ordered amplitudes and impose the [[0152 Colour-kinematics duality|Bern-Carrasco-Johansson (BCJ) relations]] as a constraint. We obtain a set of BCJ-satisfying amplitudes as solutions to our procedure, which can be thought of as special higher-derivative corrections to $SU(N)$ non-linear sigma model amplitudes satisfying BCJ relations to arbitrary multiplicity at leading order. The surprising outcome of our analysis is that BCJ conditions on higher-point amplitudes impose constraints on lower-point amplitudes, and they relate coefficients at different orders in the derivative expansion. This shows that BCJ conditions are much more restrictive than soft limit behavior, allowing only for a very small set of solutions.\] # Bu, Seet ## Celestial holography and AdS3/CFT2 from a scaling reduction of twistor space \[Links: [arXiv](https://arxiv.org/abs/2306.11850), [PDF](https://arxiv.org/pdf/2306.11850.pdf)\] \[Abstract: Celestial amplitudes obtained from [[0079 Mellin transform|Mellin transforming]] 4d momentum space scattering amplitudes contain distributional delta functions, hindering the application of conventional CFT techniques. In this paper, we propose to bypass this problem by recognizing Mellin transforms as integral transforms projectivizing certain components of the angular momentum. It turns out that the Mellin transformed wavefunctions in the conformal primary basis can be regarded as representatives of certain cohomology classes on the minitwistor space of the hyperbolic slices of 4d Minkowski space. Geometrically, this amounts to treating 4d Minkowski space as the embedding space of AdS3. By considering scattering of such on-shell wavefunctions on the projective spinor bundle PS of Euclidean AdS3, we bypass the difficulty of the distributional properties of celestial correlators using the traditional [[0073 AdS3-CFT2|AdS3/CFT2]] dictionary and find conventional 2d CFT correlators for the scaling reduced Yang-Mills theory living on the hyperbolic slices. In the meantime, however, one is required to consider action functionals on the auxiliary space PS, which introduces additional difficulties. Here we provide a framework to work on the projective spinor bundle of hyperbolic slices, obtained from a careful scaling reduction of the twistor space of 4d Minkowski spacetime.\] # Buchel, Cremonini, Early ## Holographic transport beyond the supergravity approximation \[Links: [arXiv](https://arxiv.org/abs/2312.05377), [PDF](https://arxiv.org/pdf/2312.05377.pdf)\] \[Abstract: We set up a unified framework to efficiently compute the shear and bulk [[0430 Holographic shear viscosity|viscosities]] of strongly coupled gauge theories with gravitational holographic duals involving [[0006 Higher-derivative gravity|higher derivative corrections]]. We consider both Weyl$^4$ corrections, encoding the finite 't Hooft coupling corrections of the boundary theory, and Riemann$^2$ corrections, responsible for non-equal central charges $c\ne a$ of the theory at the ultraviolet fixed point. Our expressions for the viscosities in higher derivative holographic models are extracted from a radially conserved current and depend only on the horizon data.\] # Bzowski, McFadden, Skenderis ## Renormalisation of IR divergences and holography in de Sitter \[Links: [arXiv](https://arxiv.org/abs/2312.17316), [PDF](https://arxiv.org/pdf/2312.17316.pdf)\] \[Abstract: We formulate a renormalisation procedure for IR divergences of tree-level in-in late-time de Sitter correlators. These divergences are due to the infinite volume of spacetime and are analogous to the divergences that appear in AdS dealt with by [[0209 Holographic renormalisation|holographic renormalisation]]. Regulating the theory using dimensional regularisation, we show that one can remove all infinities by adding local counterterms at the future boundary of dS in the [[0042 Schwinger-Keldysh techniques|Schwinger-Keldysh path integral]]. The counterterms amount to renormalising the late-time bulk field. We frame the discussion in terms of bulk scalar fields in dS, using tree-level correlators of massless and conformal scalars for illustration. The relation to AdS via analytic continuation is discussed, and we show that different versions of the analytic continuation appearing in the literature are equivalent to each other. In AdS, one needs to add counterterms that are related to [[0306 Weyl anomaly|conformal anomalies]], and also to renormalise the source part of the bulk field. The analytic continuation to dS projects out the traditional AdS counterterms, and links the renormalisation of the sources to the renormalisation of the late-time bulk field. We use these results to establish holographic formulae that relate tree-level dS in-in correlators to CFT correlators at up to four points, and we provide two proofs: one using the connection between the dS wavefunction and the partition function of the dual CFT, and a second by direct evaluation of the in-in correlators using the Schwinger-Keldysh formalism. The renormalisation of the bulk IR divergences is mapped by these formulae to UV renormalisation of the dual CFT via local counterterms, providing structural support for a possible duality. We also recast the regulated holographic formulae in terms of the AdS amplitudes of shadow fields, but show that this relation breaks down when renormalisation is required.\] # Caceres, Guglielmo, Kent, Misobuchi ## Out-of-time-order correlators and Lyapunov exponents in sparse SYK \[Links: [arXiv](https://arxiv.org/abs/2306.07345), [PDF](https://arxiv.org/pdf/2306.07345.pdf)\] \[Abstract: We use a combination of analytical and numerical methods to study [[0482 Out-of-time-order correlator|out-of-time order correlators (OTOCs)]] in the [[0569 Sparse SYK|sparse Sachdev-Ye-Kitaev]] (SYK) model. We find that at a given order of $N$, the standard result for the $q$-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter, $k$. We present an algorithm to sum the diagrams at any given order of $1/(kq)n$. We also study OTOCs numerically as a function of the sparsity parameter and determine the [[0466 Lyapunov exponent|Lyapunov exponent]]. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finite $N$ becomes more significant for larger values of $N$ .\] # Campoleoni, Delfante, Pekar, Petropoulos, Rivera-Betancour, Vilatte ## Flat from anti-de Sitter \[Links: [arXiv](https://arxiv.org/abs/2309.15182), [PDF](https://arxiv.org/pdf/2309.15182.pdf)\] \[Abstract: Ricci-flat solutions to Einstein's equations in four dimensions are obtained as the flat limit of Einstein spacetimes with negative cosmological constant. In the limiting process, the anti-de Sitter energy--momentum tensor is expanded in Laurent series in powers of the cosmological constant, endowing the system with the infinite number of boundary data, characteristic of the asymptotically flat solution space. The governing flat Einstein dynamics is recovered as the limit of the original energy--momentum conservation law and from the additional requirement of the line-element finiteness, providing at each order the necessary set of flux-balance equations for the boundary data. This analysis is conducted using a covariant version of the Newman--Unti gauge designed for taking advantage of the boundary Carrollian structure emerging at vanishing cosmological constant and its Carrollian attributes such as the Cotton tensor.\] # Caron-Huot, Giroux, Hannesdottir, Mizera (Aug) ## What can be measured asymptotically? \[Links: [arXiv](https://arxiv.org/abs/2308.02125), [PDF](https://arxiv.org/pdf/2308.02125.pdf)\] \[Abstract: We consider asymptotic observables in quantum field theories in which the S-matrix makes sense. We argue that in addition to scattering amplitudes, a whole compendium of inclusive observables exists where the time-ordering is relaxed. These include expectation values of electromagnetic or gravitational radiation fields as well as [[0482 Out-of-time-order correlator|out-of-time-order]] amplitudes. We explain how to calculate them in two ways: by relating them to amplitudes and products of amplitudes, and by using a generalization of the LSZ reduction formula. As an application, we discuss one-loop master integrals contributing to gravitational radiation in the post-Minkowski expansion, emphasizing the role of classical cut contributions and highlighting the different infrared physics of in-in observables.\] # Caron-Huot, Giroux, Hannesdottir, Mizera (Oct) ## Crossing beyond scattering amplitudes \[Links: [arXiv](https://arxiv.org/abs/2310.12199), [PDF](https://arxiv.org/pdf/2310.12199.pdf)\] \[Abstract: We find that different asymptotic measurements in quantum field theory can be related to one another through new versions of crossing symmetry. Assuming analyticity, we conjecture generalized crossing relations for multi-particle processes and the corresponding paths of analytic continuation. We prove them to all multiplicity at tree-level in quantum field theory and string theory. We illustrate how to practically perform analytic continuations on loop-level examples using different methods, including unitarity cuts and differential equations. We study the extent to which anomalous thresholds away from the usual physical region can cause an analytic obstruction to crossing when massless particles are involved. In an appendix, we review and streamline historical proofs of four-particle crossing symmetry in gapped theories.\] # Casini, Landea, Torroba ## Irreversibility, QNEC, and defects \[Links: [arXiv](https://arxiv.org/abs/2303.16935), [PDF](https://arxiv.org/pdf/2303.16935.pdf)\] \[Abstract: We first present an analysis of infinitesimal null deformations for the entanglement entropy, which leads to a major simplification of the proof of the $C$, $F$ and $A$-theorems in quantum field theory. Next, we study the [[0405 Quantum null energy condition|quantum null energy condition]] (QNEC) on the light-cone for a CFT. Finally, we combine these tools in order to establish the irreversibility of renormalization group flows on planar $d$-dimensional defects, embedded in $D$-dimensional conformal field theories. This proof completes and unifies all known defect irreversibility theorems for defect dimensions $d\le 4$. The $F$-theorem on defects ($d=3$) is a new result using information-theoretic methods. For $d \ge 4$ we also establish the monotonicity of the relative entropy coefficient proportional to $R^{d-4}$. The geometric construction connects the proof of irreversibility with and without defects through the QNEC inequality in the bulk, and makes contact with the proof of [[0218 Strong subadditivity|strong subadditivity]] of [[0145 Generalised area|holographic entropy]] taking into account quantum corrections.\] ## In holography - scenario I: if we do not fix $G_N$ - need [[0218 Strong subadditivity|SSA]] for [[0007 RT surface|RT]] (ensured by [[0480 Null energy condition|NEC]]) - scenario II: if we fix $G_N$ - needs [[0218 Strong subadditivity|SSA]] for the bulk entropy with quantum corrections (ensured by [[0243 Quantum focusing conjecture|QFC]]) - the bulk is considered as having a defect flow irreversibility theorem - "In this case, the bulk remains pure AdS, but there is a bulk scalar field whose boundary condition changes between Newman and Dirichlet. From the bulk point of view this looks precisely like a defect flow." # Cassani, Ruiperez, Turetta ## Boundary terms and conserved charges in higher-derivative gauged supergravity \[Links: [arXiv](https://arxiv.org/abs/2304.06101), [PDF](https://arxiv.org/pdf/2304.06101.pdf)\] \[Abstract: We address some issues in [[0385 Supergravity corrections|higher-derivative gauged supergravity]] with [[0089 Chern-Simons theory|Chern-Simons]] terms, focusing on the five-dimensional case. We discuss the [[0138 Variational principle|variational problem]] with Dirichlet boundary conditions as well as holographic renormalization in asymptotically locally AdS spacetimes, and derive the corresponding boundary terms. We then employ Wald's formalism in order to define conserved charges associated to local symmetries (diffeomorphisms and $U(1)$ gauge transformations), taking into account the effect of generic gauge Chern-Simons terms. We prove that the first law of black hole mechanics and the quantum statistical relation hold in this setup. Chern-Simons terms also lead us to distinguish between [[0019 Covariant phase space|Noether charges]] and Page (or Komar) charges which satisfy the Gauss law. We make use of the latter to compute corrections to the angular momentum and electric charge of the supersymmetric black hole in AdS$_5$ from its corrected near-horizon geometry. This also allows us to derive the microcanonical form of the [[0004 Black hole entropy|entropy]] as a function of the conserved charges relying entirely on the near-horizon geometry. Finally, we comment on four-derivative gauged supergravity in four dimensions, showing that field redefinitions permit to simplify the action at linear order in the corrections, so that the equations of motion are those of the two-derivative theory.\] # Castro, Coman, Fliss, Zukowski (Mar) ## Keeping matter in the loop in dS$_3$ quantum gravity \[Links: [arXiv](https://arxiv.org/abs/2302.12281), [PDF](https://arxiv.org/pdf/2302.12281)\] \[Abstract: We propose a mechanism that couples matter fields to three-dimensional [[0545 de Sitter quantum gravity|de Sitter quantum gravity]]. Our construction is based on the [[0089 Chern-Simons theory|Chern-Simons]] formulation of [[0002 3D gravity|three-dimensional Euclidean gravity]], and it centers on a collection of Wilson loops winding around Euclidean de Sitter space. We coin this object a [[0653 Wilson spool|Wilson spool]]. To construct the spool, we build novel representations of $\mathfrak{su}(2)$. To evaluate the spool, we adapt and exploit several known exact results in Chern-Simons theory. Our proposal correctly reproduces the one-loop determinant of a free massive scalar field on $S^3$ as $G_N\to 0$. Moreover, allowing for quantum metric fluctuations, it can be systematically evaluated to any order in perturbation theory.\] # Castro, Coman, Fliss, Zukowski (Apr, Letter) ## Coupling Fields to 3D Quantum Gravity via Chern-Simons Theory \[Links: [arXiv](https://arxiv.org/abs/2304.02668), [PDF](https://arxiv.org/pdf/2304.02668)\] \[Abstract: We propose a mechanism that couples matter fields to [[0002 3D gravity|three-dimensional quantum gravity]], which can be used for theories with a positive or negative cosmological constant. Our proposal is rooted in the Chern-Simons formulation of three-dimensional gravity and makes use of the [[0653 Wilson spool|Wilson spool]], a collection of Wilson loops winding around closed paths of the background. We show that the Wilson spool correctly reproduces the one-loop determinant of a free massive scalar field on rotating black holes in AdS$_3$ and Euclidean dS$_3$ as $G_N\to 0$. Moreover, we describe how to incorporate quantum metric fluctuations into this formalism.\] # Chakraborty, Chakravarty, Godet, Paul, Raju (a) ## The Hilbert space of de Sitter quantum gravity \[Links: [arXiv](https://arxiv.org/abs/2303.16315), [PDF](https://arxiv.org/pdf/2303.16315.pdf)\] \[Abstract: We obtain solutions of the [[0345 Wheeler-DeWitt (WdW) equation|Wheeler-DeWitt equation]] with positive cosmological constant for a closed universe in the large-volume limit. We argue that this space of solutions provides a complete basis for the Hilbert space of [[0545 de Sitter quantum gravity|quantum gravity in an asymptotically de Sitter spacetime]]. Our solutions take the form of a universal phase factor multiplied by distinct diffeomorphism invariant functionals, with simple Weyl transformation properties, that obey the same [[0106 Ward identity|Ward identities]] as a CFT partition function. The Euclidean vacuum corresponds to a specific choice of such a functional but other choices are equally valid. Each functional can be thought of as specifying a "theory" and, in this sense, the space of solutions is like "theory space". We describe another basis for the Hilbert space where all states are represented as excitations of the vacuum that have a specific constrained structure. This gives the finite $G_N$ generalization of the basis proposed by Higuchi in terms of group averaging, which we recover in the nongravitational limit.\] ## Refs - simultaneously released [[2023#Chakraborty, Chakravarty, Godet, Paul, Raju (b)]] # Chakraborty, Chakravarty, Godet, Paul, Raju (b) ## Holography of information in de Sitter space \[Links: [arXiv](https://arxiv.org/abs/2303.16316), [PDF](https://arxiv.org/pdf/2303.16316.pdf)\] \[Abstract: We study the natural norm on the space of solutions to the [[0345 Wheeler-DeWitt (WdW) equation|Wheeler-DeWitt equation]] in an asymptotically de Sitter spacetime. We propose that the norm is obtained by integrating the squared wavefunctional over field configurations and dividing by the volume of the diff-and-Weyl group. We impose appropriate gauge conditions to fix the diff-and-Weyl redundancy and obtain a finite expression for the norm using the Faddeev-Popov procedure. This leads to a ghost action that has zero modes corresponding to a residual conformal subgroup of the diff-and-Weyl group. By keeping track of these zero modes, we show that Higuchi's norm for group-averaged states emerges from our prescription in the nongravitational limit. We apply our formalism to cosmological correlators and propose that they should be understood as gauge-fixed observables. We identify the symmetries of these observables. In a nongravitational theory, it is necessary to specify such correlators everywhere on a Cauchy slice to identify a state in the Hilbert space. In a theory of quantum gravity, we demonstrate a version of the principle of holography of information: cosmological correlators in an arbitrarily small region suffice to completely specify the state.\] ## Refs - simultaneously released [[2023#Chakraborty, Chakravarty, Godet, Paul, Raju (a)]] - [[0545 de Sitter quantum gravity]] # Chakraborty, Ordonez, Valdivia-Mera ## Path integral derivation of the thermofield double state in causal diamonds \[Links: [arXiv](https://arxiv.org/abs/2312.03541), [PDF](https://arxiv.org/pdf/2312.03541.pdf)\] \[Abstract: In this article, we follow the framework given in the article Physica A, 158, pg 58-63 (1989) by R. Laflamme to derive the [[0574 Thermofield double|thermofield double]] state for a causal diamond using the Euclidean path integral formalism, and subsequently derive the causal diamond temperature. The interpretation of the physical and fictitious system in the thermofield double state arises naturally from the boundary conditions of the fields defined on the Euclidean sections of the cylindrical background geometry $S^{1}_{\beta}\times \mathbb{R}$, where $\beta$ defines the periodicity of the Euclidean time coordinate and $S^{1}_{\beta}$ is the one-dimensional sphere (circle). The temperature detected by a static diamond observer at $x=0$ matches with the thermofield double temperature derived via this path integral procedure.\] # Chakraborty, Maggio, Silvestrini, Pani ## Dynamical tidal Love numbers of Kerr-like compact objects \[Links: [arXiv](https://arxiv.org/abs/2310.06023), [PDF](https://arxiv.org/pdf/2310.06023.pdf)\] \[Abstract: We develop a framework to compute the tidal response of a Kerr-like compact object in terms of its reflectivity, compactness, and spin, both in the static and the frequency-dependent case. Here we focus on the low-frequency regime, which can be solved fully analytically. We highlight some remarkable novel features, in particular: i) Even in the zero-frequency limit, the [[0581 Tidal Love numbers|tidal Love numbers]] (TLNs) depend on the linear-in-frequency dependence of the object's reflectivity in a nontrivial way. ii) Intriguingly, the static limit of the frequency-dependent TLNs is discontinuous, therefore the static TLNs differ from the static limit of the (phenomenologically more interesting) frequency-dependent TLNs. This shows that earlier findings regarding the static TLNs of ultracompact objects correspond to a measure-zero region in the parameter space, though the logarithmic behavior of the TLNs in the black hole limit is retained. iii) In the non-rotating case, the TLNs generically vanish in the zero-frequency limit (just like for a black hole), except when the reflectivity is ${\cal R}=1+{\cal O}(M\omega)$, in which case they vanish with a model-dependent scaling, which is generically logarithmic, in the black-hole limit. The TLNs initially grow with frequency, for any nonzero reflectivity, and then display oscillations and resonances tied up with the quasi-normal modes of the object. iv) For rotating compact objects, the TLNs decrease when the reflectivity decreases or the rotation parameter increases. Our results lay the theoretical groundwork to develop model-independent tests of the nature of compact objects using tidal effects in gravitational-wave signals.\] # Chandra ## Euclidean wormholes for individual 2d CFTs \[Links: [arXiv](https://arxiv.org/abs/2305.07183), [PDF](https://arxiv.org/pdf/2305.07183.pdf)\] \[Abstract: We interpret appropriate families of Euclidean wormhole solutions of AdS$_3$ gravity in individual 2d CFTs as replica wormholes described by branching around the time-symmetric apparent horizons of black holes sourced by the backreaction of heavy point particles. These wormholes help describe a rich formalism to coarse grain pure states in 2d CFTs dual to the black hole geometries because the wormhole amplitudes match with the [[0293 Renyi entropy|Renyi entropies]] of CFT states obtained by decohering the pure states in a specific way. This formalism can be generalised to coarse grain pure states in several copies of the dual CFT dual to multi-boundary black holes using wormhole solutions with higher genus boundaries using which we illustrate that coarse graining away the interior of multi-boundary black holes sets the [[0300 Mutual information|mutual information]] between any two copies of the dual CFT to zero. Furthermore, this formalism of coarse graining pure states can be extended to decohere transition matrices between pure states which helps interpret more general families of wormhole solutions including those with non replica-symmetric boundary conditions in individual CFTs. The [[0052 Pseudo-entropy|pseudo entropy]] of the decohered transition matrices has interesting holographic interpretation in terms of the area of minimal surfaces on appropriate black hole or wormhole geometries. The wormhole solutions which show up in the coarse graining formalism also compute the Renyi entropies of [[0304 Hawking radiation|Hawking radiation]] after the Page time in a setup which generalizes the West Coast model to [[0002 3D gravity|3d gravity]]. Using this setup, we discuss the evaporation of one-sided black holes sourced by massive point particles and multi-boundary black holes in 3d gravity.\] # Chandra, Hartman ## Toward random tensor networks and holographic codes in CFT \[Links: [arXiv](https://arxiv.org/abs/2302.02446), [PDF](https://arxiv.org/pdf/2302.02446.pdf)\] \[Abstract: In holographic CFTs satisfying eigenstate thermalization, there is a regime where the operator product expansion can be approximated by a [[0368 Random tensor network|random tensor network]]. The geometry of the tensor network corresponds to a spatial slice in the holographic dual, with the tensors discretizing the radial direction. In spherically symmetric states in any dimension and more general states in 2d CFT, this leads to a holographic [[0146 Quantum error correction|error-correcting code]], defined in terms of OPE data, that can be systematically corrected beyond the random tensor approximation. The code is shown to be isometric for light operators outside the horizon, and non-isometric inside, as expected from general arguments about bulk reconstruction. The transition at the horizon occurs due to a subtle breakdown of the Virasoro identity block approximation in states with a complex interior.\] # Chen ## Complex-valued Holographic Pseudo Entropy via Real-time AdS/CFT Correspondence \[Links: [arXiv](https://arxiv.org/abs/2302.14303), [PDF](https://arxiv.org/pdf/2302.14303.pdf)\] \[Abstract: The pseudo entropy is a promising recent generalization of the [[0301 Entanglement entropy|entanglement entropy]] to the situations in which both the initial and final state are involved, with the density matrix promoted to the transition matrix. However, contrast to the non-Hermiticity of the generic transition matrix, the [[0052 Pseudo-entropy|holographic pseudo entropy]] formulated via the Euclidean [[0001 AdS-CFT|AdS/CFT]] turns out to be always real-valued, which potentially conceals the crucial natures of this novel quantity. In this note, we make first attempt to formulate a real-time prescription for computations to incorporate naturally the pseudo entropy, as a generally complex-valued entanglement measure, into the AdS/CFT context. It is then conjectured that the holographic pseudo entropy is dual to the extremal codimension-2 area surface in Lorentzian AdS spacetime, but may receive imaginary contributions from the extrinsic curvature of the area surface, which is not included in the covariant holographic entanglement entropy. In this real-time prescription, the holographic pseudo entropy can be considered as a generalization of the covariant holographic entanglement entropy, as well.\] # Chen, de Rham, Margalit, Tolley ## Surfin' pp-waves with Good Vibrations: Causality in the presence of stacked shockwaves \[Links: [arXiv](https://arxiv.org/abs/2309.04534), [PDF](https://arxiv.org/pdf/2309.04534.pdf)\] \[Abstract: Relativistic [[0118 Causality constraints for gravity|causality]] constrains the S-matrix both through its [[0120 Analyticity constraints|analyticity]], and by imposing lower bounds on the scattering [[0091 Boundary causality|time delay]]. These bounds are easiest to determine for spacetimes which admit either a timelike or null Killing vector. We revisit a class of pp-wave spacetimes and carefully determine the scattering time delay for arbitrary incoming states in the eikonal, semi-classical, and Born approximations. We apply this to the EFT of gravity in arbitrary dimensions. It is well-known that higher-dimension operators such as the [[0425 Gauss-Bonnet gravity|Gauss-Bonnet]] term, when treated perturbatively at low energies, can appear to make both positive and negative contributions to the time delays of the background geometry. We show that even when multiple [[0117 Shockwave|shockwaves]] are stacked, the corrections to the scattering time delay relative to the background are generically unresolvable within the regime of validity of the effective field theory so long as the Wilson coefficients are of order unity. This is in agreement with previously derived [[0119 Positivity bounds|positivity]]/bootstrap bounds and the requirement that infrared causality be maintained in consistent low-energy effective theories, irrespective of the UV completion.\] # Chen, Heydeman, Wang, Zhang ## Probing Supersymmetric Black Holes with Surface Defects \[Links: [arXiv](https://arxiv.org/abs/2306.05463), [PDF](https://arxiv.org/pdf/2306.05463.pdf)\] \[Abstract: It has long been conjectured that the large $N$ [[0441 Confinement-deconfinement transition|deconfinement phase transition]] of $\mathcal{N}=4$ ${\rm SU}(N)$ super-Yang-Mills corresponds via AdS/CFT to the [[0012 Hawking-Page transition|Hawking-Page transition]] in which black holes dominate the thermal ensemble, and quantitative evidence of this has come through the recent matching of the superconformal index of ${1\over 16}$-BPS states to the supersymmetric [[0004 Black hole entropy|black hole entropy]]. We introduce the half-BPS Gukov-Witten surface defect as a probe of the superconformal index, which also serves as an order parameter for the deconfinement transition. This can be studied directly in field theory as a modification of the usual unitary matrix model or in the dual description as a D3-brane probe in the background of a (complex) supersymmetric black hole. Using a saddle point approximation, we determine our defect index in the large N limit as a simple function of the chemical potentials and show independently that it is reproduced by the renormalized action of the brane in the black hole background. Along the way, we also comment on the Cardy limit and the thermodynamics of the D3-brane in the generalized ensemble. The defect index sharply distinguishes between the confining and the deconfining phases of the gauge theory and thus is a supersymmetric non-perturbative order parameter for these large $N$ phase transitions which deserves further investigation. Finally, our work provides an example where the properties of a black hole coupled to an external system can be analyzed precisely.\] # Chen, Hu ## Bulk reconstruction in flat holography \[Links: [arXiv](https://arxiv.org/abs/2312.13574), [PDF](https://arxiv.org/pdf/2312.13574.pdf)\] \[Abstract: In this note, we discuss bulk reconstruction of massless free fields in flat space from the highest-weight representation of boundary Carrollian conformal field theory (CCFT). We expand the bulk field as a sum of infinite descendants of a primary state defined in the boundary CCFT, and discuss the Lorentz invariant bulk-boundary propagator in detail for the BMS$_3$/CCFT$_2$ case. In our calculation, it is necessary to introduce a nonzero mass at the very beginning and take it to be vanishing at the end. The framework we proposed has potential to probe local bulk physics from the boundary CCFT.\] # Chen, Hikida, Taki, Uetoko ## Complex saddles of Chern-Simons gravity and dS$_3$/CFT$_2$ correspondence \[Links: [arXiv](https://arxiv.org/abs/2306.03330), [PDF](https://arxiv.org/pdf/2306.03330)\] \[Abstract: We examine the black hole solutions of dS$_3$ gravity by applying the explicit [[0545 de Sitter quantum gravity|dS3/CFT2]] correspondence. The gravity theory is described by [[0089 Chern-Simons theory|Chern-Simons theory]] with complex gauge group $SL(2,\mathbb{C})$, and the complexified theory is known to have too many saddle points. We determine the set of "allowable geometry" from dual CFT correlators. Concretely, we classify the possible complex solutions corresponding to dS$_3$ [[0465 de Sitter black holes|black holes]] from [[0562 Liouville theory|Liouville]] two-point functions. We extend the analysis to Liouville multi-point functions and among others we study geometry corresponding to two linked Wilson loops on $S^3$ by the monodromy matrix of Liouville four-point function. Some parts of the results were presented in a previous letter but here they are explained in more details and extended in various ways. In particular, we generalize the results to the case with [[0421 Higher-spin gravity|higher-spin gravity]] by focusing the effects of higher-spin charges.\] # Chen, Ivo, Maldacena ## Comments on the double cone wormhole \[Links: [arXiv](https://arxiv.org/abs/2310.11617), [PDF](https://arxiv.org/pdf/2310.11617.pdf)\] \[Abstract: In this paper we revisit the double cone wormhole introduced by [[2018#Saad, Shenker, Stanford|Saad, Shenker, and Stanford]] (SSS), which was shown to reproduce the ramp in the spectral form factor. As a first approximation we can say that this solution computes $\textrm{Tr}[e^{-iKT}]$, a trace of the "evolution" operator that generates Schwarzschild time translations on the two sided wormhole geometry. This point of view leads to a simple way to compute the normalization factor of the wormhole. When we have bulk matter fields, SSS suggested using a modified evolution $\tilde K$ which involves a slightly complex geometry, so that we are really computing $\textrm{Tr}[e^{-i\tilde{K}T}]$. We argue that, for general black holes, the spectrum of $\tilde K$ is given by quasinormal mode frequencies. We explain that this reproduces various features that were previously predicted from the spectral form factor on hydrodynamics grounds. We also give a general algebraic construction of the modified boost in terms of operators constructed from half sided modular inclusions. For the special case of [[0050 JT gravity|JT gravity]], we work out the backreaction of matter on the geometry of the double cone and find that it deforms the geometry in an undesirable direction. We finally give some comments on the possible physical interpretation of $\tilde K$.\] # Chen, Turiaci ## Spin-Statistics for Black Hole Microstates \[Links: [arXiv](https://arxiv.org/abs/2309.03478), [PDF](https://arxiv.org/pdf/2309.03478.pdf)\] \[Abstract: The [[0555 Gravitational path integral|gravitational path integral]] can be used to compute the number of [[0248 Black hole microstates|black hole states]] for a given energy window, or the free energy in a thermal ensemble. In this article we explain how to use the gravitational path integral to compute the separate number of bosonic and fermionic black hole microstates. We do this by comparing the partition function with and without the insertion of $(-1)^{\sf F}$. In particular we introduce a universal rotating black hole that contributes to the partition function in the presence of $(-1)^{\sf F}$. We study this problem for black holes in asymptotically flat space and in AdS, putting constraints on the high energy spectrum of holographic CFTs (not necessarily supersymmetric). Finally, we analyze wormhole contributions to related quantities.\] ## Refs - boundary study of boson-fermion cancellations: [[2018#Cherman, Shifman, Unsal]] ## Boundary conditions ![[ChenTuriaci2023_fig1a.png|300]] - fermions are always antiperiodic around the blue cycle and around the horizontal cycle $\varphi\sim\varphi+2\pi$; they get a factor of $-e^{\beta \Omega J}$ around the red cycle (bosons get $+e^{\beta \Omega J}$). - when $\beta \Omega=2\pi i$, $\operatorname{Tr}\left(e^{-\beta H} e^{\beta \Omega J}\right)=\operatorname{Tr}\left(e^{-\beta H} e^{2\pi i J}\right)$ - but this is just $Z_{\text {spin }}(\beta)=\operatorname{Tr}(-1)^{\mathrm{F}} e^{-\beta H}$ since $(-1)^{\mathrm{F}}=e^{2 \pi \mathrm{i} J}$ (n.b. $J$ is half-integer for fermions) - so fermions get $-e^{2\pi iJ}=+1$ around the red cycle, which is periodic. ## Saddle dominance - in the canonical ensemble, for the dimensions studied, thermal AdS always dominates - with gauge field, can fix charge and make thermal AdS disallowed - in microcanonical ensemble, there is large contribution from the rotating black hole in AdS$_4$ and AdS$_3$ but not in AdS$_5$ ## Some results ### Charged case in flat space - $Q=0$: $S_{\mathrm{spin}}(E, Q=0)=\frac{1}{2} \cdot S(E, Q=0)$ - $Q\to E$: $S_{\mathrm{spin}}$ approaches $S$, i.e., all states have the same statistics (either all bosonic or all fermionic) ## Spectral form factor - at late time, the [[0062 Spectral form factor|spectral form factor]] is insensitive to the insertion of $(-1)^\mathsf{F}$ - with susy, wormholes do not contribute to the square of the index; without susy, there is no such argument ## Questions - what if there are two directions of rotation, $J_1$ and $J_2$ - what if the boundary is a product of two spheres # Cheung, Derda, Helset, Parra-Martinez ## Soft Phonon Theorems \[Links: [arXiv](https://arxiv.org/abs/2301.11363), [PDF](https://arxiv.org/pdf/2301.11363.pdf)\] \[Abstract: A variety of condensed matter systems describe gapless modes that can be interpreted as Nambu-Goldstone bosons of spontaneously broken Poincaré symmetry. In this paper we derive new [[0009 Soft theorems|soft theorems]] constraining the tree-level scattering of these degrees of freedom, as exhibited in solids, fluids, superfluids, and framids. These soft theorems are in one-to-one correspondence with various broken symmetries, including spacetime translations, Lorentz boosts, and, for the case of fluids, volume-preserving diffeomorphisms. We also implement a bootstrap in which the enhanced vanishing of amplitudes in the soft limit is taken as an input, thus sculpting out a subclass of exceptional solid, fluid, and framid theories.\] # Choi, Larsen ## AdS$_2$ Holography and Effective QFT \[Links: [arXiv](https://arxiv.org/abs/2302.13917), [PDF](https://arxiv.org/pdf/2302.13917.pdf)\] \[Abstract: We discuss AdS$_2$ quantum gravity from an unconventional perspective that emphasizes bulk geometry. In our approach, AdS$_2$ has no boundary, there are no divergences that require renormalization, and the dilaton of [[0050 JT gravity|JT-gravity]] can be omitted altogether. The result is the standard Schwarzian theory. However, it may be advantageous that our derivation just relies on conventional [[0001 AdS-CFT|AdS/CFT correspondence]] and effective quantum field theory. For example, it clarifies the symmetry breaking pattern. It also puts the non-compact AdS$_2$ topology on the same footing as compact Riemann surfaces.\] # Chougule ## Explorations in 2+1 AdS Pure Gravity: Path Integral Formulation and Partition Function Analyses in BTZ Mini-Superspace \[Links: [arXiv](https://arxiv.org/abs/2308.05363), [PDF](https://arxiv.org/pdf/2308.05363.pdf)\] \[Abstract: In this work, we employ the Hamiltonian approach to analyze the [[0464 Lorentzian path integral|Lorentzian path integral]] in 2+1 AdS gravity, with an aim to sum over all possible geometries, including naked singularities and [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black holes, between fixed initial and final surfaces. A novel path integral measure, grounded on the metric over [[0254 Minisuperspace|mini-superspace]], is proposed for executing the path integral. Shifting to Euclidean geometries, we derive the temperature and angular potential of Euclidean naked singularities within the partition function. Significantly, without utilizing conformal field theory, we extract logarithmic corrections to the entropy of BTZ black holes and compute the entropy of naked singularities, along with their log corrections.\] # Chua, Hartman ## Black hole wavefunctions and microcanonical states \[Links: [arXiv](https://arxiv.org/abs/2309.05041), [PDF](https://arxiv.org/pdf/2309.05041.pdf)\] \[Abstract: We consider the problem of defining a [[0462 Microcanonical ensemble|microcanonical]] [[0574 Thermofield double|thermofield double state]] at fixed energy and angular momentum from the [[0555 Gravitational path integral|gravitational path integral]]. A semiclassical approximation to this state is obtained by imposing a mixed boundary condition on an initial time surface. We analyze the corresponding boundary value problem and gravitational action. The overlap of this state with the canonical thermofield double state, which is interpreted as the [[0162 No-boundary wavefunction|Hartle-Hawking wavefunction]] of an eternal black hole in a mini-superspace approximation, is calculated semiclassically. The relevant saddlepoint is a higher-dimensional, rotating generalization of the wedge geometry that has been studied in two-dimensional gravity.\] # Chua, Jiang ## Hartle-Hawking state and its factorization in 3d gravity \[Links: [arXiv](https://arxiv.org/abs/2309.05126), [PDF](https://arxiv.org/pdf/2309.05126.pdf)\] \[Abstract: We study 3d quantum gravity with two asymptotically anti-de Sitter regions, in particular, using its relation with coupled Alekseev-Shatashvili theories and Liouville theory. Expressions for the [[0162 No-boundary wavefunction|Hartle-Hawking state]], thermal 2$n$-point functions, torus wormhole correlators and [[0345 Wheeler-DeWitt (WdW) equation|Wheeler-DeWitt wavefunctions]] in different bases are obtained using the ZZ boundary states in Liouville theory. Exact results in 2d [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] are uplifted to [[0002 3D gravity|3d gravity]], with two copies of [[0562 Liouville theory|Liouville theory]] in 3d gravity playing a similar role as Schwarzian theory in JT gravity. The connection between 3d gravity and the Liouville ZZ boundary states are manifested by viewing [[0086 Banados-Teitelboim-Zanelli black hole|BTZ black holes]] as Maldacena-Maoz wormholes, with the two wormhole boundaries glued along the ZZ boundaries. In this work, we also study the [[0249 Factorisation problem|factorization problem]] of the Hartle-Hawking state in 3d gravity. With the relevant defect operator that imposes the necessary topological constraint for contractibility, the trace formula in gravity is modified in computing the [[0301 Entanglement entropy|entanglement entropy]]. This trace matches with the one from [[0415 Von Neumann algebra|von Neumann algebra]] considerations, further reproducing the [[0004 Black hole entropy|Bekenstein-Hawking area formula]] from entanglement entropy. Lastly, we propose a calculation for off-shell geometrical quantities that are responsible for the ramp behavior in the late time two-point functions, which follows from the understanding of the Liouville FZZT boundary states in the context of 3d gravity, and the identification between Verlinde loop operators in Liouville theory and ''[[0051 Baby universes|baby universe]]'' operators in 3d gravity.\] ## Comments - canonical quantisation, where the spatial slice is an annulus - because there are two boundaries, we get two Liouville theories # Ciambelli, Freidel, Leigh ## Null Raychaudhuri: Canonical Structure and the Dressing Time \[Links: [arXiv](https://arxiv.org/abs/2309.03932), [PDF](https://arxiv.org/pdf/2309.03932.pdf)\] \[Abstract: We initiate a study of gravity [[0408 Raychaudhuri equation|focusing]] on generic null hypersurfaces, non-perturbatively in the Newton coupling. We present an off-shell account of the extended phase space of the theory, which includes the expected spin-2 data as well as spin-0, spin-1 and arbitrary matter degrees of freedom. We construct the charges and the corresponding kinematic [[0360 Poisson bracket|Poisson brackets]], employing a Beltrami parameterization of the spin-2 modes. We explicitly show that the constraint algebra closes, the details of which depend on the non-perturbative mixing between spin-0 and spin-2 modes. Finally we show that the spin zero sector encodes a notion of a clock, called dressing time, which is dynamical and conjugate to the constraint. It is well-known that the null [[0408 Raychaudhuri equation|Raychaudhuri equation]] describes how the geometric data of a null hypersurface evolve in null time in response to gravitational radiation and external matter. Our analysis leads to three complementary viewpoints on this equation. First, it can be understood as a Carrollian stress tensor conservation equation. Second, we construct spin-0, spin-2 and matter stress tensors that act as generators of null time reparametrizations for each sector. This leads to the perspective that the null Raychaudhuri equation can be understood as imposing that the sum of CFT-like stress tensors vanishes. Third, we solve the Raychaudhuri constraint non-perturbatively. The solution relates the dressing time to the spin-2 and matter boost charge operators. Finally we establish that the corner charge corresponding to the boost operator in the dressing time frame is concave. These results show that the notion of an observer can be thought of as emerging from the gravitational degrees of freedom themselves. We briefly mention that the construction offers new insights into focusing conjectures.\] # Cohen, Lu, Sutherland ## On Amplitudes and Field Redefinitions \[Links: [arXiv](https://arxiv.org/abs/2312.06748), [PDF](https://arxiv.org/pdf/2312.06748.pdf)\] \[Abstract: We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic [[0355 Field redefinitions|field redefinitions]], starting from an assumed behavior of the one-particle-irreducible effective action. The form of the recursion relation resembles the operation of raising the rank of a tensor by acting with a covariant derivative. This inspires a geometric interpretation, whose features and flaws we investigate.\] # Colafranceschi, Dong, Marolf, Wang ## Algebras and Hilbert spaces from gravitational path integrals: Understanding Ryu-Takayanagi/HRT as entropy without invoking holography \[Links: [arXiv](https://arxiv.org/abs/2310.02189), [PDF](https://arxiv.org/pdf/2310.02189.pdf)\] \[Abstract: Recent works by [[2022#Chandrasekaran, Penington, Witten|Chandrasekaran, Penington, and Witten]] have shown in various special contexts that the quantum-corrected [[0007 RT surface|Ryu-Takayanagi]] (RT) entropy (or its covariant Hubeny-Rangamani-Takayanagi (HRT) generalization) can be understood as computing an entropy on an algebra of bulk observables. These arguments do not rely on the existence of a holographic dual field theory. We show that analogous-but-stronger results hold in any UV-completion of asymptotically anti-de Sitter quantum gravity with a [[0555 Gravitational path integral|Euclidean path integral]] satisfying a simple and familiar set of axioms. We consider a quantum context in which a standard Lorentz-signature classical bulk limit would have Cauchy slices with asymptotic boundaries $B_L \sqcup B_R$ where both $B_L$ and $B_R$ are compact manifolds without boundary. Our main result is then that (the UV-completion of) the quantum gravity path integral defines type I [[0415 Von Neumann algebra|von Neumann algebras]] ${\cal A}^{B_L}_L, {\cal A}^{B_R}_{R}$ of observables acting respectively at $B_L$, $B_R$ such that ${\cal A}^{B_L}_L, {\cal A}^{B_R}_{R}$ are commutants. The path integral also defines entropies on ${\cal A}^{B_L}_L, {\cal A}^{B_R}_R$. Positivity of the Hilbert space inner product then turns out to require the entropy of any projection operator to be quantized in the form $\ln N$ for some $N \in {\mathbb Z}^+$ (unless it is infinite). As a result, our entropies can be written in terms of standard density matrices and standard Hilbert space traces. Furthermore, in appropriate semiclassical limits our entropies are computed by the RT-formula with quantum corrections. Our work thus provides a Hilbert space interpretation of the RT entropy. Since our axioms do not severely constrain UV bulk structures, they may be expected to hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.\] # Colafranceschi, Marolf, Wang ## A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture) \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higher-dimensional anti-de Sitter space. One aspect of the correspondence is an equivalence of density matrices or, if one ignores normalizations, of positive operators. On the CFT side of the correspondence, any two positive operators $A,B$ will satisfy the trace inequality $\operatorname{Tr}(AB) \leq \operatorname{Tr}(A) \operatorname{Tr}(B)$. This relation holds on any Hilbert space ${\cal H}$ and is deeply associated with the fact that the algebra $B({\cal H})$ of bounded operators on ${\cal H}$ is a type I [[0415 Von Neumann algebra|von Neumann]] factor. Holographic bulk theories must thus satisfy a corresponding condition, which we investigate below. In particular, we argue that the Euclidean [[0555 Gravitational path integral|gravitational path integral]] respects this inequality at all orders in the semi-classical expansion and with arbitrary higher-derivative corrections. The argument relies on a conjectured property of the classical gravitational action, which in particular implies a positive action conjecture for quantum gravity wavefunctions. We prove this conjecture for [[0050 JT gravity|Jackiw-Teitelboim gravity]] and we also motivate it for more general theories.\] # Collier, Eberhardt, Muhlmann, Rodriguez ## The Virasoro Minimal String \[Links: [arXiv](https://arxiv.org/abs/2309.10846), [PDF](https://arxiv.org/pdf/2309.10846.pdf)\] \[Abstract: We introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral. The worldsheet theory consists of Liouville CFT with central charge $c\geq 25$ coupled to timelike Liouville CFT with central charge $26-c$. The double-scaled matrix integral has as its leading density of states the universal Cardy density of primaries in a two-dimensional CFT, thus motivating the name Virasoro minimal string. The duality holds for any value of the continuous parameter c and reduces to the JT gravity/matrix integral duality in the large central charge limit. It thus provides a precise stringy realization of [[0050 JT gravity|JT gravity]]. The main observables of the Virasoro minimal string are quantum analogues of the Weil-Petersson volumes, which are computed as absolutely convergent integrals of worldsheet CFT correlators over the moduli space of Riemann surfaces. By exploiting a relation of the Virasoro minimal string to three-dimensional gravity and intersection theory on the moduli space of Riemann surfaces, we are able to give a direct derivation of the duality. We provide many checks, such as explicit numerical - and in special cases, analytic - integration of string diagrams, the identification of the CFT boundary conditions with asymptotic boundaries of the two-dimensional spacetime, and the matching between the leading non-perturbative corrections of the worldsheet theory and the matrix integral. As a byproduct, we discover natural conformal boundary conditions for timelike Liouville CFT.\] # Collier, Eberhardt, Zhang ## Solving 3d Gravity with Virasoro TQFT \[Links: [arXiv](https://arxiv.org/abs/2304.13650), [PDF](https://arxiv.org/pdf/2304.13650.pdf); Talks: [Collier at INI](https://youtu.be/fWYiJDh6Hp4?feature=shared); [Eberhardt at Dual Mystery](https://youtu.be/ZzBHWGnnnCE?feature=shared)\] \[Abstract: We propose a precise reformulation of [[0002 3D gravity|3d quantum gravity]] with negative cosmological constant in terms of a [[0607 Topological QFT|topological quantum field theory]] based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as ''[[0596 Virasoro TQFT|Virasoro TQFT]].'' This TQFT is similar, but importantly not equivalent, to $\text{SL}(2,\mathbb{R})$ [[0089 Chern-Simons theory|Chern-Simons]] theory. This sharpens the folklore that 3d gravity is related to $\text{SL}(2,\mathbb{R})$ Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level. Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity. In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the [[0033 Central charge|central charge]]. Mathematically, the relation leads to many nontrivial conjectures for hyperbolic 3-manifolds, Virasoro [[0031 Conformal block|conformal blocks]] and [[0573 Crossing kernel|crossing kernels]].\] # Colville, Harrison, Maloney, Namjou ## Liouville theory and the Weil-Petersson geometry of moduli space: bordered, conic, and higher genus surfaces \[Links: [arXiv](https://arxiv.org/abs/2312.00323), [PDF](https://arxiv.org/pdf/2312.00323.pdf)\] \[Abstract: [[0003 2D CFT|Two-dimensional conformal field theory]] is a powerful tool to understand the geometry of surfaces. Here, we study [[0562 Liouville theory|Liouville conformal field theory]] in the classical (large [[0033 Central charge|central charge]]) limit, where it encodes the geometry of the moduli space of Riemann surfaces. Generalizing previous work, we employ this to study moduli spaces of higher genus surfaces, surfaces with boundaries, and surfaces with cone points. In each case, the knowledge of classical conformal blocks provides an extremely efficient approximation to the Weil-Petersson metric on moduli space. We find detailed agreement with analytic results for volumes and geodesic lengths on moduli space.\] # Compere, Gralla, Wei ## An asymptotic framework for gravitational scattering \[Links: [arXiv](https://arxiv.org/abs/2303.17124), [PDF](https://arxiv.org/pdf/2303.17124.pdf)\] \[Abstract: Asymptotically flat spacetimes have been studied in five separate regions: future/past timelike infinity $i^\pm$, future/past null infinity $\mathcal{I}^\pm$, and spatial infinity $i^0$. We formulate assumptions and definitions such that the five infinities share a single [[0064 BMS group|Bondi-Metzner-Sachs (BMS) group]] of [[0060 Asymptotic symmetry|asymptotic symmetries]] and associated charges. We show how individual ingoing/outgoing massive bodies may be ascribed initial/final BMS charges and derive global conservation laws stating that the change in total charge is balanced by the corresponding radiative flux. This framework provides a foundation for the study of asymptotically flat spacetimes containing ingoing and outgoing ==massive bodies==, i.e., for generalized gravitational scattering. Among the new implications are rigorous definitions for quantities like initial/final spin, scattering angle, and impact parameter in multi-body spacetimes, without the use of any preferred background structure.\] ## Refs - [[0064 BMS group]] - [[0060 Asymptotic symmetry]] # Costello ## Bootstrapping two-loop QCD amplitudes \[Links: [arXiv](https://arxiv.org/abs/2302.00770), [PDF](https://arxiv.org/pdf/2302.00770.pdf)\] \[Abstract: Form factors of [[0136 Self-dual Yang-Mills|self-dual gauge theory]] are equal to correlators of an (extended) celestial chiral algebra. This suggests that these form factors can be computed using the "bootstrap" method familiar from 2d CFTs. The method can also be applied to certain QCD amplitudes, which are built from form-factors of self-dual gauge theory. In this paper this bootstrap method is applied to compute two-loop all-plus QCD amplitudes, for $SU(N)$ gauge theory with certain special matter content. A closed formula is presented for all single-trace amplitudes.\] ## Refs - [[0384 4d-2d twistorial correspondence]] # Cotler, Miller, Strominger ## An Integer Basis for Celestial Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2302.04905), [PDF](https://arxiv.org/pdf/2302.04905.pdf)\] \[Abstract: We present a discrete basis of solutions of the massless Klein-Gordon equation in 3+1 Minkowski space which transform as $sl(2,C)$ Lorentz/conformal primaries and descendants, and whose elements all have integer conformal dimension. We show that the basis is complete in the sense that the Wightman function can be expressed as a quadratic sum over the basis elements.\] # Cotler, Strominger ## Cosmic ER=EPR in dS/CFT \[Links: [arXiv](https://arxiv.org/abs/2302.00632), [PDF](https://arxiv.org/pdf/2302.00632.pdf)\] \[Abstract: In the [[0251 dS-CFT|dS/CFT]] correspondence, bulk states on global spacelike slices of de Sitter space are dual to (in general) entangled states in the tensor product of the dual CFT Hilbert space with itself. We show, using a [[0325 Quasi-normal modes|quasinormal mode]] basis, that the Euclidean vacuum (for free scalars in a certain mass range) is a thermofield double state in the dual CFT description, and that the global de Sitter geometry emerges from quantum entanglement between two copies of the CFT. Tracing over one copy of the CFT produces a mixed thermal state describing a single static causal diamond.\] # Crawley, Guevara, Himwich, Strominger ## Self-Dual Black Holes in Celestial Holography \[Links: [arXiv](https://arxiv.org/abs/2302.06661), [PDF](https://arxiv.org/pdf/2302.06661.pdf)\] \[Abstract: We construct two-dimensional quantum states associated to four-dimensional linearized rotating [[0234 Self-dual gravity|self-dual]] black holes in $(2,2)$ signature Klein space. The states are comprised of global conformal primaries circulating on the [[0250 Celestial torus|celestial torus]], the Kleinian analog of the [[0022 Celestial sphere|celestial sphere]]. By introducing a generalized tower of Goldstone operators we identify the states as coherent exponentiations carrying an infinite tower of ${\rm w}_{1+\infty}$ charges or soft hair. We relate our results to recent approaches to black hole scattering, including a connection to Wilson lines, $\mathcal{S}$-matrix results, and [[0010 Celestial holography|celestial holography]] in curved backgrounds.\] # Cremonini, McPeak, Tang ## Electric shocks: bounding Einstein-Maxwell theory with time delays on boosted RN backgrounds \[Links: [arXiv](https://arxiv.org/abs/2312.17328), [PDF](https://arxiv.org/pdf/2312.17328.pdf)\] \[Abstract: The requirement that particles propagate causally on non-trivial backgrounds implies interesting constraints on higher-derivative operators. This work is part of a systematic study of the [[0119 Positivity bounds|positivity bounds]] derivable from time delays on shockwave backgrounds. First, we discuss shockwaves in field theory, which are infinitely boosted Coulomb-like field configurations. We show how a positive time delay implies positivity of four-derivative operators in scalar field theory and electromagnetism, consistent with the results derived using dispersion relations, and we comment on how additional higher-derivative operators could be included. We then turn to gravitational [[0117 Shockwave|shockwave]] backgrounds. We compute the infinite boost limit of Reissner-Nordström black holes to derive charged shockwave backgrounds. We consider photons traveling on these backgrounds and interacting through four-derivative corrections to Einstein-Maxwell theory. The inclusion of gravity introduces a logarithmic term into the time delay that interferes with the straightforward bounds derivable in pure field theory, a fact consistent with [[2014#Camanho, Edelstein, Maldacena, Zhiboedov|CEMZ]] and with recent results from dispersion relations. We discuss two ways to extract a physically meaningful quantity from the logarithmic time delay -- by introducing an IR cutoff, or by considering the derivative of the time delay -- and comment on the bounds implied in each case. Finally, we review a number of additional shockwave backgrounds which might be of use in future applications, including spinning shockwaves, those in higher dimensions or with a cosmological constant, and shockwaves from boosted extended objects.\] # Czech, Shuai, Tang ## Information recovery in the Hayden-Preskill protocol \[Links: [arXiv](https://arxiv.org/abs/2310.16988), [PDF](https://arxiv.org/pdf/2310.16988.pdf)\] \[Abstract: We revisit information retrieval from evaporating black holes in the [[0217 Hayden-Preskill decoding criterion|Hayden-Preskill protocol]], treating the black hole dynamics as Haar-random. We compute, down to the first exponentially suppressed terms, all integer-indexed Rényi [[0300 Mutual information|mutual informations]] between a black hole, its radiation, and a reference that catalogues Alice's diaries. We find that dropping a diary into a young black hole effectively delays the Page time. We also compute the radiation : diary [[0166 Reflected entropy|reflected]] Rényi entropies, and identify a technical reason why they cannot be continued to the reflected entropy by the replica trick.\] # Czech, Shuai, Wang, Zhang ## Holographic Entropy Inequalities and the Topology of Entanglement Wedge Nesting \[Links: [arXiv](https://arxiv.org/abs/2309.15145), [PDF](https://arxiv.org/pdf/2309.15145.pdf)\] \[Abstract: We prove two new infinite families of [[0259 Holographic entropy cone|holographic entropy inequalities]]. A key tool is a graphical arrangement of terms of inequalities, which is based on [[0142 Entanglement wedge nesting|entanglement wedge nesting]] (EWN). It associates the inequalities with tessellations of the torus and the projective plane, which reflect a certain topological aspect of EWN. The inequalities prove a prior conjecture about the structure of the holographic entropy cone and show an interesting interplay with differential entropy.\] # Dabholkar, Moitra (Jun) ## Finite Entanglement Entropy in String Theory \[Links: [arXiv](https://arxiv.org/abs/2306.00990), [PDF](https://arxiv.org/pdf/2306.00990.pdf)\] \[Abstract: We analyze the one-loop quantum entanglement entropy in ten-dimensional Type-II string theory using the orbifold method by analytically continuing in $N$ the genus-one partition function for string orbifolds on $\mathbb{R}^2/\mathbb{Z}_N$ conical spaces known for all odd integers $N > 1$. We show that the tachyonic contributions to the orbifold partition function can be appropriately summed and analytically continued to an expression that is finite in the physical region $0 < N \leq 1$ resulting in a finite and calculable answer for the [[0301 Entanglement entropy|entanglement entropy]]. We discuss the implications of the finiteness of the entanglement entropy for the [[0131 Information paradox|information paradox]], quantum gravity, and [[0001 AdS-CFT|holography]].\] # Dabholkar, Moitra (Dec) ## Quantum Entanglement on Black Hole Horizons in String Theory and Holography \[Links: [arXiv](https://arxiv.org/abs/2312.14253), [PDF](https://arxiv.org/pdf/2312.14253.pdf)\] \[Abstract: We compute the exact one-loop partition function of $\mathbb{Z}_N$ orbifolds of Euclidean BTZ black hole with the aim to compute the [[0301 Entanglement entropy|entanglement entropy]] of the black hole horizon [[0565 Entanglement entropy in string theory|in string theory]] as a function of the mass and spin of the black hole and the $\mathrm{AdS}_3$ radius. We analyze the tachyonic contribution to the modular integrand for the partition function known for odd integers $N>1$ and show that it admits an analytic continuation resulting in a finite answer for the modular integral in the physical region $0< N \leq 1$. We discuss the flat space limit and the relevance of this computation for quantum gravity near black hole horizons and holography in relation to the thermal entropy.\] # Das, Ganguli ## Quantum Butterfly Effect at the Crossroads of Spontaneous Symmetry Breaking \[Links: [arXiv](https://arxiv.org/abs/2304.14272), [PDF](https://arxiv.org/pdf/2304.14272.pdf)\] \[Abstract: In classical mechanics, spontaneous symmetry breaking of the Hamiltonian can embroil the dynamics of some regular systems into [[0008 Quantum chaos|chaos]]. The classical and quantum pictures are not entirely different in these broken symmetric regions. There exists a correspondence between them, but for a brief time window. However, our numerical observations show that quantum mechanics can emulate the opposite role and forge exponential fluctuations in classically non-chaotic systems within an early-time window by introducing a symmetry-breaking term to the Hamiltonian. In this work, we spontaneously break the existing symmetry in three one-dimensional quantum mechanical models by varying perturbation strength to bring anomaly into the system. With the help of numerical diagnostic tools such as [[0482 Out-of-time-order correlator|OTOC]], Loschmidt echo and [[0062 Spectral form factor|spectral form factor]] (SFF) we detect the anomalies that may sweep into the system with the introduction of the asymmetry. Our primary focus is on the exponential growth of OTOC as it reduces to the [[0466 Lyapunov exponent|Lyapunov exponent]] in the classical limit. However, these exponential growths of OTOC are not widespread over the entire potential well but are limited only to the eigenstates in the neighbourhood of the broken symmetry. These results suggest that the exponential growth of OTOC, backed by Loschmidt echo and SFF, is due to asymmetry. In other words, OTOC detects the effect of symmetry-breaking, which is often synonymous with the butterfly effect.\] ## Summary - exponential growth of [[0482 Out-of-time-order correlator|OTOC]] is usually associated with having a local maximum; but using examples, it is demonstrated that symmetry breaking, rather than the existence of local maximum, is actually responsible - with symmetry breaking, even though the system is classically non-chaotic, it can still exhibit exponential OTOC growth! # Das, Sachdeva, Sarkar ## Bulk reconstruction using timelike entanglement in (A)dS \[Links: [arXiv](https://arxiv.org/abs/2312.16056), [PDF](https://arxiv.org/pdf/2312.16056.pdf)\] \[Abstract: It is well-known that the entanglement entropies for spacelike subregions, and the associated modular Hamiltonians play a crucial role in the [[0026 Bulk reconstruction|bulk reconstruction]] program within Anti de-Sitter (AdS) holography. Explicit examples of [[0016 HKLL|HKLL]] map exist mostly for the cases where the emergent bulk region is the so-called entanglement wedge of the given boundary subregion. However, motivated from the complex pseudo-entropy in Euclidean conformal field theories (CFT), one can talk about a '[[0606 Timelike entanglement|timelike entanglement]]' in Lorentzian CFTs dual to AdS spacetimes. One can then utilize this boundary timelike entanglement to define a boundary 'timelike modular Hamiltonian'. We use constraints involving these Hamiltonians in a manner similar to how it was used for spacelike cases, and write down bulk operators in regions which the spacelike [[0007 RT surface|Ryu-Takayanagi surfaces]] do not probe. In the context of two dimensional CFT, we re-derive the HKLL formulas for free bulk scalar fields behind the AdS black hole, and for de Sitter flat slicings. In this method, one no longer requires the knowledge of bulk dynamics for sub-horizon holography.\] # Davies, Reall ## A non-perturbative second law of black hole mechanics in effective field theory \[Links: [arXiv](https://arxiv.org/abs/2312.07659), [PDF](https://arxiv.org/pdf/2312.07659.pdf)\] \[Abstract: We describe a method for defining dynamical [[0004 Black hole entropy|black hole entropy]] in gravitational effective field theories (EFTs). The entropy is constructed order by order in derivatives. For any fixed number of derivatives, the entropy satisfies a non-perturbative [[0005 Black hole second law|second law of black hole mechanics]] if the black hole remains within the regime of validity of EFT. In equilibrium the entropy reduces to the [[0559 Wald entropy|Wald entropy]]. It reduces to the entropy defined by Hollands et al in theories of vacuum gravity with up to 10 derivatives.\] # de Boer, Hollander, Rolph ## Page curves and replica wormholes from random dynamics \[Links: [arXiv](https://arxiv.org/abs/2311.07655), [PDF](https://arxiv.org/pdf/2311.07655.pdf)\] \[Abstract: We show how to capture both the non-unitary Page curve and [[0206 Replica wormholes|replica wormhole]]-like contributions that restore unitarity in a toy quantum system with random dynamics. The motivation is to find the simplest dynamical model that captures this aspect of gravitational physics. In our model, we evolve with an ensemble of Hamiltonians with GUE statistics within microcanonical windows. The entropy of the averaged state gives the non-unitary curve, the averaged entropy gives the unitary curve, and the difference comes from matrix index contractions in the Haar averaging that connect the density matrices in a replica wormhole-like manner.\] # de Boer, Liska, Post, Sasieta ## A principle of maximum ignorance for semiclassical gravity \[Links: [arXiv](https://arxiv.org/abs/2311.08132), [PDF](https://arxiv.org/pdf/2311.08132.pdf)\] \[Abstract: The principle of maximum ignorance posits that the coarse-grained description of a system is maximally agnostic about its underlying microscopic structure. We briefly review this principle for [[0579 Random matrix theory|random matrix theory]] and for the [[0040 Eigenstate thermalisation hypothesis|eigenstate thermalization hypothesis]]. We then apply this principle in holography to construct ensembles of random mixed states. This leads to an ensemble of microstates which models our microscopic ignorance, and which on average reproduces the effective semiclassical physics of a given bulk state. We call this ensemble the state-averaging ansatz. The output of our model is a prediction for semiclassical contributions to variances and higher statistical moments over the ensemble of microstates. The statistical moments provide coarse-grained -- yet gravitationally non-perturbative -- information about the microstructure of the individual states of the ensemble. We show that these contributions exactly match the on-shell action of known [[0278 Euclidean wormholes|wormhole]] configurations of the [[0555 Gravitational path integral|gravitational path integral]]. These results strengthen the view that wormholes simply parametrize the ignorance of the microstructure of a fundamental state, given a fixed semiclassical bulk description.\] # de Gioia, Raclariu ## Celestial Sector in CFT: Conformally Soft Symmetries \[Links: [arXiv](https://arxiv.org/abs/2303.10037), [PDF](https://arxiv.org/pdf/2303.10037.pdf)\] \[Abstract: We show that time intervals of width $\Delta \tau$ in 3-dimensional conformal field theories (CFT$_3$) on the Lorentzian cylinder admit an infinite dimensional symmetry enhancement in the limit $\Delta \tau \rightarrow 0$. The associated vector fields are approximate solutions to the conformal Killing equations in the strip labelled by a function and a conformal Killing vector on the sphere. An Inonu-Wigner contraction yields a set of symmetry generators obeying the extended [[0064 BMS group|BMS]]$_4$ algebra. We analyze the shadow stress tensor [[0106 Ward identity|Ward identities]] in CFT$_d$ on the Lorentzian cylinder with all operator insertions in infinitesimal time intervals separated by $\pi$. We demonstrate that both the ==leading and subleading conformally soft graviton theorems== in (d-1)-dimensional celestial CFT (CCFT$_{d-1}$) can be recovered from the transverse traceless components of these Ward identities in the limit $\Delta \tau \rightarrow 0$. A similar construction allows for the leading ==conformally soft gluon theorem== in CCFT$_{d-1}$ to be recovered from [[0039 Shadow transform|shadow]] current Ward identities in CFT$_d$.\] ## Refs - [[0009 Soft theorems]] - [[0454 Flat holography from AdS-CFT]] # Delgado ## The Bubble of Nothing under T-duality \[Links: [arXiv](https://arxiv.org/abs/2312.09291), [PDF](https://arxiv.org/pdf/2312.09291.pdf)\] \[Abstract: The [[0168 Bubble of nothing|bubble of nothing]] is a solution to Einstein's equations where a circle shrinks and pinches off smoothly. As such, it is one of the simplest examples of a dynamical cobordism to nothing. We take a first step in studying how this solution transforms under T-duality in bosonic string theory. Applying Buscher's rules reveals that the dual solution features a singular, strongly coupled core, with a circle blowing-up rather than pinching off. This naive approach to T-duality solely accounts for the zero-modes of the fields after dimensional reduction on the circle. For this reason, we argue that this is not the full picture that the T-dual solution should depend non-trivially on the dual circle. We point out evidence to this effect both in the gravity description and on the worldsheet. A more complete description of the T-dual object would require a full-fledged sigma model for the bubble of nothing. Nevertheless, inspired by similar examples in the literature, we detail one possible scenario where the stringy bubble of nothing is mediated by closed string tachyon condensation and we discuss its T-duality.\] # Deo, Dhivakar, Kundu ## Entropy-current for dynamical black holes in Chern-Simons theories of gravity \[Links: [arXiv](https://arxiv.org/abs/2306.12491), [PDF](https://arxiv.org/pdf/2306.12491)\] \[Abstract: We construct an entropy current and establish a local version of the classical [[0005 Black hole second law|second law of thermodynamics]] for dynamical black holes in Chern-Simons (CS) theories of gravity. We work in a chosen set of Gaussian null coordinates and assume the dynamics to be small perturbations around the Killing horizon. In explicit examples of both purely gravitational and mixed gauge gravity CS theories in (2+1) and (4+1)-dimensions, the entropy current is obtained by studying the off-shell structure of the equations of motion evaluated on the horizon. For the CS theory in (2+1) dimensions, we argue that the second law holds to quadratic order in perturbations by considering it as a low energy effective field theory with the leading piece given by Einstein gravity. In all such examples, we show that the construction of entropy current is invariant under the reparameterization of the null horizon coordinates. Finally, extending an existing formalism for diffeomorphism invariant theories, we construct an abstract proof for the linearised second law in arbitrary Chern-Simons theories in any given odd dimensions by studying the off-shell equations of motion. As a check of consistency, we verify that the outcome of this algorithmic proof matches precisely with the results obtained in explicit examples.\] # DeWolfe, Higginbotham ## Non-isometric codes for the black hole interior from fundamental and effective dynamics \[Links: [arXiv](https://arxiv.org/abs/2304.12345), [PDF](https://arxiv.org/pdf/2304.12345.pdf)\] \[Abstract: We introduce a new holographic map for encoding black hole interiors by including both fundamental and effective dynamics. This holographic map is constructed by evolving a state in the effective, semiclassical gravity description of the interior backwards in time to pull the degrees of freedom outside the black hole, before evolving forwards in time in the fundamental description. We show this ''backwards-forwards'' map is equivalent to a post-selection map of the type introduced by [[2022#Akers, Engelhardt, Harlow, Penington, Vardhan|Akers, Engelhardt, Harlow, Penington, and Vardhan]], and in the case of trivial effective interactions reduces to their model, while providing a suitable generalization when those interactions are nontrivial. We show the map is equivariant with respect to time evolution, and independent of any interactions outside the black hole. This construction includes interactions with an infaller in a way that preserves the unitarity of black hole evolution exactly and does not allow for superpolynomial computational [[0204 Quantum complexity|complexity]].\] # Dhivakar, Jalan ## Generalized Second Law for Non-minimally Coupled Matter Theories \[Links: [arXiv](https://arxiv.org/abs/2309.12782), [PDF](https://arxiv.org/pdf/2309.12782.pdf)\] \[Abstract: We prove the [[0082 Generalised second law|generalized second law]] (GSL) for [[0006 Higher-derivative gravity|higher curvature gravity]] theories when the matter sector is [[0338 Non-minimally coupled fields|non-minimally coupled]]. The validity of our proof is in the regime of linearized fluctuations about equilibrium black holes, which is the same regime as considered in the previous proofs by Wall and Sarkar. These proofs were provided in different gravity theories - for instance, [[0341 Lovelock gravity|Lovelock theory]] and higher curvature gravity - but the matter sector was always taken to be minimally coupled. In this article, we describe how to generalize the proof of linearized semi-classical GSL when the matter sector comes with non-minimal couplings. The proof proceeds by suitably evaluating the matter path integral in the stress tensor expectation value by treating the higher derivative couplings in an effective field theory setting. We use the recently established result of the linearized [[0005 Black hole second law|second law]] for such theories.\] # Di Ubaldo, Perlmutter (Jul) ## AdS$_3$/RMT$_2$ Duality \[Links: [arXiv](https://arxiv.org/abs/2307.03707), [PDF](https://arxiv.org/pdf/2307.03707.pdf)\] \[Abstract: We introduce a framework for quantifying [[0579 Random matrix theory|random matrix]] behavior of 2d CFTs and AdS$_3$ quantum gravity. We present a 2d CFT trace formula, precisely analogous to the Gutzwiller trace formula for [[0008 Quantum chaos|chaotic]] quantum systems, which originates from the $SL(2,\mathbb{Z})$ spectral decomposition of the [[0032 Virasoro algebra|Virasoro]] primary density of states. An analogy to Berry's diagonal approximation allows us to extract spectral statistics of individual 2d CFTs by coarse-graining, and to identify signatures of chaos and random matrix universality. This leads to a necessary and sufficient condition for a 2d CFT to display a linear ramp in its coarse-grained [[0062 Spectral form factor|spectral form factor]]. Turning to gravity, AdS$_3$ torus wormholes are cleanly interpreted as diagonal projections of squared partition functions of microscopic 2d CFTs. The projection makes use of Hecke operators. The Cotler-Jensen wormhole of AdS$_3$ pure gravity is shown to be extremal among wormhole amplitudes: it is the minimal completion of the random matrix theory correlator compatible with Virasoro symmetry and $SL(2,\mathbb{Z})$-invariance. We call this MaxRMT: the maximal realization of random matrix universality consistent with the necessary symmetries. Completeness of the $SL(2,\mathbb{Z})$ spectral decomposition as a trace formula allows us to factorize the Cotler-Jensen wormhole, extracting the microscopic object $Z_{\rm RMT}(\tau)$ from the coarse-grained product. This captures details of the spectrum of BTZ black hole microstates. $Z_{\rm RMT}(\tau)$ may be interpreted as an AdS$_3$ half-wormhole. We discuss its implications for the dual CFT and modular bootstrap at large central charge.\] # Di Ubaldo, Perlmutter (Aug) ## AdS$_3$ Pure Gravity and Stringy Unitarity \[Links: [arXiv](https://arxiv.org/abs/2308.01787), [PDF](https://arxiv.org/pdf/2308.01787.pdf)\] \[Abstract: We construct a unitary, modular-invariant torus partition function of a two-dimensional conformal field theory with a Virasoro primary spectral gap of $\Delta_* = \frac{c-1}{12}$ above the vacuum. The twist gap is identical, apart from two states $\mathcal{O}_*$ with spin scaling linearly in the central charge $c$. These states admit an AdS$_3$ interpretation as strongly coupled strings. All other states are black hole microstates.\] # Dodelson, Iossa, Karlsson, Lupsasca, Zhiboedov ## Black hole bulk-cone singularities \[Links: [arXiv](https://arxiv.org/abs/2310.15236), [PDF](https://arxiv.org/pdf/2310.15236.pdf)\] \[Abstract: Lorentzian correlators of local operators exhibit surprising [[0163 Bulk cone singularity|singularities]] in theories with gravity duals. These are associated with null geodesics in an emergent bulk geometry. We analyze singularities of the thermal response function dual to propagation of waves on the AdS Schwarzschild black hole background. We derive the analytic form of the leading singularity dual to a bulk geodesic that winds around the black hole. Remarkably, it exhibits a boundary group velocity larger than the speed of light, whose dual is the angular velocity of null geodesics at the photon sphere. The strength of this singularity is controlled by the classical [[0466 Lyapunov exponent|Lyapunov exponent]] associated with the instability of nearly bound photon orbits. In this sense, the bulk-cone singularity can be identified as the universal feature that encodes the ubiquitous black hole photon sphere in a dual holographic CFT. To perform the computation analytically, we express the two-point correlator as an infinite sum over Regge poles, and then evaluate this sum using WKB methods. We also compute the smeared correlator numerically, which in particular allows us to check and support our analytic predictions. We comment on the resolution of black hole bulk-cone singularities by stringy and gravitational effects into black hole bulk-cone "bumps". We conclude that these bumps are robust, and could serve as a target for simulations of black hole-like geometries in table-top experiments.\] # Dodelson, Iossa, Karlsson, Zhiboedov ## A thermal product formula \[Links: [arXiv](https://arxiv.org/abs/2304.12339), [PDF](https://arxiv.org/pdf/2304.12339.pdf)\] \[Abstract: We show that holographic thermal two-sided two-point correlators take the form of a product over [[0325 Quasi-normal modes|quasi-normal modes (QNMs)]]. Due to this fact, the two-point function admits a natural dispersive representation with a positive discontinuity at the location of QNMs. We explore the general constraints on the structure of QNMs that follow from the [[0030 Operator product expansion|operator product expansion]], the presence of the singularity inside the black hole, and the hydrodynamic expansion of the correlator. We illustrate these constraints through concrete examples. We suggest that the product formula for thermal correlators may hold for more general large $N$ [[0008 Quantum chaos|chaotic]] systems, and we check this hypothesis in several models.\] # Doi, Harper, Mollabashi, Takayanagi, Taki ## Timelike entanglement entropy \[Links: [arXiv](https://arxiv.org/abs/2302.11695), [PDF](https://arxiv.org/pdf/2302.11695)\] \[Abstract: We define a new complex-valued measure of information called the [[0606 Timelike entanglement|timelike entanglement entropy]] (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit definition of the timelike EE in 2d field theories is provided followed by numerical computations which agree with the analytic continuation of the replica method for CFTs. We argue that timelike EE should be correctly interpreted as another measure previously considered, the [[0052 Pseudo-entropy|pseudo entropy]], which is the [[0301 Entanglement entropy|von Neumann entropy]] of a reduced transition matrix. Our results strongly imply that the imaginary part of the pseudo entropy describes an emergent time which generalizes the notion of an emergent space from quantum entanglement. For holographic systems we define the timelike EE as the total complex valued area of a particular stationary combination of both space and timelike extremal surfaces which are homologous to the boundary region. For the examples considered we find explicit matching of our optimization procedure and the careful implementation of the Wick rotation in the boundary CFT. We also make progress on higher dimensional generalizations and relations to holographic pseudo entropy in de Sitter space.\] # Dong, Kudler-Flam, Rath ## A Modified Cosmic Brane Proposal for Holographic Renyi Entropy \[Links: [arXiv](https://arxiv.org/abs/2312.04625), [PDF](https://arxiv.org/pdf/2312.04625.pdf)\] \[Abstract: We propose a new formula for computing holographic [[0293 Renyi entropy|Renyi entropies]] in the presence of multiple extremal surfaces. Our proposal is based on computing the wave function in the basis of fixed-area states and assuming a diagonal approximation for the Renyi entropy. For Renyi index $n\geq1$, our proposal agrees with the existing cosmic brane proposal for holographic Renyi entropy. For $n<1$, however, our proposal predicts a new phase with leading order (in Newton's constant $G$) corrections to the cosmic brane proposal, even far from entanglement phase transitions and when bulk quantum corrections are unimportant. Recast in terms of optimization over [[0024 Fixed area states|fixed-area states]], the difference between the two proposals can be understood to come from the order of optimization: for $n<1$, the cosmic brane proposal is a minimax prescription whereas our proposal is a maximin prescription. We demonstrate the presence of such leading order corrections using illustrative examples. In particular, our proposal reproduces existing results in the literature for the PSSY model and high-energy eigenstates, providing a universal explanation for previously found leading order corrections to the $n<1$ Renyi entropies.\] # Dong, McBride, Weng ## Holographic Tensor Networks with Bulk Gauge Symmetries \[Links: [arXiv](https://arxiv.org/abs/2309.06436), [PDF](https://arxiv.org/pdf/2309.06436.pdf)\] \[Abstract: [[0054 Tensor network|Tensor networks]] are useful toy models for understanding the structure of entanglement in holographic states and [[0219 Entanglement wedge reconstruction|reconstruction of bulk operators within the entanglement wedge]]. They are, however, constrained to only prepare so-called "[[0024 Fixed area states|fixed-area states]]" with flat entanglement spectra, limiting their utility in understanding general features of holographic entanglement. Here, we overcome this limitation by constructing a variant of random tensor networks that enjoys bulk gauge symmetries. Our model includes a gauge theory on a general graph, whose gauge-invariant states are fed into a random tensor network. We show that the model satisfies the [[0212 Quantum extremal surface|quantum-corrected Ryu-Takayanagi formula]] with a nontrivial area operator living in the center of a gauge-invariant algebra. We also demonstrate nontrivial, $n$-dependent contributions to the [[0293 Renyi entropy|Rényi entropy]] and Rényi [[0300 Mutual information|mutual information]] from this area operator, a feature shared by general holographic states.\] # Dong, Remmen, Wang, Weng, Wu ## Holographic entanglement from the UV to the IR \[Links: [arXiv](https://arxiv.org/abs/2308.07952), [PDF](https://arxiv.org/pdf/2308.07952.pdf)\] \[Abstract: In [[0001 AdS-CFT|AdS/CFT]], observables on the boundary are invariant under renormalization group (RG) flow in the bulk. In this paper, we study [[0007 RT surface|holographic entanglement entropy]] under bulk RG flow and find that it is indeed invariant. We focus on tree-level RG flow, where massive fields in a UV theory are integrated out to give the IR theory. We explicitly show that in several simple examples, holographic entanglement entropy calculated in the UV theory agrees with that calculated in the IR theory. Moreover, we give an argument for this agreement to hold for general tree-level RG flow. Along the way, we generalize the replica method of calculating holographic entanglement entropy to bulk theories that include matter fields with nonzero spin.\] # Donnay (Review) ## Celestial holography: An asymptotic symmetry perspective \[Links: [arXiv](https://arxiv.org/abs/2310.12922), [PDF](https://arxiv.org/pdf/2310.12922.pdf)\] \[Abstract: We review the role that infinite-dimensional symmetries arising at the boundary of asymptotically flat spacetimes play in the context of the [[0010 Celestial holography|celestial holography]] program. Once recast into the language of conformal field theory, asymptotic symmetries provide key constraints on the sought-for celestial dual to quantum gravity in flat spacetimes.\] # Donnay, Giribet, Gonzalez, Puhm, Rojas ## Celestial open strings at one-loop \[Links: [arXiv](https://arxiv.org/abs/2307.03551), [PDF](https://arxiv.org/pdf/2307.03551.pdf)\] \[Abstract: We study [[0262 Celestial amplitude calculations|celestial amplitudes]] in string theory at one-loop. Celestial amplitudes describe scattering processes of boost eigenstates and relate to amplitudes in the more standard basis of momentum eigenstates through a [[0079 Mellin transform|Mellin transform]]. They are thus sensitive to both the ultraviolet and the infrared, which raises the question of how to appropriately take the field theory limit of string amplitudes in the celestial basis. We address this problem in the context of four-dimensional genus-one scattering processes of gluons in open string theory which reach the two-dimensional celestial sphere at null infinity. We show that the Mellin transform commutes with the adequate limit in the worldsheet moduli space and reproduces the celestial one-loop field theory amplitude expressed in the worldline formalism. The dependence on $\alpha'$ continues to be a simple overall factor in one-loop celestial amplitudes albeit with a power that is shifted by three units with respect to tree-level, thus making manifest that the dimensionless parameter $g_{10}^2/\alpha'^3$ organizes the loop expansion in the celestial basis.\] # Dowling, Kos, Modi ## Scrambling is Necessary but Not Sufficient for Chaos \[Links: [arXiv](https://arxiv.org/abs/2304.07319), [PDF](https://arxiv.org/pdf/2304.07319.pdf)\] \[Abstract: We show that [[0482 Out-of-time-order correlator|out-of-time-order correlators (OTOCs)]] constitute a probe for Local-Operator Entanglement (LOE). There is strong evidence that a volumetric growth of LOE is a faithful dynamical signature of [[0008 Quantum chaos|quantum chaos]], while OTOC decay corresponds to operator scrambling, often conflated with chaos. We show that rapid OTOC decay is a necessary but not sufficient condition for linear (chaotic) growth of the LOE entropy. We analytically support our results through wide classes of local-circuit models of many-body dynamics, including both ==integrable and non-integrable dual-unitary circuits==. We show sufficient conditions under which local dynamics leads to an equivalence of scrambling and chaos.\] # Draper, Farkas, Karydas ## Path Integral Factorization and the Gravitational Effective Action \[Links: [arXiv](https://arxiv.org/abs/2310.02101), [PDF](https://arxiv.org/pdf/2310.02101.pdf)\] \[Abstract: We discuss the factorization and continuity properties of fields in the Euclidean [[0555 Gravitational path integral|gravitational path integral]] with higher dimension operators constructed from powers of the Riemann tensor. We construct the boundary terms corresponding to the microcanonical ensemble and show that the saddle point approximation to the path integral with a quasilocal energy constraint generally yields a saddle point with discontinuous temperature. This extends a previous result for the Euclidean Schwarzschild-de Sitter geometry in Einstein gravity and shows that it is robust against at least some types of quantum corrections from heavy fields. As an application, we compute the entropy of SdS in $\text{D}=4$ using the BTZ method. Our result matches the entropy calculated using [[0559 Wald entropy|Wald's formula]].\] ## Factorisation - factorisation means: - $Z=\int_{\mathcal{T}} D \mathcal{B}_i Z\left(\mathcal{M}_1 | \mathcal{B}_i\right) Z\left(\mathcal{M}_2 |\mathcal{B}_i\right)$ - where $\mathcal{T}$ is an interface separating $\mathcal{M}$ into $\mathcal{M}_1$ and $\mathcal{M}_2$ - the questions is what field variables are included in $\mathcal{B}_i$? - not all data should be integrated over: some should be fixed (not generally continuous) and others should be integrated over (continuous) - consequences: when the interface is fixed or in the presence of a constraint, the fields at the stationary point may not be continuous # Eberhardt, Turiaci ## 2D dilaton gravity and the Weil-Petersson volumes with conical defects \[Links: [arXiv](https://arxiv.org/abs/2304.14948), [PDF](https://arxiv.org/pdf/2304.14948.pdf)\] \[Abstract: We derive the Weil-Petersson measure on the moduli space of hyperbolic surfaces with defects of arbitrary opening angles and use this to compute its volume. We conjecture a matrix integral computing the corresponding volumes and confirm agreement in simple cases. We combine this mathematical result with the equivariant localization approach to [[0050 JT gravity|Jackiw-Teitelboim gravity]] to justify a proposed exact solution of pure 2d dilaton gravity for a large class of dilaton potentials.\] # Ecker, Grumille, Valcarcel, Vassilevich ## Equivalences between 2D dilaton gravities, their asymptotic symmetries, and their holographic duals \[Links: [arXiv](https://arxiv.org/abs/2304.08523), [PDF](https://arxiv.org/pdf/2304.08523.pdf)\] \[Abstract: Dilaton gravities in two dimensions can be formulated as particular Poisson sigma models. Target space diffeomorphisms map different models to each other and establish a one-to-one correspondence between their classical solutions. We obtain a general form of such diffeomorphisms in Lorentzian and Euclidean signatures and use them to extend known holographic results, including the Schwarzian action on the asymptotic boundary, from [[0050 JT gravity|JT]] to a large class of dilaton gravity models.\] # Engelhardt, Liu ## Algebraic ER=EPR and Complexity Transfer \[Links: [arXiv](https://arxiv.org/abs/2311.04281), [PDF](https://arxiv.org/pdf/2311.04281.pdf)\] \[Abstract: We propose an algebraic definition of [[0220 ER=EPR|ER=EPR]] in the $G_N \to 0$ limit, which associates bulk spacetime connectivity/disconnectivity to the operator algebraic structure of a quantum gravity system. The new formulation not only includes information on the amount of entanglement, but also more importantly the structure of entanglement. We give an independent definition of a quantum wormhole as part of the proposal. This algebraic version of ER=EPR sheds light on a recent puzzle regarding spacetime disconnectivity in holographic systems with ${\cal O}(1/G_{N})$ entanglement. We discuss the emergence of quantum connectivity in the context of black hole evaporation and further argue that at the Page time, the black hole-radiation system undergoes a transition involving the transfer of an emergent type III$_{1}$ subalgebra of high [[0204 Quantum complexity|complexity]] operators from the black hole to radiation. We argue this is a general phenomenon that occurs whenever there is an exchange of dominance between two competing [[0212 Quantum extremal surface|quantum extremal surfaces]].\] # Engelhardt, Penington, Shahbazi-Moghaddam ## Twice Upon a Time: Timelike-Separated Quantum Extremal Surfaces \[Links: [arXiv](https://arxiv.org/abs/2308.16226), [PDF](https://arxiv.org/pdf/2308.16226.pdf)\] \[Abstract: The [[0196 Python's lunch|Python's Lunch]] conjecture for the [[0204 Quantum complexity|complexity]] of bulk reconstruction involves two types of nonminimal [[0212 Quantum extremal surface|quantum extremal surfaces ]] (QESs): bulges and throats, which differ by their local properties. The conjecture relies on the connection between bulk spatial geometry and quantum codes: a constricting geometry from bulge to throat encodes the bulk state nonisometrically, and so requires an exponentially complex Grover search to decode. However, thus far, the Python's Lunch conjecture is only defined for spacetimes where all QESs are spacelike-separated from one another. Here we explicitly construct (time-reflection symmetric) spacetimes featuring both timelike-separated bulges and timelike-separated throats. Interestingly, all our examples also feature a third type of QES, locally resembling a de Sitter bifurcation surface, which we name a bounce. By analyzing the Hessian of generalized entropy at a QES, we argue that this classification into throats, bulges and bounces is exhaustive. We then propose an updated Python's Lunch conjecture that can accommodate general timelike-separated QESs and bounces. Notably, our proposal suggests that the gravitational analogue of a [[0054 Tensor network|tensor network]] is not necessarily the time-reflection symmetric slice, even when one exists.\] # Erdmenger, Jian, Xian ## Universal chaotic dynamics from Krylov space \[Links: [arXiv](https://arxiv.org/abs/2303.12151), [PDF](https://arxiv.org/pdf/2303.12151.pdf)\] \[Abstract: Krylov state complexity measures the spread of the wavefunction in the Krylov basis, a particular basis that is uniquely constructed using the Hamiltonian of a given physical system. Viewing each basis vector as one site, this basis naturally constitutes a one-dimensional chain, so that the state evolution can be mapped to a particle propagating on the chain, and its position is the Krylov state complexity. Based on this interpretation, we derive an Ehrenfest theorem for the Krylov complexity, which reveals its close relation to the spectrum. In particular, we find that the Krylov state complexity is directly driven by the properly normalized [[0062 Spectral form factor|spectral form factor]]. This allows us to give an analytical expression for Krylov state complexity in random matrix theory. We also study the time evolution of the wavefunction in the Krylov basis. This provides the transition probability associated to the evolution of the initial state to the basis vector at a given site. For chaotic systems, including [[0579 Random matrix theory|random matrix theories]] and the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev model]], we numerically observe a universal rise-slope-ramp-plateau behavior of the transition probability, with a long linear ramp. For the Gaussian unitary ensemble, we analytically explain this universal behavior for the sites located on the first half of the chain. The long linear ramp in the transition probability at each site leads to a peak in the Krylov complexity at late times. For non-chaotic systems, the transition probability shows a different behavior without the linear ramp. Our results clarify which features of the wave function time evolution in Krylov space characterize chaos.\] # Eynard, Garcia-Failde, Gregori, Lewanski, Schippa ## Resurgent Asymptotics of Jackiw-Teitelboim Gravity and the Nonperturbative Topological Recursion \[Links: [arXiv](https://arxiv.org/abs/2305.16940), [PDF](https://arxiv.org/pdf/2305.16940.pdf)\] \[Abstract: Jackiw-Teitelboim dilaton-quantum-gravity localizes on a double-scaled random-matrix model, whose perturbative free energy is an asymptotic series. Understanding the resurgent properties of this asymptotic series, including its completion into a full transseries, requires understanding the nonperturbative instanton sectors of the matrix model for [[0050 JT gravity|Jackiw-Teitelboim gravity]]. The present work addresses this question by setting-up instanton calculus associated to eigenvalue tunneling (or ZZ-brane contributions), directly in the matrix model. In order to systematize such calculations, a nonperturbative extension of the topological recursion formalism is required -- which is herein both constructed and applied to the present problem. Large-order tests of the perturbative genus expansion validate the resurgent nature of Jackiw-Teitelboim gravity, both for its free energy and for its (multi-resolvent) correlation functions. Both ZZ and FZZT nonperturbative effects are required by resurgence, and they further display resonance upon the Borel plane. Finally, the resurgence properties of the multi-resolvent correlation functions yield new and improved resurgence formulae for the large-genus growth of Weil-Petersson volumes.\] # Fegebank, Kuzenko ## Quantisation of the gauge-invariant models for massive higher-spin bosonic fields \[Links: [arXiv](https://arxiv.org/abs/2310.00951), [PDF](https://arxiv.org/pdf/2310.00951)\] \[Abstract: In 2001, Zinoviev proposed a gauge-invariant formulation for a [[0588 Higher-spin fields|massive bosonic field with spin]] $s≥2$ in a spacetime of constant curvature. In this paper we carry out the Faddeev-Popov quantisation of this theory in $d$-dimensional Minkowski space. We also make use of the Zinoviev theory to derive a generalisation of the Singh-Hagen model for a massive integer-spin field in $d>4$ dimensions.\] # Feng, Yan, Gao, Lau, Yau ## Geometric Inequality for Axisymmetric Black Holes With Angular Momentum \[Links: [arXiv](https://arxiv.org/abs/2312.10590), [PDF](https://arxiv.org/pdf/2312.10590.pdf)\] \[Abstract: In an attempt to understand the [[0476 Penrose inequality|Penrose inequality]] for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi stationary conditions is considered for a case study. A new geometric definition of angular velocity of a rotating black hole is defined in terms of the momentum constraint, without any reference to a stationary Killing vector field. The momentum constraint is then shown to be equivalent to a Beltrami equation for compressible fluid flow. In terms of spinors, a generalised first law for rotating black holes (possibly with multi-connected horizon located along the symmetry axis) is then proven and may be regarded as a Penrose type inequality for black holes with angular momentum.\] # Fernandes, Lin, Mitra ## Celestial Eikonal Amplitudes in the Near-Horizon Region \[Links: [arXiv](https://arxiv.org/abs/2310.03430), [PDF](https://arxiv.org/pdf/2310.03430.pdf)\] \[Abstract: We investigate the [[0010 Celestial holography|celestial]] description of [[0436 Eikonal approximation|eikonal amplitudes]] mediated by soft gravitons in the near-horizon region of a Schwarzschild black hole. Our construction thus provides a celestial conformal field theory corresponding to a non-perturbative scattering process that accounts for event horizons on asymptotically flat spacetimes. We first construct the four-dimensional near-horizon eikonal amplitude from the known two-dimensional effective field theory amplitude, and then derive its celestial description from a [[0079 Mellin transform|Mellin transform]] in the near-horizon region. This celestial eikonal amplitude provides a result to all loop orders with a universal leading ultraviolet (UV) soft scaling behavior of the conformally invariant cross-ratio, and an infrared (IR) pole for the scaling dimension at each loop order. We argue these properties manifest soft graviton exchanges in the near-horizon region and consequently the soft UV behaviour of the amplitude.\] # Fernandez ## One-loop corrections to the celestial chiral algebra from Koszul Duality \[Links: [arXiv](https://arxiv.org/abs/2302.14292), [PDF](https://arxiv.org/pdf/2302.14292.pdf)\] \[Abstract: We consider [[0136 Self-dual Yang-Mills|self-dual Yang-Mills theory]] (SDYM) in four dimensions and its lift to holomorphic [[0557 BF theory|BF theory]] on [[0330 Twistor theory|twistor space]]. Following the work of Costello and Paquette, we couple SDYM to a quartic axion field, which guarantees associativity of the (extended) celestial chiral algebra at the quantum level. We demonstrate how to reproduce their one-loop quantum deformation to the chiral algebra using [[0510 Koszul duality|Koszul duality]].\] # Fiorucci, Grumiller, Ruzziconi ## Logarithmic Celestial Conformal Field Theory \[Links: [arXiv](https://arxiv.org/abs/2305.08913), [PDF](https://arxiv.org/pdf/2305.08913.pdf)\] \[Abstract: We argue that the [[0010 Celestial holography|celestial conformal field theory]] exhibits patterns of a logarithmic conformal field theory. We uncover a Jordan block structure involving the celestial stress tensor and its logarithmic partner, a composite operator built from the stress tensor and the Liouville field. Using a limiting process whose parameter corresponds to the infrared cut-off of gravity, we perform some basic consistency checks, in particular, the calculation of two-point correlators, which reveals the expected logarithmic behavior. We comment on the vanishing value of the [[0033 Central charge|central charge]] in the celestial conformal field theory and explain how the logarithmic partner is relevant to make the theory well-behaved.\] # Flanagan, Nichols ## Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: The [[0060 Asymptotic symmetry|asymptotic symmetry]] group of [[0554 Einstein gravity|general relativity]] in asymptotically flat spacetimes can be extended from the [[0064 BMS group|Bondi-Metzner-Sachs]] (BMS) group to the generalized BMS (GMBS) group suggested by Campiglia and Laddha, which includes arbitrary diffeomorphisms of the celestial two-sphere. It can be further extended to the Weyl BMS (BMSW) group suggested by Freidel, Oliveri, Pranzetti and Speziale, which includes general conformal transformations. We compute the action of fully nonlinear BMSW transformations on the leading order Bondi-gauge metric functions: specifically, the induced metric, Bondi mass aspect, angular momentum aspect, and shear. These results generalize previous linearized results in the BMSW context by Freidel et al., and also nonlinear results in the BMS context by Chen, Wang, Wang and Yau. The transformation laws will be useful for exploring implications of the BMSW group.\] # Freidel, Geiller, Wieland (Review, Chapter) ## Corner symmetry and quantum geometry \[Links: [arXiv](https://arxiv.org/abs/2302.12799), [PDF](https://arxiv.org/pdf/2302.12799.pdf)\] \[Abstract: By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called corners. The presence of non-trivial corner symmetries associated with any entangling cut provides stringent constraints on the theory's mathematical structure and a guide through quantization. This report reviews new and recent results for non-perturbative quantum gravity, which are natural consequences of this structure. First, we establish that the corner symmetry derived from the gauge principle encodes quantum entanglement across internal boundaries. We also explain how the quantum representation of the corner symmetry algebra provides us with a notion of quantum geometry. We then focus our discussion on the first-order formulation of gravity and show how many results obtained in the continuum connect naturally with previous results in loop quantum gravity. In particular, we show that it is possible to get, purely from quantization and without discretization, an area operator with discrete spectrum, which is covariant under local Lorentz symmetry. We emphasize that while loop gravity correctly captures some of the gravitational quantum numbers, it does not capture all of them, which points towards important directions for future developments. Finally, we discuss the understanding of the gravitational dynamics along null surfaces as a conservation of symmetry charges associated with a Carrollian fluid.\] ## Refs - [[0529 Corner symmetry]] # Freidel, Pranzetti, Raclariu ## On infinite symmetry algebras in Yang-Mills theory \[Links: [arXiv](https://arxiv.org/abs/2306.02373), [PDF](https://arxiv.org/pdf/2306.02373.pdf)\] \[Abstract: Similar to gravity, an infinite tower of symmetries generated by higher-spin charges has been identified in Yang-Mills theory by studying [[0078 Collinear limit|collinear limits]] or [[0114 Celestial OPE|celestial operator products]] of gluons. This work aims to recover this loop symmetry in terms of charge aspects constructed on the gluonic Fock space. We propose an explicit construction for these higher spin charge aspects as operators which are polynomial in the gluonic annihilation and creation operators. The core of the paper consists of a proof that the charges we propose form a closed loop algebra to quadratic order. This closure involves using the commutator of the cubic order expansion of the charges with the linear (soft) charge. Quite remarkably, this shows that this infinite-dimensional symmetry constrains the non-linear structure of Yang-Mills theory. We provide a similar all spin proof in gravity for the so-called global quadratic (hard) charges which form the loop wedge subalgebra of $\mathrm{w}_{1+\infty}$.\] # Furugori, Ogawa, Sugishita, Waki ## Celestial two-point functions and rectified dictionary \[Links: [arXiv](https://arxiv.org/abs/2312.07057), [PDF](https://arxiv.org/pdf/2312.07057.pdf)\] \[Abstract: A naive celestial dictionary causes massless two-point functions to take the delta-function forms in the [[0010 Celestial holography|celestial conformal field theory]] (CCFT). We rectify the dictionary, involving the [[0039 Shadow transform|shadow transformation]] so that the two-point functions follow the standard power-law. In this new definition, we can smoothly take the massless limit of the massive dictionary. We also compute a three-point function using the new dictionary and discuss the [[0114 Celestial OPE|OPE in CCFT]].\] # Furuya, Lashkari, Moosa, Ouseph ## Information loss, mixing and emergent type III$_1$ factors \[Links: [arXiv](https://arxiv.org/abs/2305.16028), [PDF](https://arxiv.org/pdf/2305.16028.pdf)\] \[Abstract: A manifestation of the black hole [[0131 Information paradox|information loss problem]] is that the two-point function of probe operators in a large Anti-de Sitter black hole decays in time, whereas, on the boundary CFT, it is expected to be an almost periodic function of time. We point out that the decay of the two-point function (clustering in time) holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity. We call operators that cluster in time "mixing" and explore the necessary and sufficient conditions for mixing. The information loss problem is a special case of the statement that in type I algebras, there exists no mixing operators. We prove that, in a thermofield double (KMS state), if mixing operators form an algebra (close under multiplication) the resulting algebra must be a von Neumann type III$_1$ factor. In other words, the physically intuitive requirement that all non-conserved operators should diffuse is so strong that it fixes the observable algebra to be an exotic algebra called a type III$_1$ factor. More generally, for an arbitrary out-of-equilibrium state of a general quantum system ([[0415 Von Neumann algebra|von Neumann algebra]]), we show that if the set of operators that mix under [[0416 Modular Hamiltonian|modular flow]] forms an algebra it is a type III$_1$ von Neumann factor. In a theory of Generalized Free Fields (GFF), we show that if the two-point function of GFF clusters in time all operators are mixing, and the algebra is a type III$_1$ factor. For instance, in $\mathscr{N=4}$ SYM, above the [[0012 Hawking-Page transition|Hawking-Page phase transition]], clustering of the single trace operators implies that the algebra is a type III$_1$ factor, settling a recent conjecture of Leutheusser and Liu. We explicitly construct the $C^*$-algebra and von Neumann subalgebras of GFF associated with time bands and more generally, open sets of the bulk spacetime using the [[0016 HKLL|HKLL reconstruction map]].\] # Gabai, Sever, Zhong ## Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories \[Links: [arXiv](https://arxiv.org/abs/2312.17132), [PDF](https://arxiv.org/pdf/2312.17132.pdf)\] \[Abstract: The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large $N$ holographic theories, these fundamental observables are dual to the open string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in [[0089 Chern-Simons theory|Chern-Simons]] matter theories. In these cases, the line bootstrap is based on three minimal assumptions -- conformal invariance of the line defect, large $N$ factorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the [[0028 Conformal symmetry|conformal symmetry]] of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique.\] # Gadde, Krishna, Sharma ## Towards classification of holographic multi-partite entanglement measures \[Links: [arXiv](https://arxiv.org/abs/2304.06082), [PDF](https://arxiv.org/pdf/2304.06082.pdf)\] \[Abstract: In this paper, we systematically study measures of [[0264 Multi-partite entanglement|multi-partite entanglement]] with the aim of constructing measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as invariants of local unitary transformations. After formulating these measures in terms of permutation group elements, we derive conditions that a probe measure should satisfy and find a large class of solutions. These solutions are generalizations of the multi-entropy introduced in [arXiv:2206.09723](https://arxiv.org/abs/2206.09723) . We derive their holographic dual with the assumption that the replica symmetry is unbroken in the bulk and check our prescription with explicit computations in 2d CFTs. We discuss the replica symmetry assumption and also how the already known entanglement measures, such as [[0210 Entanglement negativity|entanglement negativity]] and [[0166 Reflected entropy|reflected entropy]] fit in our framework.\] ## Comments - uses [[0102 Hayward term|Hayward term]] for a codimension-3 junction between bulk codimension-2 surfaces # Gao, Liu ## An effective field theory for non-maximal quantum chaos \[Links: [arXiv](https://arxiv.org/abs/2301.05256), [PDF](https://arxiv.org/pdf/2301.05256.pdf)\] \[Abstract: In non-maximally quantum chaotic systems, the exponential behavior of [[0482 Out-of-time-order correlator|out-of-time-ordered correlators (OTOCs)]] results from summing over exchanges of an infinite tower of higher "spin" operators. We construct an effective field theory (EFT) to capture these exchanges in $(0+1)$ dimensions. The EFT generalizes the one for maximally chaotic systems, and reduces to it in the limit of maximal chaos. The theory predicts the general structure of OTOCs both at leading order in the $1/N$ expansion ($N$ is the number of degrees of freedom), and after resuming over an infinite number of higher order $1/N$ corrections. These general results agree with those previously explicitly obtained in specific models. We also show that the general structure of the EFT can be extracted from the large q [[0201 Sachdev-Ye-Kitaev model|SYK]] model.\] ## Comments - there is no explicit summation over spins; rather, take as an input that the effective [[0466 Lyapunov exponent|Lyapunov exponent]] is sub-maximal and use an EFT to capture that deviation from maximality ## Criteria for constructing the EFT 1. exponential behaviour for OTOC but not for TOC 2. capture of all KMS properties of thermal 4-point functions ## Maximal chaos - write $W(t)$ as a function of two new variables: $W_0(t)$ and $\varphi(t)$ - $W(t)=W\left[W_0(t), \varphi(t)\right]$ - linear in $W_0$ but general in $\varphi$ - linear order in $\varphi$ - $W(t)=W_0(t)+L_t\left[W_0(t)\right] \varphi(t)+O\left(\varphi^2\right)$ - then $L_t\left[W_0(t)\right] \varphi(t)=\sum_{m, n=0}^{\infty} c_{m n} \partial_t^m W_0(t) \partial_t^n \varphi(t)$ ## Generalisation to non-maximal - $W(t) W\left(t^{\prime}\right)=W_0(t) W_0\left(t^{\prime}\right)+\sum_{i=1}^2 \mathcal{D}_W^{(i)}\left(t, t^{\prime}\right) \phi_i\left(t, t^{\prime}\right)+O\left(\phi^2\right)$ # Garner, Paquette ## Twistorial monopoles & chiral algebras \[Links: [arXiv](https://arxiv.org/abs/2305.00049), [PDF](https://arxiv.org/pdf/2305.00049.pdf)\] \[Abstract: We initiate the study of how the insertion of magnetically charged states in 4d self-dual gauge theories impacts the 2d chiral algebras supported on the [[0022 Celestial sphere|celestial sphere]] at asymptotic null infinity, from the point of view of the [[0384 4d-2d twistorial correspondence|4d/2d twistorial correspondence]] introduced by [[2022#Costello, Paquette (Jan)]]. By reducing the 6d twistorial theory to a 3d holomorphic-topological theory with suitable boundary conditions, we can motivate certain non-perturbative enhancements of the celestial chiral algebra corresponding to extensions by modules arising from 3d boundary monopole operators. We also identify the insertion of 4d (non-abelian) monopoles with families of spectral flow automorphisms of the celestial chiral algebra.\] # Galante (Lectures) ## Modave Lecture Notes on de Sitter Space & Holography \[Links: [arXiv](https://arxiv.org/abs/2306.10141), [PDF](https://arxiv.org/pdf/2306.10141.pdf)\] \[Abstract: These lecture notes provide an overview of different aspects of de Sitter space and their plausible [[0545 de Sitter quantum gravity|holographic]] interpretations. We start with a general description of the classical spacetime. We note the existence of a cosmological horizon and its associated thermodynamic quantities, such as the Gibbons-Hawking entropy. We discuss geodesics and [[0117 Shockwave|shockwave]] solutions, that might play a role in a holographic description of de Sitter. Finally, we discuss different approaches to quantum theories of de Sitter space, with an emphasis on recent developments in static patch holography.\] # Garousi ## The data on the boundary at order $\alpha'$ \[Links: [arXiv](https://arxiv.org/abs/2305.04527), [PDF](https://arxiv.org/pdf/2305.04527.pdf)\] \[Abstract: The least action principle indicates that for the open spacetime manifolds, there are data on the boundary. Recently, it has been proposed that the data for the [[0329 String effective action|effective actions]] at order $\alpha'$ are the values of the massless fields and their first derivatives. These data should be respected by the T-duality transformations at order $\alpha'$. Moreover, the T-duality transformations should not change the unit vector to the boundary which in turns implies that the base space metric should be also invariant. Assuming such restricted T-duality transformations, we show that the transformation of the circular reduction of the parity-odd part of the effective action of the heterotic string theory at order $\alpha'$ under the Buscher rules is cancelled by some total derivative terms and by some restricted T-duality transformations at order $\alpha'$. Using the Stokes' theorem, we then show that the boundary terms in the base space corresponding to the total derivative terms are exactly cancelled by transformation of the circular reduction of the [[0138 Variational principle|Gibbons-Hawking boundary term]] under the above restricted T-duality transformations. These calculations confirm the above proposal for the data on the boundary for the effective actions at order $\alpha'$.\] # Geng, Karch, Perez-Pardavila, Randall, Riojas, Shashi, Youssef ## Constraining braneworlds with entanglement entropy \[Links: [arXiv](https://arxiv.org/abs/2306.15672), [PDF](https://arxiv.org/pdf/2306.15672.pdf)\] \[Abstract: We propose [[0184 Swampland|swampland]] criteria for [[0452 Karch-Randall braneworld|braneworlds]] viewed as effective field theories of defects coupled to semiclassical gravity. We do this by exploiting their holographic interpretation. We focus on general features of [[0301 Entanglement entropy|entanglement entropies]] and their [[0007 RT surface|holographic entanglement entropy]] calculations. Entropies have to be positive. Furthermore, causality imposes certain constraints on the surfaces that are used holographically to compute them, most notably a property known as [[0143 Causal wedge inclusion|causal wedge inclusion]]. As a test case, we explicitly constrain the Dvali--Gabadadze--Porrati term as a second-order-in-derivatives correction to the Randall--Sundrum action. We conclude by discussing the implications of these criteria for the question on whether entanglement [[0213 Islands|islands]] in theories with massless gravitons are possible in [[0452 Karch-Randall braneworld|Karch-Randall braneworlds]].\] # Genolini, Toldo ## Magnetic charge and black hole supersymmetric quantum statistical relation \[Links: [arXiv](https://arxiv.org/abs/2304.00605), [PDF](https://arxiv.org/pdf/2304.00605.pdf)\] \[Abstract: We study the thermodynamics in the [[0178 BPS|BPS]] limit of static AdS black holes realizing the topological twist. We use a recently proposed limiting procedure that allows us to reach the extremal point along a trajectory in the space of [[0359 Supersymmetry|supersymmetric]] Euclidean solutions. We show that on this space we can write a quantum statistical relation, justifying taking the Legendre transform of the on-shell action to obtain the [[0004 Black hole entropy|Bekenstein-Hawking entropy]]. A key feature is the imposition of a suitable constraint among the chemical potentials, which follows from supersymmetry and regularity. We stress the importance of this in relating the thermal partition function of the dual field theory to the [[0546 Topologically twisted index|topologically twisted index]].\] ## Difficulty with BPS - $\beta=\infty$ so action diverges (naively) - solution: study thermodynamics for supersymmetric non-extremal Euclidean BHs and extend it to BPS (extremal and supersymmetric) ones # Gesteau ## Large $N$ von Neumann algebras and the renormalization of Newton's constant \[Links: [arXiv](https://arxiv.org/abs/2302.01938), [PDF](https://arxiv.org/pdf/2302.01938.pdf)\] \[Abstract: I derive a family of [[0007 RT surface|Ryu--Takayanagi formulae]] that are valid in the large $N$ limit of holographic [[0146 Quantum error correction|quantum error-correcting codes]], and parameterized by a choice of UV cutoff in the bulk. The bulk entropy terms are matched with a family of von Neumann factors nested inside the large $N$ [[0415 Von Neumann algebra|von Neumann algebra]] describing the bulk effective field theory. These factors are mapped onto one another by a family of conditional expectations, which are interpreted as a renormalization group flow for the code subspace. Under this flow, I show that the renormalizations of the area term and the bulk entropy term exactly compensate each other. This result provides a concrete realization of the [[0220 ER=EPR|ER=EPR]] paradigm, as well as an explicit proof of a conjecture due to [[1994#Susskind, Uglum|Susskind and Uglum]].\] ## Refs - talk at KITP on 20 April 2023; at It-From-Qubit 2023 ## Ambiguities in QES - it is hard to define each term in the QES formula - paradox: the boundary entanglement entropy is independent of the UV cutoff but $S_{bulk}$ is regulator-dependent - resolution: Susskind and Uglum conjecture that the renormalisation of $G_N$ cancels that of $S_{bulk}$ ## The Leutheusser-Liu construction - there is an emergent type III von Neumann algebra ## Properties of the large N algebra - below [[0012 Hawking-Page transition|HP]] temperature, the bulk saddle is disconnected, and the algebra is type I - above HP temperature, the bulk algebra is type III ## Bulk to boundary map - it should map from the $N=\infty$ type III$_1$ algebra to the large but finite $N$ type I algebra on the boundary ## Asymptotically isometric code - [[2022#Faulkner, Li]] - only pointwise convergence is required, rather than uniform convergence ## Connection to [[0220 ER=EPR|ER=EPR]] - entanglement entropy can either be attributed to the area term or the bulk term - so this suggests that there is no physical distinction between entanglement and geometry ## Area - to define an area, define a state of bulk fields by maximally entangling the states on the left and on the right with auxiliary systems - then they are two busy entangling with the auxiliary fields to entanglement with each other - so the entropy can only come from the area ## Constraints from complementary recovery - a conditional expectation is what is needed - Takesaki's theorem # Ghodsi, Kiritsis, Nitti ## Holographic CFTs on AdS$_d\times S^n$ and conformal defects \[Links: [arXiv](https://arxiv.org/abs/2309.04880), [PDF](https://arxiv.org/pdf/2309.04880.pdf)\] \[Abstract: We consider ($d+n+1$)-dimensional solutions of Einstein gravity with constant negative curvature. Regular solutions of this type are expected to be dual to the ground states of ($d+n$)-dimensional holographic CFTs on AdS$_d\times S^n$. Their only dimensionless parameter is the ratio of radii of curvatures of AdS$_d$ and $S^n$. The same solutions may also be dual to ($d-1$)-dimensional conformal defects in holographic QFT$_{d+n}$. We solve the gravity equations with an associated conifold ansatz, and we classify all solutions both singular and regular by a combination of analytical and numerical techniques. There are no solutions, regular or singular, with two boundaries along the holographic direction. Out of the infinite class of regular solutions, only one is diffeomorphic to AdS$_{d+n+1}$ and another to AdS$_d\times$ AdS$_{n+1}$. For the regular solutions, we compute the on-shell action as a function of the relevant parameters.\] # Griguolo, Guerrini, Panerai, Papalini, Seminara ## Supersymmetric localization of (higher-spin) JT gravity: a bulk perspective \[Links: [arXiv](https://arxiv.org/abs/2307.01274), [PDF](https://arxiv.org/pdf/2307.01274.pdf)\] \[Abstract: We study two-dimensional [[0050 JT gravity|Jackiw-Teitelboim gravity]] on the disk topology by using a [[0557 BF theory|BF gauge theory]] in the presence of a boundary term. The system can be equivalently written in a supersymmetric way by introducing auxiliary gauginos and scalars with suitable boundary conditions on the hemisphere. We compute the exact partition function thanks to supersymmetric [[0186 Localisation|localization]] and we recover the result obtained from the Schwarzian theory by accurately identifying the physical scales. The calculation is then easily extended to the [[0421 Higher-spin gravity|higher-spin]] generalization of Jackiw-Teitelboim gravity, finding perfect agreement with previous results. We argue that our procedure can also be applied to boundary-anchored Wilson line correlators.\] # Grozdanov, Lemut, Pedraza ## Reconstruction of the quasinormal spectrum from pole-skipping \[Links: [arXiv](https://arxiv.org/abs/2308.01371), [PDF](https://arxiv.org/pdf/2308.01371.pdf)\] \[Abstract: The holographic gauge/gravity duality provides an explicit reduction of quantum field theory (QFT) calculations in the semi-classical large-$N$ limit to sets of 'gravitational' differential equations whose analysis can reveal all details of the spectra of thermal QFT correlators. We argue that in certain cases, a complete reconstruction of the spectrum and of the corresponding correlator is possible from only the knowledge of an infinite, discrete set of [[0179 Pole skipping|pole-skipping]] points traversed by a single (hydrodynamic) mode computed in a series expansion in an inverse number of spacetime dimensions. Conceptually, this reduces the computation of a QFT correlator spectrum to performing a set of purely algebraic manipulations. With the help of the pole-skipping analysis, we also uncover a novel structure underpinning the coefficients that enter the [[0429 Hydrodynamics|hydrodynamic]] dispersion relations.\] # Grozdanov, Vrbica ## Pole-skipping of gravitational waves in the backgrounds of four-dimensional massive black holes \[Links: [arXiv](https://arxiv.org/abs/2303.15921), [PDF](https://arxiv.org/pdf/2303.15921.pdf)\] \[Abstract: [[0179 Pole skipping|Pole-skipping]] is a property of gravitational waves dictated by their behaviour at horizons of black holes. It stems from the inability to unambiguously impose ingoing boundary conditions at the horizon at an infinite discrete set of Fourier modes. The phenomenon has been best understood, when such a description exists, in terms of dual [[0001 AdS-CFT|holographic (AdS/CFT)]] correlation function that take the value of '0/0' at these special points. In this work, we investigate details of pole-skipping purely from the point of view of classical gravity in 4d massive black hole geometries with ==flat, spherical and hyperbolic horizons==, and with an ==arbitrary cosmological constant==. We show that pole-skipping points naturally fall into two categories: the algebraically special points and a set of pole-skipping points that is common to the even and odd channels of perturbations. Our analysis utilises and generalises (to arbitrary maximally symmetric horizon topology and cosmological constant) the 'integrable' structure of the Darboux transformations, which relate the master field equations that describe the evolution of gravitational perturbations in the two channels. Finally, we provide new insights into a number of special cases: spherical black holes, asymptotically Anti-de Sitter black branes and pole-skipping at the cosmological horizon in de Sitter space.\] ## Leading horizon behaviour - $\psi^{\mathrm{in}}\left(r \rightarrow r_0\right) \sim e^{-i \omega r_*} \sim\left(r-r_0\right)^{-\frac{i \omega}{4 \pi T}}$ - $\psi^{\text {out }}\left(r \rightarrow r_0\right) \sim e^{i \omega r_*} \sim\left(r-r_0\right)^{\frac{i \omega}{4 \pi T}}$ ## Two types of pole-skipping points - algebraically special pole-skipping points: algebraically special solutions - common pole-skipping points: common because it happens for both channels ## Different frequencies - $\omega=\omega_n=-2 \pi T i n$ with $n\ge-1$ - if $n\ge2$: pole skipping follows straightforwardly from master function formalism - if $n=\pm1$: require special attention to determine what is ingoing versus outgoing - if $n=0$: require special attention # Grumiller, Riegler ## Carrollian c-functions and flat space holographic RG flows in BMS3/CCFT2 \[Links: [arXiv](https://arxiv.org/abs/2309.11539), [PDF](https://arxiv.org/pdf/2309.11539.pdf)\] \[Abstract: We discuss c-functions and their holographic counterpart for two-dimensional field theories with Carrollian conformal fixed points in the UV and the IR. Specifically, we construct asymptotically flat domain wall solutions of three-dimensional Einstein-dilaton gravity that model holographic RG flows between [[0064 BMS group|BMS3 invariant]] UV and IR fixed points. We prove three theorems for such flows: 1. for every [[0257 Holographic RG flow|holographic RG flow]] in AdS3, there is a corresponding one in flat space, 2. the BMS [[0033 Central charge|central charge]] in the UV cannot be smaller than in the IR, and 3. the UV/IR ratio of Virasoro central charges is identical to the UV/IR ratio of corresponding BMS central charges. Finally, we tentatively propose a Casini-Huerta-like c-functions for BMS3-invariant quantum field theories, inspired by the AdS3/CFT2 relation between monotonicity of the c-function and the [[0405 Quantum null energy condition|quantum null energy condition]].\] # Guevara, Kol ## Black Hole Hidden Symmetries from the Self-Dual Point \[Links: [arXiv](https://arxiv.org/abs/2311.07933), [PDF](https://arxiv.org/pdf/2311.07933.pdf)\] \[Abstract: Rotating black holes exhibit a remarkable set of hidden symmetries near their horizon. They have been shown to determine phenomena such as absorption scattering, superradiance and more recently tidal deformations, also known as Love numbers. They have also led to a proposal for a dual thermal CFT with left and right movers recovering the entropy of the black hole. In this work we provide a constructive explanation of these hidden symmetries via analytic continuation to Klein signature. We first show that the near-horizon region of extremal black holes is a Kleinian static solution with mass $M$ and NUT charge $N$. We then analyze the self-dual solution, namely a Kerr black hole with a NUT charge $N=\pm M$. Remarkably, the self-dual solution is self-similar to its near-horizon and hence approximate symmetries become exact: in particular, the original two isometries of Kerr are promoted to seven exact symmetries embedded in a conformal algebra. We analyze its full conformal group in Kleinian twistor space, where a breaking $SO(4,2)$ $\to$ $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ occurs due to the insertion of a preferred time direction for the black hole. Finally, we show that its spectrum is integrable and behaves as the Hydrogen atom, being solvable in terms of elementary polynomials. Perturbing to astrophysical black holes with $N=0$, we obtain a hyperfine splitting structure.\] # Haehl, Marteau, Reeves, Rozali ## Symmetries and spectral statistics in chaotic conformal field theories \[Links: [arXiv](https://arxiv.org/abs/2302.14482), [PDF](https://arxiv.org/pdf/2302.14482.pdf)\] \[Abstract: We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large [[0033 Central charge|central charge]]. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic properties of the spectrum from those which are a consequence of [[0032 Virasoro algebra|Virasoro]] symmetry and modular invariance. We argue that random matrix universality in the near-extremal limit is an independent feature of each spin sector separately; this is a non-trivial statement because the exact spectrum is fully determined by only the spectrum of spin zero primaries and those of a single non-zero spin ("spectral determinacy"). We then describe an argument analogous to the one leading to [[0406 Cardy formula|Cardy's formula]] for the averaged density of states, but in our case applying it to spectral correlations: assuming statistical universalities in the near-extremal spectrum in all spin sectors, we find similar random matrix universality in a large spin regime far from extremality.\] # Haehl, Reeves, Rozali ## Euclidean wormholes in two-dimensional CFTs from quantum chaos and number theory \[Links: [arXiv](https://arxiv.org/abs/2309.02533), [PDF](https://arxiv.org/pdf/2309.02533.pdf)\] \[Abstract: We consider two-dimensional [[0481 Conformal field theory|conformal field theories]] (CFTs), which exhibit a hallmark feature of [[0008 Quantum chaos|quantum chaos]]: universal repulsion of energy levels as described by a regime of linear growth of the [[0062 Spectral form factor|spectral form factor]]. This physical input together with modular invariance strongly constrains the spectral correlations and the subleading corrections to the linear growth. We show that these are determined by the Kuznetsov trace formula, which highlights an intricate interplay of universal physical properties of chaotic CFTs and analytic number theory. The trace formula manifests the fact that the simplest possible CFT correlations consistent with quantum chaos are precisely those described by a Euclidean wormhole in AdS${}_3$ gravity with [torus]$\times$[interval] topology. For contrast, we also discuss examples of non-chaotic CFTs in this language.\] # Hao ## Real time holography for higher spin theories \[Links: [arXiv](https://arxiv.org/abs/2311.05382), [PDF](https://arxiv.org/pdf/2311.05382.pdf)\] \[Abstract: [[0042 Schwinger-Keldysh techniques|Real time holography]] is studied in the context of the embedding space formalism. In the first part of this paper, we present matching conditions for on-shell integer spin fields when going from Euclidean to Lorentzian signature on AdS background. Using the [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black hole as an example, we discuss various ways of lifting the physical solution from the AdS surface to the whole embedding space. The BTZ propagator for higher spin field is expressed elegantly in terms of the embedding coordinates. In the second part of the paper, we develop the proposed duality between higher spin theory and vector models. We obtain a specific map between the field configurations of these two theories in real time, so called Lorentzian AdS/CFT map. We conclude by exploring the matching conditions for higher spin fields satisfying the proposed bulk quadratic action. The physical and ghost modes can be treated independently during the Wick rotation; only physical modes are considered to be external modes.\] # Hao, Taylor ## Flat holography and celestial shockwaves \[Links: [arXiv](https://arxiv.org/abs/2309.04307), [PDF](https://arxiv.org/pdf/2309.04307.pdf)\] \[Abstract: In this paper we systematically develop the flat/CFT holographic dictionary, building on [[0001 AdS-CFT|AdS/CFT]] holography. After analysing the behaviour of scalar field modes on hyperbolic slices of Minkowski and performing the holographic renormalisation for the associated onshell action, we obtain a holography dictionary between the bulk theory and the corresponding dual theory on the [[0022 Celestial sphere|celestial sphere]]. We propose that a single scalar field in the bulk is dual to two series of operators on the celestial sphere; the scaling dimension of these operators takes values on the principal series. The real time features of the bulk theory, such as the dynamical and the casual structure, are encoded in the construction of correlation functions on the boundary via the coefficients of the bulk modes. Moreover, we will see that the two series of operators can be interpreted as ingoing and outgoing waves in the bulk. We illustrate our dictionary with the example of a single [[0117 Shockwave|shock wave]]. Our results lay foundations for further computation within the [[0010 Celestial holography|flat/celestial CFT]] correspondence.\] # Harlow (Review) ## Black holes in quantum gravity \[Links: [arXiv](https://arxiv.org/abs/2304.10367), [PDF](https://arxiv.org/pdf/2304.10367.pdf)\] \[Abstract: This chapter gives an overview of the quantum aspects of black holes, focusing on the [[0131 Information paradox|black hole information problem]], the [[0248 Black hole microstates|counting of black hole entropy]] in string theory, and the emergence of spacetime in [[0001 AdS-CFT|holography]]. It is aimed at a broad physics audience, and does not presuppose knowledge of string theory or holography.\] # Hartman, Mathys (Sep) ## Averaged Null Energy and the Renormalization Group \[Links: [arXiv](https://arxiv.org/abs/2309.14409), [PDF](https://arxiv.org/pdf/2309.14409.pdf)\] \[Abstract: We establish a connection between the [[0417 Averaged null energy condition|averaged null energy condition]] (ANEC) and the [[0351 Irreversibility theorems|monotonicity]] of the renormalization group, by studying the light-ray operator $\int du T_{uu}$ in quantum field theories that flow between two conformal fixed points. In four dimensions, we derive an exact sum rule relating this operator to the Euler coefficient in the trace anomaly, and show that the ANEC implies the a-theorem. The argument is based on matching anomalies in the stress tensor 3-point function, and relies on special properties of contact terms involving [[0450 Light-ray operators|light-ray operators]]. We also illustrate the sum rule for the example of a free massive scalar field. Averaged null energy appears in a variety of other applications to quantum field theory, including [[0132 Causality constraints in CFT|causality constraints]], Lorentzian inversion, and quantum information. The quantum information perspective provides a new derivation of the a-theorem from the monotonicity of [[0199 Relative entropy|relative entropy]]. The equation relating our sum rule to the dilaton scattering amplitude in the forward limit suggests an inversion formula for non-conformal theories.\] # Hartman, Mathys (Oct) ## Null energy constraints on two-dimensional RG flows \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: We study applications of spectral positivity and the [[0417 Averaged null energy condition|averaged null energy condition]] (ANEC) to renormalization group (RG) flows in two-dimensional quantum field theory. We find a succinct new proof of the Zamolodchikov [[0351 Irreversibility theorems|c-theorem]], and derive further independent constraints along the flow. In particular, we identify a natural C-function that is a completely monotonic function of scale, meaning its derivatives satisfy the alternating inequalities $(-1)^nC^{(n)}(\mu^2) \geq 0$. The completely monotonic C-function is identical to the Zamolodchikov C-function at the endpoints, but differs along the RG flow. In addition, we apply Lorentzian techniques that we developed recently to study anomalies and RG flows in four dimensions, and show that the Zamolodchikov c-theorem can be restated as a Lorentzian sum rule relating the change in the [[0033 Central charge|central charge]] to the average null energy. This establishes that the ANEC implies the c-theorem in two dimensions, and provides a second, simpler example of the Lorentzian sum rule.\] # Harvey, Jensen ## Eternal traversable wormholes in three dimensions \[Links: [arXiv](https://arxiv.org/abs/2302.14049), [PDF](https://arxiv.org/pdf/2302.14049.pdf)\] \[Abstract: We consider [[0002 3D gravity|three-dimensional gravity]] with negative cosmological constant coupled to a large number of light matter fields dual to relevant operators. By imposing suitable boundary conditions on the matter fields we find eternal [[0083 Traversable wormhole|traversable wormhole]] deformations of the BTZ black hole, leading to a three-dimensional analogue of the AdS$_{2}$ eternal traversable wormhole found by [[2018#Maldacena, Qi|Maldacena and Qi]]. We further identify the field theory of boundary gravitons in this setting, which we then use to compute the spectrum of gravitational fluctuations.\] # Hashimoto, Murata, Tanahashi, Watanabe ## Krylov complexity and chaos in quantum mechanics \[Links: [arXiv](https://arxiv.org/abs/2305.16669), [PDF](https://arxiv.org/pdf/2305.16669.pdf)\] \[Abstract: Recently, [[0564 Krylov complexity|Krylov complexity]] was proposed as a measure of [[0204 Quantum complexity|complexity]] and [[0008 Quantum chaos|chaoticity]] of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic system, and numerically evaluate Krylov complexity for operators and states. Despite no exponential growth of the Krylov complexity, we find a clear correlation between variances of Lanczos coefficients and classical Lyapunov exponents, and also a correlation with the statistical distribution of adjacent spacings of the quantum energy levels. This shows that the variances of Lanczos coefficients can be a measure of quantum chaos. The universality of the result is supported by our similar analysis of Sinai billiards. Our work provides a firm bridge between Krylov complexity and classical/quantum chaos.\] # Hayden, Wang ## What exactly does Bekenstein bound? \[Links: [arXiv](https://arxiv.org/abs/2309.07436), [PDF](https://arxiv.org/pdf/2309.07436.pdf)\] \[Abstract: The [[0418 Bekenstein bound|Bekenstein bound]] posits a maximum entropy for matter with finite energy confined to a spacetime region. It is often interpreted as a fundamental limit on the information that can be stored by physical objects. In this work, we test this interpretation by asking whether the Bekenstein bound imposes constraints on a channel's communication capacity, a context in which information can be given a mathematically rigorous and operationally meaningful definition. We first derive a bound on the accessible information and demonstrate that the Bekenstein bound constrains the decoding instead of the encoding. Then we study specifically the Unruh channel that describes a stationary Alice exciting different species of free scalar fields to send information to an accelerating Bob, who is therefore confined to a Rindler wedge and exposed to the noise of Unruh radiation. We show that the classical and quantum capacities of the Unruh channel obey the Bekenstein bound. In contrast, the entanglement-assisted capacity is as large as the input size even at arbitrarily high Unruh temperatures. This reflects that the Bekenstein bound can be violated if we do not properly constrain the decoding operation in accordance with the bound. We further find that the Unruh channel can transmit a significant number of zero-bits, which are communication resources that can be used as minimal substitutes for the classical/quantum bits needed for many primitive information processing protocols, such as dense coding and teleportation. We show that the Unruh channel has a large zero-bit capacity even at high temperatures, which underpins the capacity boost with entanglement assistance and allows Alice and Bob to perform quantum identification. Therefore, unlike classical bits and qubits, zero-bits and their associated information processing capability are not constrained by the Bekenstein bound.\] # Heller, Serantes, Spalinski, Withers ## The Hydrohedron: Bootstrapping Relativistic Hydrodynamics \[Links: [arXiv](https://arxiv.org/abs/2305.07703), [PDF](https://arxiv.org/pdf/2305.07703.pdf)\] \[Abstract: As an effective theory, relativistic hydrodynamics is fixed by symmetries up to a set of transport coefficients. A lot of effort has been devoted to explicit calculations of these coefficients. Here we propose a shift in perspective: we deploy bootstrap techniques to rule out theories that are inconsistent with microscopic causality. What remains is a universal convex geometry in the space of transport coefficients, which we call the hydrohedron. The landscape of all consistent theories necessarily lie inside or on the edges of the hydrohedron. We analytically construct cross-sections of the hydrohedron corresponding to bounds on [[0511 Transport coefficients|transport coefficients]] that appear in sound and diffusion modes for theories without stochastic fluctuations.\] ## Refs - [[2022#Heller, Serantes, Spalinski, Withers]] # He, Mitra ## Asymptotic Structure of Higher Dimensional Yang-Mills Theory \[Links: [arXiv](https://arxiv.org/abs/2306.04571), [PDF](https://arxiv.org/pdf/2306.04571.pdf)\] \[Abstract: Using the [[0019 Covariant phase space|covariant phase space formalism]], we construct the phase space for non-Abelian gauge theories in ($d+2$)-dimensional Minkowski spacetime for any $d \geq 2$, including the edge modes that symplectically pair to the low energy degrees of freedom of the gauge field. Despite the fact that the symplectic form in odd and even-dimensional spacetimes appear ostensibly different, we demonstrate that both cases can be treated in a unified manner by utilizing the [[0039 Shadow transform|shadow transform]]. Upon quantization, we recover the algebra of the vacuum sector of the Hilbert space and derive a [[0106 Ward identity|Ward identity]] that implies the leading [[0009 Soft theorems|soft gluon theorem]] in ($d+2$)-dimensional spacetime.\] # He, Li ## Holographic Euclidean thermal correlator \[Links: [arXiv](https://arxiv.org/abs/2308.13518), [PDF](https://arxiv.org/pdf/2308.13518.pdf)\] \[Abstract: In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and $U(1)$ current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein's gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact [[0103 Two-point functions|two-point thermal correlators]] for $U(1)$ current and stress tensor in the scalar and shear channel.\] # He, Li, Zhang ## Holographic torus correlators in $\text{AdS}_3$ gravity coupled to scalar field \[Links: [arXiv](https://arxiv.org/abs/2311.09636), [PDF](https://arxiv.org/pdf/2311.09636.pdf)\] \[Abstract: This paper investigates holographic torus correlators of generic operators at conformal infinity and a finite cutoff within AdS$_3$ gravity coupled with a free scalar field. Using a near-boundary analysis and solving the gravitational boundary value problem, we solve Einstein's equation and calculate mixed correlators for massless and massive coupled scalar fields. The conformal ward identity on the torus has been reproduced holographically, which can be regarded as a consistency check. Further, recurrence relations for a specific class of higher-point correlators are derived, validating AdS$_3$/CFT$_2$ with non-trivial boundary topology. While the two-point scalar correlator is accurately computed on the thermal AdS$_3$ saddle, the higher-point correlators associated with scalar and stress tensor operators are explored.\] # He, Raclariu, Zurek ## From Shockwaves to the Gravitational Memory Effect \[Links: [arXiv](https://arxiv.org/abs/2305.14411), [PDF](https://arxiv.org/pdf/2305.14411.pdf)\] \[Abstract: We study the relationship between [[0117 Shockwave|shockwave]] geometries and the [[0287 Memory effect|gravitational memory effect]] in four-dimensional asymptotically flat spacetime. In particular, we show the 't Hooft commutation relations of shockwave operators are equivalent to the commutation relation between soft and Goldstone modes parametrizing a sector of the gravitational phase space. We demonstrate this equivalence via a diffeomorphism that takes the shockwave metric to a metric whose transverse traceless component is the gravitational memory. The shockwave momentum in 't Hooft's analysis is related to the soft graviton mode, which is responsible for the memory effect, while the shift in the shockwave position is related to the Goldstone mode. This equivalence opens new directions to utilize the gravitational memory effect to explore the observational implications of shockwave geometries in flat space.\] ## A "duality" - the shockwave and the memory effect are similar: - momenta $P$ $\leftrightarrow$ news $N$ - positions $X$ $\leftrightarrow$ shear $C$ ## Shockwave effective action - from [[1993#Verlinde, Verlinde]] # Herderschee, Maldacena (Dec, a) ## Three Point Amplitudes in Matrix Theory \[Links: [arXiv](https://arxiv.org/abs/2312.12592), [PDF](https://arxiv.org/pdf/2312.12592.pdf)\] \[Abstract: We compute the three graviton amplitude in the [[0479 BFSS matrix model|Banks-Fischler-Shenker-Susskind]] matrix model for [[0517 M-theory|M-theory]]. Even though the three point amplitude is determined by super Poincare invariance in eleven dimensional M-theory, it requires a non-trivial computation in the matrix model. We consider a configuration where all three gravitons carry non-zero longitudinal momentum. To simplify the problem, we compactify one additional dimension and relate the amplitude to a supersymmetric index computation. We find agreement with the expected answer even at finite values of $N$.\] # Herderschee, Maldacena (Dec, b) ## Soft Theorems in Matrix Theory \[Links: [arXiv](https://arxiv.org/abs/2312.15111), [PDF](https://arxiv.org/pdf/2312.15111.pdf)\] \[Abstract: We show that the [[0479 BFSS matrix model|Banks-Fischler-Shenker-Susskind]] matrix model for [[0517 M-theory|M-theory]] obeys the leading and subleading [[0009 Soft theorems|soft theorems]] expected from eleven-dimensional supergravity. The subleading soft theorem implies the amplitude is Lorentz symmetric. This is argued for general four point amplitudes, but only for restricted kinematics for five and higher point amplitudes.\] # Hernandez-Cuenca, Hubeny, Jia ## Holographic Entropy Inequalities and Multipartite Entanglement \[Links: [arXiv](https://arxiv.org/abs/2309.06296), [PDF](https://arxiv.org/pdf/2309.06296.pdf)\] \[Abstract: We study [[0259 Holographic entropy cone|holographic entropy inequalities]] and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much simpler ones which share interestingly rigid structures. By performing a systematic search over some of these structures, we are able to discover more than 300 novel entropy inequalities for six parties, thereby demonstrating that these recastings provide a fruitful generating technique for uncovering new holographic entropy inequalities. In attempting to interpret the corresponding sign-definite quantities as correlation measures, we also obtain a no-go result: the superbalance property of holographic entropy inequalities turns out to preclude them from being monotonic under partial tracing. In the process, we also comment on the geometrical significance of multipartite information quantities and present various structural relations amongst them.\] # Himwich, Pate ## ${\rm w}_{1+\infty}$ in 4D Gravitational Scattering \[Links: [arXiv](https://arxiv.org/abs/2312.08597), [PDF](https://arxiv.org/pdf/2312.08597.pdf)\] \[Abstract: In four-dimensional asymptotically flat spacetimes, an infinite tower of soft graviton modes is known to generate the [[0328 w(1+infinity)|symmetry algebra]] of ${\rm w}_{1+\infty}$ at tree-level. Here we demonstrate that the symmetry action follows from soft graviton theorems and acts non-trivially on massive scalar particles. By generalizing previous analyses that were specifically tailored to the scattering of massless particles, our results clarify that ${\rm w}_{1+\infty}$ symmetry is a universal feature of tree-level gravitational scattering in four-dimensional asymptotically flat spacetimes and originates from minimally-coupled gravitational interactions. In addition, we show that the ${\rm w}_{1+\infty}$ symmetry acts non-diagonally on massive states by mixing an infinite number of conformal families. We also present a concrete example of non-local behavior on the [[0022 Celestial sphere|celestial sphere]] in the presence of massive scattering states.\] ## Modified partition of soft factor: massless For $l=-1,0,1$, the following expression transform like a primary under $\mathrm{SL}(2,\mathbb{C})$:$S_k^{\prime(\ell)}(z, \bar{z})=\frac{\varepsilon_{+\mu \nu} p_k^\mu p_k^\nu}{\hat{q} \cdot p_k} \frac{1}{(\ell+1) !}\left(\frac{F_{+} \cdot \mathcal{J}_k}{\varepsilon_{+} \cdot p_k}\right)^{\ell+1},$which actually reduces to $S''$ for $\ell=-1,0$. But this depends on the reference vector for $\ell>1$, so the partition is not conformally invariant strictly speaking. However, this does not pose a fundamental obstacle to establish w symmetry: it is sufficient to define the generators using a primary descendant of this expression. ## Modified partition of soft factor: massive For massive particles, the primary descendant of $S'$ mentioned above is independent of the reference vector only for $\ell=-1,0,1$. But for $\ell>1$, we can further split $S'$ into a sum of terms, one of which is independent of the reference. Then one can define a new soft factor partition and denote $S$ to be the reference-independent term. From there, it is then shown that the modes of the (specific) primary descendant of $S$ generates w symmetry. # Horowitz, Leung, Queimada, Zhao ## Boundary signature of singularity in the presence of a shock wave \[Links: [arXiv](https://arxiv.org/abs/2310.03076), [PDF](https://arxiv.org/pdf/2310.03076.pdf)\] \[Abstract: Matter falling into a Schwarzschild-AdS black hole from the left causes increased focussing of ingoing geodesics from the right, and, as a consequence, they reach the singularity sooner. In a standard Penrose diagram, the singularity "bends down". We show how to detect this feature of the singularity [[0001 AdS-CFT|holographically]], using a boundary [[0103 Two-point functions|two-point function]]. We model the matter with a [[0117 Shockwave|shock wave]], and show that this bending down of the singularity can be read off from a novel analytic continuation of the boundary two-point function. Along the way, we obtain a generalization of the recently proposed thermal product formula for two-point correlators.\] # Hoult, Kovtun ## Causality and classical dispersion relations \[Links: [arXiv](https://arxiv.org/abs/2309.11703), [PDF](https://arxiv.org/pdf/2309.11703.pdf)\] \[Abstract: We explore the consequences of relativistic causality and covariant stability for short-wavelength dispersion relations in classical systems. For excitations described by a finite number of partial differential equations, as is the case in relativistic hydrodynamics, we give causality and covariant stability constraints on the excitation's frequency at large momenta.\] # Hu, Zhou ## Recursive construction for expansions of tree Yang-Mills amplitudes from soft theorem \[Links: [arXiv](https://arxiv.org/abs/2311.03112), [PDF](https://arxiv.org/pdf/2311.03112.pdf)\] \[Abstract: In this paper, we have introduced a fundamentally different approach, based on a bottom-up methodology, to expand tree-level Yang-Mills (YM) amplitudes into Yang-Mills-scalar (YMS) amplitudes and Bi-adjoint-scalar (BAS) amplitudes. Our method relies solely on the intrinsic [[0009 Soft theorems|soft]] behavior of external gluons, eliminating the need for external aids such as Feynman rules or [[0543 Cachazo-He-Yuan formalism|CHY]] rules. The recursive procedure consistently preserves explicit gauge invariance at every step, ultimately resulting in a manifest gauge-invariant outcome when the initial expression is already framed in a gauge-invariant manner. The resulting expansion can be directly analogized to the expansions of gravitational (GR) amplitudes using the [[0067 Double copy|double copy]] structure. When combined with the expansions of Einstein-Yang-Mills amplitudes obtained using the covariant double copy method from existing literature, the expansions presented in this note yield gauge-invariant [[0152 Colour-kinematics duality|BCJ]] numerators.\] # Jafferis, Zlokapa, Lykken, Kolchmeyer, Davis, Lauk, Neven, Spiropulu ## Comment on "Comment on "Traversable wormhole dynamics on a quantum processor" " \[Links: [arXiv](https://arxiv.org/abs/2303.15423), [PDF](https://arxiv.org/pdf/2303.15423.pdf)\] \[Abstract: We observe that the comment of \[[[2023#Kobrin, Schuster, Yao|1]]\] is consistent with \[[[2022#Jafferis, Zlokapa, Lykken, Kolchmeyer, Davis, Lauk, Neven, Spiropulu|2]]\] on key points: i) the microscopic mechanism of the experimentally observed teleportation is size winding and ii) the system thermalizes and scrambles at the time of teleportation. These properties are consistent with a gravitational interpretation of the teleportation dynamics, as opposed to the late-time dynamics. The objections of [1] concern counterfactual scenarios outside of the experimentally implemented protocol.\] ## Refs - reply to [[2023#Kobrin, Schuster, Yao]] which was a comment on [[2022#Jafferis, Zlokapa, Lykken, Kolchmeyer, Davis, Lauk, Neven, Spiropulu]] # Jain, Kundu, Minwalla, Parrikar, Prabhu, Shrivastava ## The S-matrix and boundary correlators in flat space \[Links: [arXiv](https://arxiv.org/abs/2311.03443), [PDF](https://arxiv.org/pdf/2311.03443.pdf)\] \[Abstract: We consider the path integral of a quantum field theory in Minkowski spacetime with fixed boundary values (for the elementary fields) on asymptotic boundaries. We define and study the corresponding boundary correlation functions obtained by taking derivatives of this path integral with respect to the boundary values. The S-matrix of the QFT can be extracted directly from these boundary correlation functions after smearing. We interpret this relation in terms of coherent state quantization and derive the constraints on the path-integral as a function of boundary values that follow from the unitarity of the S-matrix. We then study the locality structure of boundary correlation functions. In the massive case, we find that the boundary correlation functions for generic locations of boundary points are dominated by a saddle point which has the interpretation of particles scattering in a small elevator in the bulk, where the location of the elevator is determined dynamically, and the S-matrix can be recovered after stripping off some dynamically determined but non-local ‘’renormalization'' factors. In the massless case, we find that while the boundary correlation functions are generically analytic as a function on the whole manifold of locations of boundary points, they have special singularities on a sub-manifold, points on which correspond to light-like scattering in the bulk. We completely characterize this singular scattering sub-manifold, and find that the corresponding residues of the boundary correlations at these singularities are precisely given by S-matrices. This analysis parallels the analysis of [[0128 Bulk point singularity|bulk-point singularities]] in AdS/CFT and generalizes it to the case of multi-bulk point singularities.\] # Jensen, Sorce, Speranza ## Generalized entropy for general subregions in quantum gravity \[Links: [arXiv](https://arxiv.org/abs/2306.01837), [PDF](https://arxiv.org/pdf/2306.01837.pdf)\] \[Abstract: We consider quantum algebras of observables associated with subregions in theories of [[0554 Einstein gravity|Einstein gravity]] coupled to matter in the $G_N\rightarrow 0$ limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we argue that the algebra is a type II von Neumann factor. To do so in the former case we introduce a model of an observer living in the region; in the latter, the [[0487 ADM mass|ADM Hamiltonian]] effectively serves as an observer. In both cases the entropy of states on which this algebra acts is UV finite, and we find that it agrees, up to a state-independent constant, with the generalized entropy. For spatially compact regions the algebra is type II$_1$, implying the existence of an entropy maximizing state, which realizes a version of Jacobson's entanglement equilibrium hypothesis. The construction relies on the existence of well-motivated but conjectural states whose [[0416 Modular Hamiltonian|modular flow]] is geometric at an instant in time. Our results generalize the recent work of [[2022#Chandrasekaran, Longo, Penington, Witten]] on an algebra of operators for the static patch of de Sitter space.\] ## Limitations of previous work - boost symmetry of background metric required ## Hamiltonian - ADM Hamiltonian, QFT Hamiltonian, and observer Hamiltonian ## Assumptions and constructions 1. QFT in curved spacetime, type III$_1$ 2. observer dof 3. gravitational constriant 4. geometric modular flow 5. local first law 6. positive energy condition ## Refs - [[BisognanoWichmann1975]]: justifies that subregions locally look like Rindler, whose vacuum modular Hamiltonian is the the boost generator - [[Jacobson2015]]: entanglement equilibrium conjecture (small causal diamonds in quantum gravity have a maximally entangled state) # Jeong ## Quantum Chaos and Pole-Skipping in Semi-Locally Critical IR \[Links: [arXiv](https://arxiv.org/abs/2309.13412), [PDF](https://arxiv.org/pdf/2309.13412.pdf)\] \[Abstract: We investigate [[0179 Pole skipping|pole-skipping]] and its connection with [[0008 Quantum chaos|quantum chaos]], emphasizing the role of the IR fixed point in the established relationship between pole-skipping and a universal bound of the [[0434 Diffusivity|energy diffusion constant]]. Using the holographic Gubser-Rocha model, which features a semi-locally critical IR fixed point, we refine the pole-skipping argument to apply to generic fixed points. Additionally, we explore the reconstruction of the full hydrodynamic dispersion relation through pole-skipping. By considering conditions in which the dispersion relation exhibits the energy diffusive mode at low wave-vector and passes through a pole-skipping point, we propose an effective heuristic approximation that relies on three physical quantities: $(D_e, \, v_B, \, \lambda_L)$, determined from horizon data. Here, $D_e$ represents the energy diffusion constant, $v_B$ the [[0167 Butterfly velocity|butterfly velocity]], and $\lambda_L$ the [[0466 Lyapunov exponent|Lyapunov exponent]]. Remarkably, this approximation demonstrates excellent agreement with the [[0325 Quasi-normal modes|quasi-normal mode]], even extending its applicability beyond the [[0429 Hydrodynamics|hydrodynamic]] regime.\] # Jeong, Ji, Kim ## Pole-Skipping in Rotating BTZ Black Holes \[Links: [arXiv](https://arxiv.org/abs/2306.14805), [PDF](https://arxiv.org/pdf/2306.14805.pdf)\] \[Abstract: Motivated by the connection between [[0179 Pole skipping|pole-skipping]] phenomena of two point functions and four point out-of-time-order correlators, we study the pole-skipping phenomena for rotating [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black holes. In particular, we investigate the effect of rotations on the pole-skipping point for various fields with spin $s = 1/2, 1, 2/3$, extending the previous research for $s=0, 2$. We derive an analytic full tower of the pole-skipping points of fermionic ($s=1/2$) and vector ($s=1$) fields by the exact holographic Green's functions. For the *non-extremal* black hole, the leading pole-skipping frequency is $\omega_{\text{leading}}=2\pi i T_h {(s-1+\nu \Omega)}/{(1-\Omega^2)}$ where $T_h$ is the temperature, $\Omega$ the rotation, and $\nu:=(\Delta_+ - \Delta_-)/2$, the difference of conformal dimensions ($\Delta_{\pm}$). These are confirmed by another independent method: the near-horizon analysis. For the *extremal* black hole, we find that the leading pole-skipping frequency can occur at $\omega_{\text{leading}}^{\text{extremal}}=-2\pi i T_R {(s+1)}$ only when $\nu = s+1$, where $T_R$ is the temperature of the right moving mode. It is non-trivial because it cannot be achieved by simply taking the extreme limit $(T_h\rightarrow 0\,, \Omega\rightarrow 1)$ of the non-extremal black hole result.\] # Jian, Zhang ## Subsystem Complexity and Measurements in Holography \[Links: [arXiv](https://arxiv.org/abs/2312.04437), [PDF](https://arxiv.org/pdf/2312.04437.pdf)\] \[Abstract: We investigate the impact of measuring one subsystem on the holographic [[0204 Quantum complexity|complexity]] of another. While a naive expectation might suggest a reduction in complexity due to the collapse of the state to a trivial product state during quantum measurements, our findings reveal a counterintuitive result: in numerous scenarios, measurements on one subsystem can amplify the complexity of another. We first present a counting argument elucidating this complexity transition in random states. Then, employing the subregion "complexity=volume" (CV) proposal, we identify a complexity phase transition induced by projection measurements in various holographic CFT setups, including CFT vacuum states, [[0574 Thermofield double|thermofield double]] states, and the joint system of a black hole coupled to a bath. According to the [[0181 AdS-BCFT|AdS/BCFT]] correspondence, the post-measurement dual geometry involves an end-of-the-world brane created by the projection measurement. The complexity phase transition corresponds to the transition of the entanglement wedge to the one connected to the brane. In the context of the thermofield double setup, complete projection on one side can transform the other side into a boundary state black hole with higher complexity or a pure AdS with lower complexity. In the joint system of a black hole coupled to a nongraviting bath, where (a part of) the radiation is measured, the BCFT features two boundaries: one for the black hole and the other for the measurement. We construct the bulk dual involving intersecting or non-intersecting branes, and investigate the complexity transition induced by the projection measurement. Notably, for a subsystem that contains the black hole brane, its [[0007 RT surface|RT surface]] may undergo a transition, giving rise to a complexity jump.\] # Johnson ## Non-Perturbative ${\cal N}=2$ JT Supergravity \[Links: [arXiv](https://arxiv.org/abs/2306.10139), [PDF](https://arxiv.org/pdf/2306.10139.pdf)\] \[Abstract: It is shown how to non-perturbatively define a [[0197 Matrix model|random matrix model]] that captures key physics of ${\cal N}{=}2$ [[0050 JT gravity|JT]] supergravity, going well beyond the perturbative topological expansion in terms of Euclidean surfaces discussed recently by [[2023#Turiaci, Witten]]. A decomposition into an infinite family of certain minimal models is derived, leading to the definition of a non-linear differential equation from which the physics may be computed. [[0178 BPS|BPS]] states are naturally described by this model, and the non-perturbative completions of the spectral densities for non-BPS sectors are readily extracted. The sectors with non-zero threshold energy have a spectral density that shares many of the key qualitative features of the standard perturbative result, although there are quantitative differences. Notably, the potential non-perturbative instability that Turiaci and Witten anticipated for such sectors is shown to be absent here.\] # Jonay, Zhou ## A Physical Theory of Two-stage Thermalization \[Links: [arXiv](https://arxiv.org/abs/2310.04491), [PDF](https://arxiv.org/pdf/2310.04491.pdf); Talks: [CMSA](https://cmsa.fas.harvard.edu/event/qm_102023/)\] \[Abstract: One indication of thermalization time is subsystem entanglement reaching thermal values. Recent studies on local quantum circuits reveal two exponential stages with decay rates $r_1$ and $r_2$ of the purity before and after thermalization. We provide an [[0433 Membrane theory of entanglement dynamics|entanglement membrane theory]] interpretation, with $r_1$ corresponding to the domain wall free energy. Circuit geometry can lead to $r_1 < r_2$, producing a "phantom eigenvalue". Competition between the domain wall and magnon leads to $r_2 < r_1$ when the magnon prevails. However, when the domain wall wins, this mechanism provides a practical approach for measuring [[0522 Entanglement dynamics|entanglement growth]] through local correlation functions.\] ## A phase transition - before saturation time: domain wall dominates - after saturation time: domain wall v.s. magnon competition ## Comments - no concept of temperature in the circuit model # Jorstad, Myers, Ruan ## Complexity=Anything: Singularity Probes \[Links: [arXiv](https://arxiv.org/abs/2304.05453), [PDF](https://arxiv.org/pdf/2304.05453.pdf)\] \[Abstract: We investigate how the complexity=anything observables proposed by [[2021#Belin, Myers, Ruan, Sarosi, Speranza]] and [[2022#Belin, Myers, Ruan, Sarosi, Speranza]] can be used to investigate the interior geometry of AdS black holes. In particular, we illustrate how the flexibility of the complexity=anything approach allows us to systematically probe the geometric properties of black hole singularities. We contrast our results for the AdS Schwarzschild and AdS Reissner-Nordström geometries, i.e., for uncharged and charged black holes, respectively. In the latter case, the holographic complexity observables can only probe the interior up to the inner horizon.\] # Jorstad, Pasterski, Sharma ## Equating Extrapolate Dictionaries for Massless Scattering \[Links: [arXiv](https://arxiv.org/abs/2310.02186), [PDF](https://arxiv.org/pdf/2310.02186.pdf)\] \[Abstract: We study features of [[0010 Celestial holography|celestial CFT]] correlation functions when the bulk theory is itself a CFT. We show that [[0028 Conformal symmetry|conformal inversions]] in the bulk map boost eigenstates to [[0039 Shadow transform|shadow transformed]] boost eigenstates. This is demonstrated explicitly for the wavefunctions of free massless scalars, and finds interesting applications to building extrapolate dictionaries. Because inversions exchange null infinity and the light cone of the origin, one finds a relation between the massless extrapolate dictionary -- involving correlators of operators inserted along null infinity -- and the slice-by-slice extrapolate dictionary recently studied by [[2023#Sleight, Taronna|Sleight and Taronna]] starting from the hyperbolic foliation of [[2003#de Boer, Solodukhin|de Boer and Solodukhin]]. Namely, boundary correlators of Sleight and Taronna coincide with celestial amplitudes of shadow transformed boost eigenstates. These considerations are unified by lifting celestial correlators to the Einstein cylinder. This also sheds new light on the extraction of the S-matrix from the [[0454 Flat holography from AdS-CFT|flat limit of AdS/CFT]].\] ## Summary - 4d conformal inversion = 2d shadow transform # Joung, Narayan, Yoon ## Gravitational Edge Mode in Asymptotically AdS$_2$: JT Gravity Revisited \[Links: [arXiv](https://arxiv.org/abs/2304.06088), [PDF](https://arxiv.org/pdf/2304.06088.pdf)\] \[Abstract: We study the gravitational edge mode of the [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] and the constrained $sl(2,\mathbb{R})$ [[0557 BF theory|BF theory]] for the asymptotically AdS$_2$. We revisit the derivation of the Schwarzian theory from the wiggling boundary as an action for the gravitational edge mode. We present an alternative description for the gravitational edge mode from the metric fluctuation with the fixed boundary, which is also known as the would-be gauge mode in the gravity. We clarify the relation between the wiggling boundary and the would-be gauge mode. We demonstrate a natural top-down derivation of $PSL(2,\mathbb{R})$ gauging and the path integral measure of the Schwarzian theory. In the constrained $sl(2,\mathbb{R})$ BF theory, we develop a method for incorporating the gravitational edge mode in the BF theory. In this BF theory coupled to the edge mode, we derive the Schwarzian theory with $PSL(2,\mathbb{R})$ gauging. We show that the Haar measure for the Iwasawa decomposition of $PSL(2,\mathbb{R})$ leads to the path integral measure.\] # Kalloor, Sharon ## More on chaos at weak coupling \[Links: [arXiv](https://arxiv.org/abs/2301.01353), [PDF](https://arxiv.org/pdf/2301.01353.pdf)\] \[Abstract: We discuss aspects of the [[0466 Lyapunov exponent|quantum Lyapunov exponent]] $\lambda_L$ in theories with an exactly marginal [[0201 Sachdev-Ye-Kitaev model|SYK]]-like random interaction, where $\lambda_L$ can be computed as a continuous function of the interaction strength $\mathcal{J}$. In 1d, we prove a conjecture from [[2021#Berkooz, Sharon, Silberstein, Urbach]] which states that at small $\mathcal{J}$, $\lambda_L$ can be found by considering a specific limit of the four-point function in the decoupled theory. We then provide additional evidence for the 2d version of this conjecture by discussing new examples of Lyapunov exponents which can be computed at weak coupling.\] ## Refs - based on earlier work [[2021#Berkooz, Sharon, Silberstein, Urbach]] # Kastikainen, Svesko (Dec, a) ## Gravitational Rényi entropy from corner terms \[Links: [arXiv](https://arxiv.org/abs/2312.06765), [PDF](https://arxiv.org/pdf/2312.06765.pdf)\] \[Abstract: We provide a consistent first principles prescription to compute gravitational [[0293 Renyi entropy|Rényi entropy]] using [[0102 Hayward term|Hayward corner terms]]. For Euclidean solutions to Einstein gravity, we compute Rényi entropy of [[0162 No-boundary wavefunction|Hartle--Hawking]] and [[0024 Fixed area states|fixed--area states]] by cutting open a manifold containing a conical singularity into a wedge with a corner. The entropy functional for fixed--area states is equal to the corner term itself, having a flat-entanglement spectrum, while extremization of the functional follows from the variation of the corner term under diffeomorphisms. Notably, our method does not require regularization of the conical singularity, and naturally extends to [[0006 Higher-derivative gravity|higher-curvature theories of gravity]].\] # Kastikainen, Svesko (Dec, b) ## Cornering gravitational entropy \[Links: [arXiv](https://arxiv.org/abs/2312.13357), [PDF](https://arxiv.org/pdf/2312.13357.pdf)\] \[Abstract: We present a new derivation of [[0145 Generalised area|gravitational entropy functionals]] in [[0006 Higher-derivative gravity|higher-curvature theories of gravity]] using [[0102 Hayward term|corner terms]] that are needed to ensure well-posedness of the variational principle in the presence of corners. This is accomplished by cutting open a manifold with a conical singularity into a wedge with boundaries intersecting at a corner. Notably, our observation provides a rigorous definition of the action of a conical singularity that does not require regularization. For Einstein gravity, we compute the [[0293 Renyi entropy|Rényi entropy]] of gravitational states with either fixed-periodicity or fixed-area boundary conditions. The entropy functional for fixed-area states is equal to the corner term, whose extremization follows from the variation of the Einstein action of the wedge under transverse diffeomorphisms. For general [[0341 Lovelock gravity|Lovelock gravity]] the entropy functional of fixed-periodicity states is equal to the Jacobson--Myers (JM) functional, while fixed-area states generalize to fixed-JM-functional states, having a flat spectrum. Extremization of the JM functional is shown to coincide with the variation of the Lovelock action of the wedge. For arbitrary F(Riemann) gravity, under special periodic boundary conditions, we recover the Dong--Lewkowycz entropy for fixed-periodicity states. Since the variational problem in the presence of corners is not well-posed, we conjecture the generalization of fixed-area states does not exist for such theories without additional boundary conditions. Thus, our work suggests the existence of entropy functionals is tied to the existence of corner terms which make the Dirichlet variational problem well-posed.\] # Katona, Lucietti ## Uniqueness of the extremal Schwarzschild de Sitter spacetime \[Links: [arXiv](https://arxiv.org/abs/2309.04238), [PDF](https://arxiv.org/pdf/2309.04238.pdf)\] \[Abstract: We prove that any analytic vacuum spacetime with a positive cosmological constant in four and higher dimensions, that contains a static extremal Killing horizon with a maximally symmetric compact cross-section, must be locally isometric to either the extremal [[0465 de Sitter black holes|Schwarzschild de Sitter solution]] or its near-horizon geometry (the Nariai solution). In four-dimensions, this implies these solutions are the [[0455 Black hole uniqueness theorems|only]] analytic vacuum spacetimes that contain a static extremal horizon with compact cross-sections (up to identifications). We also consider the analogous [[0455 Black hole uniqueness theorems|uniqueness problem]] for the four-dimensional extremal hyperbolic Schwarzschild anti-de Sitter solution and show that it reduces to an open problem for the spectrum of the laplacian on compact hyperbolic surfaces.\] # Karch, Kusuki, Ooguri, Sun, Wang ## Universality of Effective Central Charge in Interface CFTs \[Links: [arXiv](https://arxiv.org/abs/2308.05436), [PDF](https://arxiv.org/pdf/2308.05436.pdf)\] \[Abstract: When an interface connects two CFTs, the [[0301 Entanglement entropy|entanglement entropy]] between the two CFTs is determined by a quantity called the [[0572 Effective central charge|effective central charge]]. The effective central charge does not have a simple form in terms of the central charges of the two CFTs, but intricately depends on the transmissive properties of the interface. In this article, we examine universal properties of the effective central charge. We first clarify how the effective central charge appears when considering general subsystems of the interface CFT. Then using this result and ideas used in the proof of the [[0351 Irreversibility theorems|c-theorem]], we provide a universal upper bound on the effective central charge. In past studies, the effective central charge was defined only in two dimensions. We propose an analogue of the effective central charge in general dimensions possessing similar universal properties as in two dimensions.\] # Karch, Perez-Pardavila, Riojas, Youssef ## Subregion Entropy for the Doubly Holographic Global Black String \[Links: [arXiv](https://arxiv.org/abs/2303.09571), [PDF](https://arxiv.org/pdf/2303.09571.pdf)\] \[Abstract: We study the growth of [[0301 Entanglement entropy|entanglement entropy]] in a [[0544 Double holography|doubly holographic model]] of gravity for a ==spherical AdS black hole==. Compared to previous work, which was limited to the case of planar black holes, this introduces an extra scale to the problem. This allows us to analyze the interplay between the reorganization of entanglement entropy due to[[0213 Islands| island]] formation and the onset of the [[0012 Hawking-Page transition|Hawking-Page phase transition]] and to find the appearance of a new critical black hole radius unrelated to the thermodynamics. We also find that the geometry of the [[0007 RT surface|Ryu-Takayanagi surface]] capturing the physics of islands exhibits drastically different behavior than in the planar case.\] ## Summary - now two types of phase transitions: [[0213 Islands|island formation]] and [[0012 Hawking-Page transition|Hawking-Page]] # Kehagias, Kokkotas, Riotto, Taskas, Tringas ## The Weak Gravity Conjecture, Overcharged Shells and Gravitational Traps \[Links: [arXiv](https://arxiv.org/abs/https://arxiv.org/abs/2305.07915), [PDF](https://arxiv.org/pdf/https://arxiv.org/abs/2305.07915.pdf)\] \[Abstract: The [[0177 Weak gravity conjecture|Weak Gravity Conjecture]] predicts that in quantum gravity there should exist overcharged states, that is states with charge larger than their mass. Extending this to large masses and charges, we are expecting similar overcharged classical solutions. This has been demonstrated in [[0006 Higher-derivative gravity|higher-derivative]] extensions of [[0554 Einstein gravity|General Relativity]]. In this paper we investigate the existence of overcharged solutions in General Relativity. We study the dynamics of a thin shell of mass $m$ and charge $Q$ under the action of its own gravitational and $U(1)$ fields. We show that shells with surface energy $\sigma$ and pressure $P$ obeying $P=w\sigma$ with $0\leq w\leq 1$ are necessarily undercharged $m\geq |Q|$ and always collapse to form Reissner-Nordström black holes. Nevertheless, if $-1\leq w<0$, we find that overcharged $m\leq |Q|$ shells exist, which however, are inevitably stabilized at finite radial distance.\] # Kim, Kraus, Monten, Myers ## S-Matrix Path Integral Approach to Symmetries and Soft Theorems \[Links: [arXiv](https://arxiv.org/abs/2307.12368), [PDF](https://arxiv.org/pdf/2307.12368.pdf)\] \[Abstract: We explore a formulation of the S-matrix in terms of the path integral with specified asymptotic data, as originally proposed by [[0589 Arefeva-Faddeev-Slavnov formalism|Arefeva, Faddeev, and Slavnov]]. In the tree approximation the S-matrix is equal to the exponential of the classical action evaluated on-shell. This formulation is well-suited to questions involving [[0060 Asymptotic symmetry|asymptotic symmetries]], as it avoids reference to non-gauge/diffeomorphism invariant bulk correlators or sources at intermediate stages. We show that the [[0009 Soft theorems|soft photon theorem]], originally derived by Weinberg and more recently connected to asymptotic symmetries by Strominger and collaborators, follows rather simply from invariance of the action under large gauge transformations applied to the asymptotic data. We also show that this formalism allows for efficient computation of the S-matrix in curved spacetime, including particle production due to a time dependent metric.\] # Kim, Kraus, Myers ## Systematics of Boundary Actions in Gauge Theory and Gravity \[Links: [arXiv](https://arxiv.org/abs/2301.02964), [PDF](https://arxiv.org/pdf/2301.02964.pdf)\] \[Abstract: We undertake a general study of the boundary (or [[0556 Edge mode|edge]]) modes that arise in gauge and gravitational theories defined on a space with boundary, either asymptotic or at finite distance, focusing on efficient techniques for computing the corresponding boundary action. Such actions capture all the dynamics of the system that are implied by its [[0060 Asymptotic symmetry|asymptotic symmetry]] group, such as correlation functions of the corresponding conserved currents. Working in the [[0019 Covariant phase space|covariant phase space]] formalism, we develop a collection of approaches for isolating the boundary modes and their dynamics, and illustrate with various examples, notably AdS$_3$ gravity (with and without a gravitational [[0089 Chern-Simons theory|Chern-Simons]] terms) subject to assorted boundary conditions.\] # Kirklin (Essay) ## Probes, purviews, purgatories, parable, paradox? \[Links: [arXiv](https://arxiv.org/abs/2304.00679), [PDF](https://arxiv.org/pdf/2304.00679.pdf)\] \[Abstract: I discuss some general information-theoretic properties of quantum mechanical probes in semiclassical gravity: their purview, i.e. what they can see and act on (in terms of a generalised entanglement wedge), their spontaneous evaporation into a cloud of highly entropic particles when one tries to make them see too much (perhaps a parable on the dangers of straining one's eyes), and the subsequent resolution of an apparent information paradox.\] ## The model - semiclassical gravity$ \mathcal{Z} \approx \min _\tau \operatorname{ext}_g e^{i S_{\text {grav } .}[\tau, g]} \mathcal{Z}_\phi[\tau, g] $ - coupling to a probe$ \mathcal{Z} \approx \min _\tau \operatorname{ext}_{g, l} e^{i S_{\text {grav. }}[\tau, g]+i S_{\text {worldline }}[\tau, g, l]} \mathcal{Z}_{\phi, q}[\tau, g, l] $ ## Phases ![[Kirklin2023Essay_fig3.png|500]] - left: alive phase; have $Z_n$ fixed points - right: dead phase; no $Z_n$ fixed points ## Lessons - the probe can see both around it and possibly an island if there is enough entanglement between the degrees of freedom at the location of the probe and another region possibly far away - a phase transition happens if the probe tries to see too much # Klinger, Leigh (Jun) ## Crossed Products, Extended Phase Spaces and the Resolution of Entanglement Singularities \[Links: [arXiv](https://arxiv.org/abs/2306.09314), [PDF](https://arxiv.org/pdf/2306.09314.pdf)\] \[Abstract: We identify a direct correspondence between the crossed product construction which plays a crucial role in the theory of Type III [[0415 Von Neumann algebra|von Neumann algebras]], and the [[0044 Extended phase space|extended phase space]] construction which restores the integrability of non-zero charges generated by gauge symmetries in the presence of spatial substructures. This correspondence provides a blue-print for resolving singularities which are encountered in the computation of [[0301 Entanglement entropy|entanglement entropy]] for subregions in quantum field theories. The extended phase space encodes quantities that would be regarded as 'pure gauge' from the perspective of the full theory, but are nevertheless necessary for gluing together, in a path integral sense, physics in different subregions. These quantities are required in order to maintain gauge covariance under such gluings. The crossed product provides a consistent method for incorporating these necessary degrees of freedom into the operator algebra associated with a given subregion. In this way, the extended phase space completes the subregion algebra and subsequently allows for the assignment of a meaningful, finite entropy to states therein.\] # Klinger, Leigh (Dec) ## Crossed Products, Conditional Expectations and Constraint Quantization \[Links: [arXiv](https://arxiv.org/abs/2312.16678), [PDF](https://arxiv.org/pdf/2312.16678.pdf)\] \[Abstract: Recent work has highlighted the importance of crossed products in correctly elucidating the operator algebraic approach to quantum field theories. In the gravitational context, the crossed product simultaneously promotes [[0415 Von Neumann algebra|von Neumann algebras]] associated with subregions in diffeomorphism covariant quantum field theories from type III to type II, and provides the necessary ingredients to gravitationally [[0180 Dressing|dress]] operators, thereby enforcing the constraints of the theory. In this note we enhance the crossed product construction to the context of general gauge theories with ==arbitrary combinations of internal and spacetime local symmetries==. This is done by leveraging the correspondence between the crossed product and the [[0044 Extended phase space|extended phase space]]. We then undertake a detailed study of constraint quantization from the perspective of a generic crossed product algebra. We study and compare three distinct approaches to constraint quantization from this point of view: refined algebraic quantization, BRST quantization, and path integral quantization. Far from simply reproducing existing analyses, the operator algebraic viewpoint sheds new light on old problems by reformulating the dressing of operators in terms of a (generalized) conditional expectation. We conclude by applying our approach to the constraint quantization of three distinct gauge theories including a discussion of gravity on null hypersurfaces.\] # Klinger, Leigh, Pai ## Extended Phase Space in General Gauge Theories \[Links: [arXiv](https://arxiv.org/abs/2303.06786), [PDF](https://arxiv.org/pdf/2303.06786.pdf)\] \[Abstract: In a recent paper, it was shown that in diffeomorphism-invariant theories, Noether charges associated with a given codimension-2 surface become integrable if one introduces an [[0044 Extended phase space|extended phase space]]. In this paper we extend the notion of extended phase space to all gauge theories with arbitrary combinations of internal and spacetime local symmetries. We formulate this in terms of a corresponding Atiyah Lie algebroid, a geometric object derived from a principal bundle which features internal symmetries and diffeomorphisms on an equal footing. In this language, gauge transformations are understood as morphisms between Atiyah Lie algebroids that preserve the geometric structures encoded therein. The extended configuration space of a gauge theory can subsequently be understood as the space of pairs ($\varphi, \Phi$), where $\varphi$ is a Lie algebroid morphism and $\Phi$ is a field configuration in the non-extended sense. Starting from this data, we outline a very powerful, manifestly geometric approach to the extended phase space. Using this approach, we find that the action of the group of gauge transformations and diffeomorphisms on the symplectic geometry of any covariant theory is integrable. We motivate our construction by carefully examining the need for extended phase space in ==[[0089 Chern-Simons theory|Chern-Simons gauge theories]]== and display its usefulness by re-computing the charge algebra. We also describe the implementation of the configuration algebroid in ==Einstein-Yang-Mills== theories.\] # Kobayashi, Zhu ## Cross-cap defects and fault-tolerant logical gates in the surface code and the honeycomb Floquet code \[Links: [arXiv](https://arxiv.org/abs/2310.06917), [PDF](https://arxiv.org/pdf/2310.06917)\] \[Abstract: We consider the $\mathbb{Z}_2$ toric code, surface code and Floquet code defined on a non-orientable surface, which can be considered as families of codes extending Shor's 9-qubit code. We investigate the fault-tolerant logical gates of the $\mathbb{Z}_2$ toric code in this setup, which corresponds to $e\leftrightarrow m$ exchanging symmetry of the underlying $\mathbb{Z}_2$ gauge theory. We find that non-orientable geometry provides a new way the emergent symmetry acts on the code space, and discover the new realization of the fault-tolerant Hadamard gate of 2d $\mathbb{Z}_2$ toric code on a surface with a single cross-cap, dubbed a non-orientable toric code. This Hadamard gate can be realized by a constant-depth local unitary circuit modulo non-locality caused by a cross-cap. Via folding, the non-orientable surface code can be turned into a bilayer local quantum code, where the folded cross-cap is equivalent to a bi-layer twist terminated on a gapped boundary and the logical Hadamard only contains local gates with intra-layer couplings. We further obtain the complete logical Clifford gate set for a stack of non-orientable surface codes. We then construct the honeycomb Floquet code in the presence of a single cross-cap, and find that the period of the sequential Pauli measurements acts as a $HZ$ logical gate on the single logical qubit, where the cross-cap enriches the dynamics compared with the orientable case. We find that the dynamics of the honeycomb Floquet code is precisely described by a condensation operator of the $\mathbb{Z}_2$ gauge theory, and illustrate the exotic dynamics of our code in terms of a condensation operator supported at a non-orientable surface.\] # Kobrin, Schuster, Yao ## Comment on "Traversable wormhole dynamics on a quantum processor" \[Links: [arXiv](https://arxiv.org/abs/2302.07897), [PDF](https://arxiv.org/pdf/2302.07897.pdf)\] \[Abstract: A recent article [[2022#Jafferis, Zlokapa, Lykken, Kolchmeyer, Davis, Lauk, Neven, Spiropulu|Nature 612, 51-55 (2022)]] claims to observe [[0083 Traversable wormhole|traversable wormhole]] dynamics in an experiment. This claim is based upon performing a teleportation protocol using a Hamiltonian that consists of seven Majorana fermions with five fully-commuting terms. The Hamiltonian is generated via a machine-learning procedure designed to replicate the teleportation behavior of the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] (SYK) model. The authors claim that the learned Hamiltonian reproduces gravitational dynamics of the SYK model and demonstrates gravitational teleportation through an emergent wormhole. We find: (i) in contrast to these claims, the learned Hamiltonian does not exhibit thermalization; (ii) the teleportation signal only resembles the SYK model for operators that were used in the machine-learning training; (iii) the observed perfect size winding is in fact a generic feature of small-size, fully-commuting models, and does not appear to persist in larger-size fully-commuting models or in non-commuting models at equivalent system sizes\] # Koch ## Microscopic Entanglement Wedges \[Links: [arXiv](https://arxiv.org/abs/2307.05032), [PDF](https://arxiv.org/pdf/2307.05032.pdf)\] \[Abstract: We study the holographic [[0421 Higher-spin gravity|duality]] between the free $O(N)$ vector model and higher spin gravity. Conserved spinning primary currents of the conformal field theory (CFT) are dual to spinning gauge fields in the gravity. Reducing to independent components of the conserved CFT currents one finds two components at each spin. After gauge fixing the gravity and then reducing to independent components, one finds two components of the gauge field at each spin. Collective field theory provides a systematic way to map between these two sets of degrees of freedom, providing a complete and explicit identification between the dynamical degrees of freedom of the CFT and the dual gravity. The resulting map exhibits many features expected of holographic duality: it provides a valid [[0026 Bulk reconstruction|bulk reconstruction]], it reproduces insights expected from the holography of information and it provides a microscopic derivation of entanglement wedge reconstruction.\] # Kolanowski, Tomasevic ## Singularities in 2D and 3D quantum black holes \[Links: [arXiv](https://arxiv.org/abs/2310.06014), [PDF](https://arxiv.org/pdf/2310.06014.pdf)\] \[Abstract: We study black holes in two and three dimensions that have spacelike curvature singularities behind horizons. The 2D solutions are obtained by dimensionally reducing certain 3D black holes, known as quantum [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] solutions. Furthermore, we identify the corresponding dilaton potential and show how it can arise from a higher-dimensional theory. Finally, we show that the rotating BTZ black hole develops a singular inner horizon once quantum effects are properly accounted for, thereby solidifying [[0208 Strong cosmic censorship|strong cosmic censorship]] for all known cases.\] # Kolchmeyer ## von Neumann algebras in JT gravity \[Links: [arXiv](https://arxiv.org/abs/2303.04701), [PDF](https://arxiv.org/pdf/2303.04701.pdf)\] \[Abstract: We quantize [[0050 JT gravity|JT gravity]] with matter on the spatial interval with two asymptotically AdS boundaries. We consider the [[0415 Von Neumann algebra|von Neumann algebra]] generated by the right Hamiltonian and the gravitationally dressed matter operators on the right boundary. We prove that the commutant of this algebra is the analogously defined left boundary algebra and that both algebras are type II$_\infty$ factors. These algebras provide a precise notion of the entanglement wedge away from the semiclassical limit. We comment on how the factorization problem differs between pure JT gravity and JT gravity with matter.\] ## Refs - see also [[2023#Penington, Witten]] # Krishna ## Celestial gluon and graviton OPE at loop level \[Links: [arXiv](https://arxiv.org/abs/2310.16687), [PDF](https://arxiv.org/pdf/2310.16687.pdf)\] \[Abstract: In this paper, we analyze the loop corrections to [[0114 Celestial OPE|celestial OPE]] for gluons and gravitons. Even at the loop level, the soft gluons and gravitons have $\Delta=1-\mathbb Z_{\geq 0}$. The only novelty is the presence of higher poles. At one loop level, there are two types of conformal soft gluons with a single pole and a double pole in the $\Delta$ plane. The celestial OPEs are obtained using the [[0078 Collinear limit|collinear]] splitting functions. In the case of gluons, the splitting functions receive loop corrections. After taking the holomorphic soft limit, we find the OPE of conformal soft gluons. In the case of gravitons, where splitting functions are known to be all loop exact, we still find a $w_{\infty}$ algebra for soft gravitons which is in addition to the $w_{1+\infty}$ algebra already found by Strominger.\] # Krishna, Sahoo ## Universality of Loop Corrected Soft Theorems in 4d \[Links: [arXiv](https://arxiv.org/abs/2308.16807), [PDF](https://arxiv.org/pdf/2308.16807.pdf)\] \[Abstract: In [1808.03288](https://arxiv.org/abs/1808.03288), logarithmic correction to subleading soft photon and soft graviton theorems have been derived in four spacetime dimensions from the ratio of IR-finite S-matrices. This has been achieved after factoring out [[0295 Infrared divergences in scattering amplitude|IR-divergent]] components from the traditional electromagnetic and gravitational S-matrices using Grammer-Yennie prescription. Although the loop corrected subleading [[0009 Soft theorems|soft theorems]] are derived from one-loop scattering amplitudes involving scalar particles in a minimally coupled theory with scalar contact interaction, it has been conjectured that the soft factors are universal (theory independent) and one-loop exact (don't receive corrections from higher loops). This paper extends the analysis conducted in [1808.03288](https://arxiv.org/abs/1808.03288) to encompass general spinning particle scattering with non-minimal couplings permitted by gauge invariance and general coordinate invariance. By re-deriving the $\ln\omega$ soft factors in this generic setup, we establish their universal nature. Furthermore, we summarize the results of loop corrected soft photon and graviton theorems up to sub-subleading order, which follows from the analysis of one and two loop QED and quantum gravity S-matrices. While the classical versions of these soft factors have already been derived in the literature, we put forth conjectures regarding the quantum soft factors and outline potential strategies for their derivation.\] # Krishna, Wang ## Celestial holography from Chiral strings \[Links: [arXiv](https://arxiv.org/abs/2308.11799), [PDF](https://arxiv.org/pdf/2308.11799.pdf)\] \[Abstract: In this paper, we studied the relationship between [[0010 Celestial holography|celestial holography]] and chiral strings. Chiral strings differ from the usual string theory by a change of boundary conditions on the string propagators. It is shown that chiral strings would reproduce graviton amplitudes and could serve as an alternative description of [[0554 Einstein gravity|Einstein's gravity]]. Celestial holography is a proposed duality between gravity in asymptotically flat space-time and a CFT living on its conformal boundary. Since both are CFT descriptions of gravity, we investigate the potential connection between these two formalisms. In this paper, we find that both the energetic as well as conformal soft theorems could be derived from the [[0030 Operator product expansion|OPEs]] of vertex operators of chiral strings. All operators in the CCFT can be described by [[0079 Mellin transform|Mellin transforming]] the vertex operators in the chiral string theories, and the [[0114 Celestial OPE|OPE coefficients of CCFT]] can also be obtained from the world-sheet description.\] # Kudler-Flam, Leutheusser, Rahman, Satishchandran, Speranza ## A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC \[Links: [arXiv](https://arxiv.org/abs/2312.07646), [PDF](https://arxiv.org/pdf/2312.07646.pdf)\] \[Abstract: While [[0301 Entanglement entropy|von Neumann entropies]] for subregions in quantum field theory universally contain ultraviolet divergences, differences between von Neumann entropies are finite and well-defined in many physically relevant scenarios. We demonstrate that such a notion of entropy differences can be rigorously defined in quantum field theory in a general curved spacetime by introducing a novel, covariant regulator for the entropy based on the modular crossed product. This regulator associates a type II [[0415 Von Neumann algebra|von Neumann algebra]] to each spacetime subregion, resulting in well-defined renormalized entropies. This prescription reproduces formulas for entropy differences that coincide with heuristic formulas widely used in the literature, and we prove that it satisfies desirable properties such as unitary invariance and concavity. As an application, we provide proofs of the [[0418 Bekenstein bound|Bekenstein bound]] and the [[0405 Quantum null energy condition|quantum null energy condition]], formulated directly in terms of vacuum-subtracted von Neumann entropies.\] # Kudler-Flam, Leutheusser, Satishchandran ## Generalized Black Hole Entropy is von Neumann Entropy \[Links: [arXiv](https://arxiv.org/abs/2309.15897), [PDF](https://arxiv.org/pdf/2309.15897.pdf)\] \[Abstract: It was recently shown that the [[0415 Von Neumann algebra|von Neumann algebras]] of observables dressed to the mass of a Schwarzschild-AdS black hole or an observer in de Sitter are Type II, and thus admit well-defined traces. The von Neumann entropies of "semi-classical" states were found to be generalized entropies. However, these arguments relied on the existence of an equilibrium ([[0521 KMS condition|KMS]]) state and thus do not apply to, e.g., black holes formed from gravitational collapse, Kerr black holes, or black holes in asymptotically de Sitter space. In this paper, we present a general framework for obtaining the algebra of dressed observables for linear fields on any spacetime with a Killing horizon. We prove, assuming the existence of a stationary (but not necessarily KMS) state and suitable decay of solutions, a structure theorem that the algebra of dressed observables always contains a Type II factor "localized" on the horizon. These assumptions have been rigorously proven in most cases of interest. Applied to the algebra in the exterior of an asymptotically flat Kerr black hole, where the fields are dressed to the black hole mass and angular momentum, we find a product of a Type II$_{\infty}$ algebra on the horizon and a Type I$_{\infty}$ algebra at past null infinity. In Schwarzschild-de Sitter, despite the fact that we introduce an observer, the quantum field observables are dressed to the perturbed areas of the black hole and cosmological horizons and is the product of Type II$_{\infty}$ algebras on each horizon. In all cases, the von Neumann entropy for semiclassical states is given by the generalized entropy. Our results suggest that in all cases where there exists another "boundary structure" (e.g., an asymptotic boundary or another Killing horizon) the algebra of observables is Type II$_{\infty}$ and in the absence of such structures (e.g., de Sitter) the algebra is Type II$_{1}$.\] # Kusuki, Tamaoka, Wei, Yoneta ## Efficient Simulation of Low Temperature Physics in One-Dimensional Gapless Systems \[Links: [arXiv](https://arxiv.org/abs/2309.02519), [PDF](https://arxiv.org/pdf/2309.02519.pdf)\] \[Abstract: We discuss the computational efficiency of the finite temperature simulation with the minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement [[0293 Renyi entropy|Renyi entropy]] of METTS for Renyi index $0<q\leq 1$. In particular, for 1D gapless systems described by CFTs, the upper bound scales as $\mathcal{O}(c N^0 \log \beta)$ where $c$ is the central charge and $N$ is the system size. Furthermore, we numerically find that the average Renyi entropy exhibits a universal behavior characterized by the [[0033 Central charge|central charge]] and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS provide a significant speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.\] ## Real time versus imaginary time evolution - real time entanglement entropy growth is bounded by a linear function of $t$ (intuition from relativistic theory but also true without causality) - imaginary time growth can be much faster: $e^\beta$ - but this paper shows that it is not true # Lee ## Trace relations and open string vacua \[Links: [arXiv](https://arxiv.org/abs/2312.00242), [PDF](https://arxiv.org/pdf/2312.00242)\] \[Abstract: We study to what extent, and in what form, the notion of gauge-string duality may persist at finite $N$. It is shown, in the half-BPS sector, that the states of D3 giant graviton branes in $\mathrm{AdS}_5 \times S^5$ are holographically dual to certain auxiliary ghosts that compensate for finite $N$ trace relations in $U(N)$ $\mathcal{N}=4$ super Yang-Mills. The complex formed from spaces of states of bulk D3 giants is observed to furnish a BRST-like resolution of the half-BPS Hilbert space of $U(N)$ $\mathcal{N}=4$ SYM at finite $N$. We argue that the identification between the states of certain bulk D-branes and the auxiliary ghosts in the boundary holds rather generally at vanishing 't Hooft coupling $\lambda = 0$. We propose that a complex, which furnishes a BRST-like resolution of the finite $N$ Hilbert space of a boundary $U(N)$ gauge theory at $\lambda = 0$, should be identified as the space of states of the dual string theory in the $\alpha' \to \infty$ limit. The Lefschetz trace formula provides the holographic map in this regime, where bulk observables are computed by taking the alternating sum of the expectation values in an ensemble of states built on each open string vacuum. The giant graviton expansion is recovered and generalized in a limit of the resolution.\] # Lehners ## Review of the No-Boundary Wave Function \[Links: [arXiv](https://arxiv.org/abs/2303.08802), [PDF](https://arxiv.org/pdf/2303.08802.pdf)\] \[Abstract: When the universe is treated as a quantum system, it is described by a wave function. This wave function is a function not only of the matter fields, but also of spacetime. The [[0162 No-boundary wavefunction|no-boundary proposal]] is the idea that the wave function should be calculated by summing over geometries that have no boundary to the past, and over regular matter configurations on these geometries. Accordingly, the universe is finite, self-contained and the big bang singularity is avoided. Moreover, given a dynamical theory, the no-boundary proposal provides probabilities for various solutions of the theory. In this sense it provides a quantum theory of initial conditions. This review starts with a general overview of the framework of quantum cosmology, describing both the canonical and path integral approaches, and their interpretations. After recalling several heuristic motivations for the no-boundary proposal, its consequences are illustrated with simple examples, mainly in the context of cosmic inflation. We review how to include perturbations, assess the classicality of spacetime and how probabilities may be derived. A special emphasis is given to explicit implementations in [[0254 Minisuperspace|minisuperspace]], to observational consequences, and to the relationship of the no-boundary wave function with string theory. At each stage, the required analytic and numerical techniques are explained in detail, including the Picard-Lefschetz approach to oscillating integrals.\] # Lei, Shu, Zhang, Zhu ## Quasinormal Modes of C-metric from SCFTs \[Links: [arXiv](https://arxiv.org/abs/2308.16677), [PDF](https://arxiv.org/pdf/2308.16677.pdf)\] \[Abstract: We study the [[0325 Quasi-normal modes|quasinormal modes]] (QNM) of the charged [[0336 C-metric|C-metric]], which physically stands for a charged accelerating black hole, with the help of Nekrasov's partition function of 4d $\mathcal{N}=2$ [[0575 Superconformal field theories|superconformal field theories]] (SCFTs). The QNM in the charged C-metric are classified into three types: the photon-surface modes, the accelerating modes and the near-extremal modes, and it is curious how the single quantization condition proposed in [arXiv:2006.06111](https://arxiv.org/abs/2006.06111) can reproduce all the different families. We show that the connection formula encoded in terms of Nekrasov's partition function captures all these families of QNM numerically and recovers the asymptotic behavior of the accelerating and the near-extremal modes analytically. Using the connection formulae of different 4d $\mathcal{N}=2$ SCFTs, one can solve both the radial and the angular part of the scalar perturbation equation respectively. The same algorithm can be applied to the [[0465 de Sitter black holes|de Sitter (dS) black holes]] to calculate both the dS modes and the photon-sphere modes.\] # Leston, Goya, Perez-Nadal, Passaglia, Giribet ## 3d Quantum Gravity Partition Function at 3 Loops: a brute force computation \[Links: [arXiv](https://arxiv.org/abs/2307.03830), [PDF](https://arxiv.org/pdf/2307.03830.pdf)\] \[Abstract: The partition function of [[0002 3D gravity|3-dimensional quantum gravity]] has been argued to be 1-loop exact. Here, we verify the vanishing of higher-orders in perturbation theory by explicit computation in the second-order, metric formulation at 3-loops. The number of 1-particle irreducible Feynman diagrams involving both gravitons and ghosts turns out to be 17. Using dimensional regularization, we solve all the diagrams. At 2-loops, we find that all such diagrams vanish separately after regularization. At 3-loops, in contrast, a series of remarkable cancellations between different diagrams takes place, with 9 diagrams beautifully conspiring to yield a vanishing result. Our techniques are suitable to be applied to higher loops as well as to similar computations in higher dimensions.\] # Lin ## Bootstrap bounds on D0-brane quantum mechanics \[Links: [arXiv](https://arxiv.org/abs/2302.04416), [PDF](https://arxiv.org/pdf/2302.04416.pdf)\] \[Abstract: We derive simple bootstrap bounds on correlation functions of the [[0479 BFSS matrix model|BFSS matrix theory]]/D0-brane quantum mechanics. The result strengthens and extends Polchinski's virial theorem bound to finite energies and gives the first non-trivial bound on $\langle \text{Tr}\, X^2\rangle$. Despite their simplicity, the bounds hint at some features of the dual black hole geometry. Our best lower bounds are already a factor of $\sim 0.73$ from the large $N$ extrapolation of Monte Carlo predictions.\] # Lin, Stanford ## A symmetry algebra in double-scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2307.15725), [PDF](https://arxiv.org/pdf/2307.15725.pdf)\] \[Abstract: The [[0503 Double-scaled SYK|double-scaled limit]] of the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] (SYK) model takes the number of fermions and their interaction number to infinity in a coordinated way. In this limit, two entangled copies of the SYK model have a bulk description of sorts known as the "chord Hilbert space." We analyze a symmetry algebra acting on this Hilbert space, generated by the two Hamiltonians together with a two-sided operator known as the chord number. This algebra is a deformation of the [[0050 JT gravity|JT]] gravitational algebra, and it contains a subalgebra that is a deformation of the $\mathfrak{sl}_2$ [[0561 Near-horizon symmetry|near-horizon symmetries]]. The subalgebra has finite-dimensional unitary representations corresponding to matter moving around in a discrete Einstein-Rosen bridge. In a semiclassical limit the discreteness disappears and the subalgebra simplifies to $\mathfrak{sl}_2$, but with a non-standard action on the boundary time coordinate. One can make the action of $\mathfrak{sl}_2$ algebra more standard at the cost of extending the boundary circle to include some "fake" portions. Such fake portions also accommodate certain subtle states that survive the semi-classical limit, despite oscillating on the scale of discreteness. We discuss applications of this algebra, including sub-maximal [[0008 Quantum chaos|chaos]], the [[0083 Traversable wormhole|traversable wormhole]] protocol, and a two-sided [[0030 Operator product expansion|OPE]].\] ## JT algebra - classical JT algebra by [[2021#Harlow, Wu]] and quantum algebra by [[2022#Lin]] - the algebra is deformed in [[0503 Double-scaled SYK|DSSYK]] ## Fake circle - take the semiclassical limit $\lambda\to0$ # Lin, Usatyuk ## Revisiting the second order formalism of JT gravity \[Links: [arXiv](https://arxiv.org/abs/2310.16081), [PDF](https://arxiv.org/pdf/2310.16081)\] \[Abstract: We revisit the gravity path integral formalism of [[0050 JT gravity|JT gravity]]. We explain how to gauge fix the path integral in the presence of asymptotic boundaries and conical defects, and resolve an ambiguity regarding the dilaton gravity operator that creates a conical defect. Along the way we study JT gravity coupled to matter on surfaces with defects of special opening angles, obtaining expressions for partition and two-point functions of matter fields. The two point function involves a summation over all geodesics on the surface, including self-intersecting geodesics, which we formally manage to include.\] # Lin, Yang ## Double copy for tree-level form factors II: generalizations and special topics \[Links: [arXiv](https://arxiv.org/abs/2306.04672), [PDF](https://arxiv.org/pdf/2306.04672.pdf)\] \[Abstract: Both the [[0152 Colour-kinematics duality|Bern, Carrasco and Johansson (BCJ)]] and the [[0398 KLT relations|Kawai, Lewellen and Tye (KLT)]] double-copy formalisms have been recently generalized to a class of scattering matrix elements (so-called [[0566 Form factors|form factors]]) that involve local gauge-invariant operators. In this paper we continue the study of double copy for form factors. First, we generalize the double-copy prescription to form factors of higher-length operators ${\rm tr}(\phi^m)$ with $m\geq3$. These higher-length operators introduce new non-trivial color identities, but the double-copy prescription works perfectly well. The closed formulae for the CK-dual numerators are also provided. Next, we discuss the $\vec{v}$ vectors which are central ingredients appearing in the factorization relations of both the KLT kernels and the gauge form factors. We present a general construction rule for the $\vec{v}$ vectors and discuss their universal properties. Finally, we consider the double copy for the form factor of the ${\rm tr}(F^2)$ operator in pure Yang-Mills theory. In this case, we propose a new prescription that involves a gauge invariant decomposition for the form factor and a combination of different CK-dual numerators appearing in the expansion.\] ## Refs - part I: [[2022#Lin, Yang]] # Maldacena ## A simple quantum system that describes a black hole \[Links: [arXiv](https://arxiv.org/abs/2303.11534), [PDF](https://arxiv.org/pdf/2303.11534.pdf)\] \[Abstract: During the past decades, theorists have been studying quantum mechanical systems that are believed to describe black holes. We review one of the simplest examples. It involves a collection of interacting oscillators and Majorana fermions. It is conjectured to describe a black hole in an emergent universe governed by Einstein equations. Based on previous numerical computations, we make an estimate of the necessary number of qubits necessary to see some black hole features.\] ## Indices - $I=1\dots9$: $SO(9)$ index - $a=1,\dots,N^2-1$: $SU(N)$ adjoint index (labelling different $SU(N)$ matrices) - $i=1,\dots,N$: $SU(N)$ matrix indices # Mao, Zhang ## Soft theorems in de Sitter spacetime \[Links: [arXiv](https://arxiv.org/abs/2308.08861), [PDF](https://arxiv.org/pdf/2308.08861.pdf)\] \[Abstract: In this paper, we derive a [[0009 Soft theorems|soft photon theorem]] and a soft gluon theorem in the de Sitter spacetime from the [[0106 Ward identity|Ward identity]] of the near cosmological horizon large gauge transformation. Taking the flat limit of the de Sitter spacetime, the soft theorems naturally recover the corresponding flat spacetime soft theorems.\] # Mason, Ruzziconi, Srikant ## Carrollian Amplitudes and Celestial Symmetries \[Links: [arXiv](https://arxiv.org/abs/2312.10138), [PDF](https://arxiv.org/pdf/2312.10138.pdf)\] \[Abstract: [[0419 Carrollian CFT|Carrollian holography]] aims to express gravity in four-dimensional asymptotically flat spacetime in terms of a dual three-dimensional Carrollian CFT living at null infinity. Carrollian amplitudes are massless scattering amplitudes written in terms of asymptotic or null data at $\mathscr I$. These position space amplitudes at $\mathscr I$ are to be re-interpreted as correlation functions in the putative dual Carrollian CFT. We derive basic results concerning tree-level Carrollian amplitudes yielding dynamical constraints on the holographic dual. We obtain surprisingly compact expressions for $n$-point [[0061 Maximally helicity violating amplitudes|MHV]] gluon and graviton amplitudes in position space at $\mathscr I$. We discuss the UV/IR behaviours of Carrollian amplitudes and investigate their [[0078 Collinear limit|collinear limit]], which allows us to define a notion of Carrollian OPE. By smearing the OPE along the generators of null infinity, we obtain the action of the [[0063 Symmetry of CCFT|celestial symmetries]] - namely, the $S$ algebra for Yang-Mills theory and $Lw_{1+\infty}$ for gravity - on the Carrollian operators. As a consistency check, we systematically relate our results with [[0516 Celestial correlators|celestial amplitudes]] using the link between the two approaches. Finally, we initiate a direct connection between [[0330 Twistor theory|twistor space]] and Carrollian amplitudes.\] # Matsuo ## Quantum focusing conjecture and the Page curve \[Links: [arXiv](https://arxiv.org/abs/2308.05009), [PDF](https://arxiv.org/pdf/2308.05009.pdf)\] \[Abstract: The focusing theorem fails for evaporating black holes because the null energy condition is violated by quantum effects. The [[0243 Quantum focusing conjecture|quantum focusing conjecture]] is proposed so that it is satisfied even if the null energy condition is violated. The conjecture states that the derivative of the sum of the area of a cross-section of the null geodesic congruence and the entanglement entropy of matters outside it is non-increasing. Naively, it is expected that the quantum focusing conjecture is violated after the Page time as both the area of the horizon and the [[0301 Entanglement entropy|entanglement entropy]] of the [[0304 Hawking radiation|Hawking radiation]] are decreasing. We calculate the entanglement entropy after the Page time by using the [[0213 Islands|island]] rule, and find the following results: (i) the page time is given by an approximately null surface, (ii) the entanglement entropy is increasing along the outgoing null geodesic even after the Page time, and (iii) the quantum focusing conjecture is not violated.\] # Maxfield ## Counting states in a model of replica wormholes \[Links: [arXiv](https://arxiv.org/abs/2311.05703), [PDF](https://arxiv.org/pdf/2311.05703.pdf)\] \[Abstract: We study the Hilbert space of a system of $n$ black holes with an inner product induced by [[0206 Replica wormholes|replica wormholes]]. This takes the form of a sum over permutations, which we interpret in terms of a gauge symmetry. The resulting inner product is degenerate, with null states lying in representations corresponding to Young diagrams with too many rows. We count the remaining states in a large $n$ limit, which is governed by an emergent collective Coulomb gas description describing the shape of typical Young diagrams. This exhibits a third-order phase transition when the null states become numerous. We find that the dimension of the black hole Hilbert space accords with a microscopic interpretation of [[0004 Black hole entropy|Bekenstein-Hawking entropy]].\] ## Setup - $n$ black holes, $S_{\mathrm{phys}} \sim n S_{\mathrm{BH}}=n \log q$ # Melnikov ## Connectomes as Holographic States \[Links: [arXiv](https://arxiv.org/abs/2312.16683), [PDF](https://arxiv.org/pdf/2312.16683.pdf)\] \[Abstract: We use the topological quantum field theory description of states in [[0089 Chern-Simons theory|Chern-Simons theory]] to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of states in Chern-Simons with properties similar to those of holographic states. While the holographic states are dual to classical geometries, these connectome states represent classical topologies, which satisfy a discrete analog of the [[0007 RT surface|Ryu-Takayanagi formula]] and characteristic inequalities for the [[0301 Entanglement entropy|entanglement entropy]]. Generic states are linear combinations of connectomes, and the theory also has nonperturbative states which are global spacetime defects formed by a large number of quantum fluctuations. Topological presentation of quantum states and emergence of topology from entanglement may be useful for building a generalization to geomentry, that is quantum gravity. Thinking of further quantum gravity comparisons we discuss replica wormholes and conclude that similar objects exist beyond gravitational theories. The topological theory perspective suggests that the sum over all wormholes is always [[0249 Factorisation problem|factorizable]], even though the individual ones might not be.\] # Melton, Narayanan ## Celestial Gluon Amplitudes from the Outside In \[Links: [arXiv](https://arxiv.org/abs/2312.12394), [PDF](https://arxiv.org/pdf/2312.12394.pdf)\] \[Abstract: We show that, given a two-dimensional realization of the [[0114 Celestial OPE|celestial OPE]] in [[0136 Self-dual Yang-Mills|self-dual Yang-Mills]], we can find a scalar source around which scattering amplitudes replicate correlation functions computed from the 2D 'gluon' operators in a limit where a dynamic massless scalar decouples. We derive conditions on the two-dimensional three-point correlation function so that such a source exists and give two particular examples of this construction, one in which gluons are constructed from vertex operators in the semiclassical limit of [[0562 Liouville theory|Liouville theory]] and another in which the soft gluons arise from generalized free fields. Finally, we identify a bulk dual to the level of the boundary [[0069 Kac-Moody algebra|Kac-Moody algebra]] and discuss moving beyond the decoupling limit.\] # Melton, Sharma, Strominger (Oct) ## Conformal Correlators on the Lorentzian Torus \[Links: [arXiv](https://arxiv.org/abs/2310.15104), [PDF](https://arxiv.org/pdf/2310.15104.pdf)\] \[Abstract: The general form of a 2D conformal field theory (CFT) correlator on a Euclidean Riemann surface, Lorentzian plane or Lorentzian cylinder is well-known. This paper describes the general form of 2- and 3-point CFT correlators on the Lorentzian torus $\mathcal{LT}^2$ which arises as the conformal boundary of the group manifold $\mathrm{SL}(2,\mathbb{R}) \simeq \text{AdS}_3/\mathbb{Z}$. We consider only generic points, thereby omitting an analysis of contact terms, which already exhibits a surprisingly rich structure. The results are relevant to [[0010 Celestial holography|celestial holography]], for which the $\mathcal{LT}^2$ at the boundary of Klein space is the home of the putative celestial CFT.\] # Melton, Sharma, Strominger (Dec) ## Celestial Leaf Amplitudes \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: [[0516 Celestial correlators|Celestial amplitudes]] may be decomposed as weighted integrals of AdS$_3$-Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point [[0061 Maximally helicity violating amplitudes|MHV]] amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the [[0072 Parke-Taylor n-gluon tree amplitude|Parke-Taylor formula]].\] # McBrideIniguez ## Entanglement Negativity Transitions in Chaotic Eigenstates \[Links: [arXiv](https://arxiv.org/abs/2303.00018), [PDF](https://arxiv.org/pdf/2303.00018.pdf)\] \[Abstract: It was recently noted that the [[0301 Entanglement entropy|entanglement entropy]] for a subsystem of a chaotic eigenstate exhibits an enhanced correction when the subsystem approaches a phase transition at half the total system size. This enhanced correction was derived for general subsystems by [[2020#Dong, Wang|Dong and Wang]] by summing over noncrossing permutations, which can be thought of as ''saddles'' either in a sum emerging from averaging over Wick contractions or in an analogous gravitational calculation. We extend these results to the case of [[0210 Entanglement negativity|entanglement negativity]], an entanglement measure defined on a bipartite density matrix. We focus on a particular transition previously studied in a toy model of [[0050 JT gravity|JT gravity]], one for which the sum over permutations was found to give similar (or even stronger) enhanced corrections. We derive and resum the relevant permutations to give a form for the averaged negativity spectrum, reproducing the gravitational answer for some quantities and finding tension with other quantities, namely the partially transposed entropy. Along the way, we extend the results of Dong and Wang to the case of $n < 1$ [[0293 Renyi entropy|Rényi entropy]], showing that it always receives volume law corrections.\] ## Summary - enhanced correction near phase transitions for [[0210 Entanglement negativity|negativity]] # Mori, Yoshida ## Exploring causality in braneworld/cutoff holography via holographic scattering \[Links: [arXiv](https://arxiv.org/abs/2308.00739), [PDF](https://arxiv.org/pdf/2308.00739.pdf)\] \[Abstract: Holography with branes and/or cutoff surfaces presents a promising approach to studying quantum gravity beyond asymptotically anti-de Sitter spacetimes. However, this generalized holography is known to face several inconsistencies, including potential violations of causality and fundamental entropic inequalities. In this work, we address these challenges by investigating the bulk scattering process and its holographic realization. Specifically, we propose that the information on a brane/cutoff surface $Q$ propagates according to the induced light cones originating from a fictitious asymptotic boundary behind $Q$, rather than the conventional ones originating from a point on $Q$. Additionally, we establish the validity of the connected wedge theorem for generalized holography with induced light cones. We also demonstrate that entropic inequalities remain valid within the induced causal diamonds. While the induced light cone seemingly permits superluminal signaling, we argue that this causality violation can be an artifact of state preparation for radially propagating excitations, rather than local operator excitations on $Q$.\] # Mukhametzhanov ## Large $p$ SYK from chord diagrams \[Links: [arXiv](https://arxiv.org/abs/2303.03474), [PDF](https://arxiv.org/pdf/2303.03474.pdf)\] \[Abstract: The $p$-body [[0201 Sachdev-Ye-Kitaev model|SYK]] model at finite temperature exhibits submaximal [[0008 Quantum chaos|chaos]] and contains stringy-like corrections to the dual [[0050 JT gravity|JT gravity]]. It can be solved exactly in two different limits: "large $pquot; SYK $1 \ll p \ll N$ and "[[0503 Double-scaled SYK|double-scaled]]" SYK $N,p \to \infty$ with $\lambda = 2 p^2/N$ fixed. We clarify the relation between the two. Starting from the exact results in the double-scaled limit, we derive several observables in the large $p$ limit. We compute euclidean $2n$-point correlators and [[0482 Out-of-time-order correlator|out-of-time-order four-point function]] at long lorentzian times. To compute the correlators we find the relevant asymptotics of the $U_{q}(su(1,1))$ 6j-symbol.\] # Natsuume, Okamura (Jun) ## Pole-skipping in a non-black hole geometry \[Links: [arXiv](https://arxiv.org/abs/2306.03930), [PDF](https://arxiv.org/pdf/2306.03930.pdf)\] \[Abstract: The [[0179 Pole skipping|pole-skipping]] has been discussed in black hole backgrounds, but we point out that the pole-skipping exists even in a non-black hole background, the [[0567 AdS soliton|AdS soliton]]. For black holes, the pole-skipping points are typically located at imaginary Matsubara frequencies $\omega=-(2\pi T)ni$ with an integer $n$. The AdS soliton is obtained by the double Wick rotation from a black hole. As a result, the pole-skipping points are located at $q_z=-(2\pi n)/l$, where $l$ is the $S^1$ periodicity and $q_z$ is the $S^1$ momentum. The "chaotic" and the "hydrodynamic" pole-skipping points lie in the physical region. We also propose a method to identify all pole-skipping points instead of the conventional method.\] ## Refs - follow up: [[2023#Natsuume, Okamura (Jul)]] # Natsuume, Okamura (Jul) ## Pole-skipping as "missing states" \[Links: [arXiv](https://arxiv.org/abs/2307.11178), [PDF](https://arxiv.org/pdf/2307.11178.pdf)\] \[Abstract: It remains unclear in general how the [[0179 Pole skipping|pole-skipping]] appears as a physical phenomenon, and we study the issue in the context of the [[0567 AdS soliton|AdS soliton]]. The pole-skipping has been discussed in black hole backgrounds, but the pole-skipping occurs even in the AdS soliton background. The geometry has a compact $S^1$-direction, and we compute the mass spectrum for the bulk scalar field, the bulk Maxwell field, and the gravitational perturbations with $S^1$ momentum. We show that the pole-skipping leaves its fingerprint in the the normal mode spectrum. The spectrum has some puzzling features because the would-be states are missing at pole-skipping points. The puzzling features disappear once one takes into account these pole-skipping points which we call "missing states."\] ## Refs - pole skipping in AdS soliton: [[2023#Natsuume, Okamura (Jun)]] # Nebabu, Qi ## Bulk Reconstruction from Generalized Free Fields \[Links: [arXiv](https://arxiv.org/abs/2306.16687), [PDF](https://arxiv.org/pdf/2306.16687.pdf)\] \[Abstract: We propose a generalized protocol for [[0026 Bulk reconstruction|constructing]] a dual free bulk theory from any boundary model of generalized free fields (GFFs). To construct the bulk operators, we employ a linear ansatz similar to the [[0016 HKLL|Hamilton-Kabat-Liftschytz and Lowe]] (HKLL) construction. However, unlike the HKLL construction, our protocol relies only on boundary data with no presupposed form for the bulk equations of motion, so our reconstructed bulk is fully emergent. For a (1+1)d bulk, imposing the bulk operator algebra as well as a causal structure is sufficient to determine the bulk operators and dynamics uniquely up to an unimportant local basis choice. We study the bulk construction for several two-sided [[0201 Sachdev-Ye-Kitaev model|SYK]] models with and without coupling between the two sides, and find good agreement with known results in the low-temperature conformal limit. In particular, we find bulk features consistent with the presence of a black hole horizon for the [[0574 Thermofield double|TFD]] state, and characterize the infalling fermion modes. We are also able to extract bulk quantities such as the curvature and bulk state correlators in terms of boundary quantities. In the presence of coupling between the two SYK models, we are able to observe evidence of the [[0117 Shockwave|shockwave]] geometry and the [[0083 Traversable wormhole|traversable wormhole]] geometry using the two-sided [[0300 Mutual information|mutual information]] between the reconstructed bulk operators. Our results show evidence that features of the geometric bulk can survive away from the low temperature conformal limit. Furthermore, the generality of the protocol allows it to be applied to other boundary theories with no canonical holographic bulk.\] ## Summary - [[0016 HKLL|HKLL]]-like reconstruction for generalised free fields - unlike HKLL, no knowledge of bulk metric or EOM is assumed ## Generalised free field - in a free theory, if you know the two-point at early time, you know everything - in a generalised free theory, early time measures do not determine late time results; you keep accessing new sets of operators, i.e., $\chi_i(t+\Delta t)$ is linearly independent from $\chi_i(t)$ in [[0201 Sachdev-Ye-Kitaev model|SYK]] ## Bulk reconstruction - if there is a linear map from the boundary fermions between two times to the bulk partial Cauchy surface, then it can be inverted ## SYK features in the bulk - thermal two-point function decays in SYK - in the bulk, this translates to the fact that a particle can go deep into the bulk and never come back to the boundary ## Bulk fermion entropy - since bulk fermion is a Gaussian state, the two point function determines the [[0301 Entanglement entropy|von Neumann entropy]] - there is a UV divergence near the horizon ## Shockwave - [[2018#Maldacena, Qi]] - coupled SYK - coupling turned on at one single time (delta function in $t$) - the shock destroys correlation between right movers in left exterior and right exterior # Neuenfeld, Srivastava ## On the Causality Paradox and the Karch-Randall Braneworld as an EFT \[Links: [arXiv](https://arxiv.org/abs/https://arxiv.org/abs/2307.10392), [PDF](https://arxiv.org/pdf/https://arxiv.org/abs/2307.10392.pdf)\] \[Abstract: Holography on cutoff surfaces can appear to be in tension with [[0091 Boundary causality|causality]]. For example, as argued by [[2022#Omiya, Wei]], [[0544 Double holography|double holography]] seemingly allows for superluminal signalling. In this paper we argue that the brane description of double holography should be treated as an effective theory and demonstrate that causality violations due to faster-than-light communication are not visible above the associated cutoff length scale. This suggests that end-of-the-world brane models are consistent with causality and that the apparent superluminal signalling is a UV effect. Moreover, we argue that short distance non-localities generically give rise to apparent faster-than-light propagation of signals in Anti-de Sitter space. Nonetheless, superluminal signalling indicates that the causal structure on holographic cutoff surfaces needs to be modified. We propose and study three different candidate regions that might replace the domain of dependence in the brane EFT of the Karch-Randall model. These regions are defined by unitarity on the brane, through bulk entanglement wedges and through the nice slice criterion, respectively. In all dimensions, these candidate regions exclude those parts of the domain of dependence which are affected by superluminal signalling. While all three definitions agree in two dimensions, they are different in higher dimensions.\] # Nguyen ## Carrollian conformal correlators and massless scattering amplitudes \[Links: [arXiv](https://arxiv.org/abs/2311.09869), [PDF](https://arxiv.org/pdf/2311.09869.pdf)\] \[Abstract: The theory of particle scattering is concerned with transition amplitudes between states that belong to unitary representations of the Poincaré group. The latter acts as the isometry group of Minkowski spacetime $\mathbb{M}$, making natural the introduction of relativistic tensor fields encoding the particles of interest. Since the Poincaré group also acts as a group of conformal isometries of null infinity $\mathcal{I}$, massless particles can also be very naturally encoded into Carrollian conformal fields living on $\mathcal{I}$. In this work we classify the two- and three-point correlation functions such Carrollian conformal fields can have in any consistent quantum theory of massless particles and arbitrary dimension. We then show that bulk correlators of massless fields in $\mathbb{M}$ explicitly reduce to these Carrollian conformal correlators when evaluated on $\mathcal{I}$, although in the case of time-ordered bulk correlators this procedure appears singular at first sight. However we show that the Carrollian correlators of the descendant fields are perfectly regular and precisely carry the information about the corresponding S-matrix elements.\] # Ning, Wang, Wang ## Pole skipping in holographic theories with gauge and fermionic fields \[Links: [arXiv](https://arxiv.org/abs/2308.08191), [PDF](https://arxiv.org/pdf/2308.08191.pdf)\] \[Abstract: Using covariant expansions, recent work showed that [[0179 Pole skipping|pole skipping]] happens in general holographic theories with bosonic fields at frequencies $\mathrm{i}(l_b-s) 2\pi T$, where $l_b$ is the highest integer spin in the theory and $s$ takes all positive integer values. We revisit this formalism in theories with gauge symmetry and upgrade the pole-skipping condition so that it works without having to remove the gauge redundancy. We also extend the formalism by incorporating fermions with general spins and interactions and show that their presence generally leads to a separate tower of pole-skipping points at frequencies $\mathrm{i}(l_f-s)2\pi T$, $l_f$ being the highest half-integer spin in the theory and $s$ again taking all positive integer values. We also demonstrate the practical value of this formalism using a selection of examples with spins $0,\frac{1}{2},1,\frac{3}{2},2$.\] # Okuyama (Apr) ## High temperature expansion of double scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2304.01522), [PDF](https://arxiv.org/pdf/2304.01522.pdf)\] \[Abstract: We study the high temperature (or small inverse temperature \beta) expansion of the free energy of [[0503 Double-scaled SYK|double scaled SYK]] model. We find that this expansion is a convergent series with a finite radius of convergence. It turns out that the radius of convergence is determined by the first zero of the partition function on the imaginary $\beta$-axis. We also show that the semi-classical expansion of the free energy obtained from the saddle point approximation of the exact result is consistent with the high temperature expansion of the free energy.\] # Okuyama (May) ## End of the world brane in double scaled SYK \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: We study the end of the world (EOW) brane in [[0503 Double-scaled SYK|double scaled SYK (DSSYK) model]]. We find that the boundary state of EOW brane is a coherent state of the q-deformed oscillators and the associated orthogonal polynomial is the continuous big $q$-Hermite polynomial. In a certain scaling limit, the big $q$-Hermite polynomial reduces to the Whittaker function, which reproduces the wavefunction of [[0050 JT gravity|JT gravity]] with an EOW brane. We also compute the [[0308 Half-wormhole|half-wormhole]] amplitude in DSSYK and show that the amplitude is decomposed into the trumpet and the factor coming from the EOW brane.\] # Okuyama (Jun) ## Discrete analogue of the Weil-Petersson volume in double scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2306.15981), [PDF](https://arxiv.org/pdf/2306.15981.pdf)\] \[Abstract: We show that the connected correlators of partition functions in [[0503 Double-scaled SYK|double scaled SYK]] model can be decomposed into ''trumpet'' and the discrete analogue of the Weil-Petersson volume, which was defined by Norbury and Scott. We explicitly compute this discrete volume for the first few orders in the genus expansion and confirm that the discrete volume reduces to the Weil-Petersson volume in a certain semi-classical limit.\] # Okuyama (Dec) ## Matter correlators through wormhole in double-scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2312.00880), [PDF](https://arxiv.org/pdf/2312.00880.pdf)\] \[Abstract: We compute the two-point function of matter operators in [[0503 Double-scaled SYK|double-scaled SYK]] (DSSYK) model, where the two matter operators are inserted at each ends of the cylindrical wormhole. We find that the wormhole amplitude in DSSYK is written as a trace over the chord Hilbert space. We also show that the length of the wormhole is stabilized in the semi-classical limit, by the same mechanism worked for the [[0050 JT gravity|JT gravity]] case.\] # Okuyama, Suyama ## Solvable limit of ETH matrix model for double-scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2311.02846), [PDF](https://arxiv.org/pdf/2311.02846.pdf)\] \[Abstract: We study the two-matrix model for double-scaled SYK model, called [[0587 ETH matrix model|ETH matrix model]] introduced by Jafferis et al [[arXiv:2209.02131](https://arxiv.org/abs/2209.02131)]. If we set the parameters $q_A$, $q_B$ of this model to zero, the potential of this two-matrix model is given by the Gaussian terms and the $q$-commutator squared interaction. We find that this model is solvable in the large $N$ limit and we explicitly construct the planar one- and two-point function of resolvents in terms of elliptic functions.\] # Okuyama, Suzuki ## Correlators of double scaled SYK at one-loop \[Links: [arXiv](https://arxiv.org/abs/2303.07552), [PDF](https://arxiv.org/pdf/2303.07552.pdf)\] \[Abstract: In this paper, we study one-loop contributions in the [[0503 Double-scaled SYK|double-scaling limit of the SYK model]] from the chord diagrams and Liouville type effective action. We compute and clarify the meaning of each component consisting of the one-loop corrections for the two- and time-ordered four-point functions of light operators. We also reproduce the exact expression of the [[0482 Out-of-time-order correlator|out-of-time-ordered four-point function]] at arbitrary temperatures within the one-loop level, which were previously computed from different methods.\] ## Refs - [[0201 Sachdev-Ye-Kitaev model]] - [[0503 Double-scaled SYK]] - [[0482 Out-of-time-order correlator]] ## Canonical Purification and the Quantum Extremal Shock \[Links: [arXiv](https://arxiv.org/abs/2302.14318), [PDF](https://arxiv.org/pdf/2302.14318.pdf)\] \[Abstract: We study the canonical purification (with respect to one of the parties) of pure, bi-partite states obtained by turning on sources in the Euclidean path integral. In holographic conformal field theories, the Lorentzian bulk dual of the canonical purification consists of the corresponding entanglement wedge glued to its CPT image at the quantum extremal surface. However, the mismatch in the classical expansions at the [[0212 Quantum extremal surface|QES]] due to quantum corrections needs to be supported by a [[0117 Shockwave|shock]] in the bulk matter stress tensor in order for the bulk to satisfy Einstein's equations. Working perturbatively to first order in double-trace sources around the thermofield double state, we demonstrate that the state of the bulk matter in the dual to the canonically purified boundary CFT state precisely has this quantum extremal shock in the bulk stress tensor. We interpret our results as [[0302 Gravity from entanglement|the emergence of gravitational physics from the CFT entanglement structure]] in a context where bulk quantum corrections are important.\] ## Refs - [[0302 Gravity from entanglement]] - [[0117 Shockwave]] # Pantelidou, Withers ## Black hole excited states from broken translations in Euclidean time \[Links: [arXiv](https://arxiv.org/abs/2309.05734), [PDF](https://arxiv.org/pdf/2309.05734.pdf)\] \[Abstract: We [[0207 Euclidean state preparation|prepare]] an excited finite temperature state in [[0155 N=4 SYM|N=4 SYM]] by means of a Euclidean path integral with a relevant deformation. The deformation explicitly breaks imaginary-time translations along the thermal circle whilst preserving its periodicity. We then study how the state relaxes to thermal equilibrium in real time. Computations are performed using real-time AdS/CFT, by constructing novel mixed-signature black holes in numerical relativity corresponding to [[0042 Schwinger-Keldysh techniques|Schwinger-Keldysh]] boundary conditions. These correspond to deformed cigar geometries in the Euclidean, glued to a pair of dynamical spacetimes in the Lorentzian. The maximal extension of the Lorentzian black hole exhibits a 'causal shadow', a bulk region which is spacelike separated from both boundaries. We show that causal shadows are generic in path-integral prepared states where imaginary-time translations along the thermal circle are broken.\] # Parrikar, Singh ## Canonical Purification and the Quantum Extremal Shock \[Links: [arXiv](https://arxiv.org/abs/2302.14318), [PDF](https://arxiv.org/pdf/2302.14318.pdf)\] \[Abstract: \] # Pelliconi, Sonner ## The Influence Functional in open holography: entanglement and Rényi entropies \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: Open quantum systems are defined as ordinary unitary quantum theories coupled to a set of external degrees of freedom, which are introduced to take on the rôle of an unobserved environment. Here we study examples of open quantum field theories, with the aid of the so-called Feynman-Vernon Influence Functional (IF), including field theories that arise in holographic duality. We interpret the system in the presence of an IF as an open effective field theory, able to capture the effect of the unobserved environment. Our main focus is on computing [[0293 Renyi entropy|Rényi]] and [[0301 Entanglement entropy|entanglement entropies]] in such systems, whose description from the IF, or "open EFT", point of view we develop in this paper. The issue of computing the entanglement-Rényi entropies in open quantum systems is surprisingly rich, and we point out how different prescriptions for the IF may be appropriate depending on the application of choice. A striking application of our methods concerns the fine-grained entropy of subsystems when including gravity in the setup, for example when considering the Hawking radiation emitted by black holes. In this case we show that one prescription for the IF leads to answers consistent with unitary evolution, while the other merely reproduces standard EFT results, well known to be inconsistent with unitary global evolution. We establish these results for asymptotically AdS gravity in arbitrary dimensions, and illustrate them with explicit analytical expressions for the IF in the case of matter-coupled JT gravity in two dimensions.\] # Penington, Witten ## Algebras and States in JT Gravity \[Links: [arXiv](https://arxiv.org/abs/2301.07257), [PDF](https://arxiv.org/pdf/2301.07257.pdf)\] \[Abstract: We analyze the algebra of boundary observables in canonically quantised [[0050 JT gravity|JT gravity]] with or without matter. In the absence of matter, this algebra is commutative, generated by the ADM Hamiltonian. After coupling to a bulk quantum field theory, it becomes a highly noncommutative algebra of Type II$_\infty$ with a trivial center. As a result, density matrices and entropies on the boundary algebra are uniquely defined up to, respectively, a rescaling or shift. We show that this algebraic definition of entropy agrees with the usual replica trick definition computed using Euclidean path integrals. Unlike in previous arguments that focused on $\mathcal{O}(1)$ fluctuations to a black hole of specified mass, this Type II$_\infty$ algebra describes states at all temperatures or energies. We also consider the role of spacetime wormholes. One can try to define operators associated with wormholes that commute with the boundary algebra, but this fails in an instructive way. In a regulated version of the theory, wormholes and topology change can be incorporated perturbatively. The bulk Hilbert space $\mathcal{H}_\text{bulk}$ that includes [[0051 Baby universes|baby universe]] states is then much bigger than the space of states $\mathcal{H}_\text{bdry}$ accessible to a boundary observer. However, to a boundary observer, every pure or mixed state on $\mathcal{H}_\text{bulk}$ is equivalent to some pure state in $\mathcal{H}_\text{bdry}$.\] ## Comments - can work at finite temperature -> more fun than higher dimensions; a lot of fluctuations - the matrix model picture is clearer: just QM - from this, we get a good understanding of why Euclidean PI works - for pure JT gravity, failed; success for JT with matter # Perry, Rodriguez ## Dynamical Love Numbers for Kerr Black Holes \[Links: [arXiv](https://arxiv.org/abs/2310.03660), [PDF](https://arxiv.org/pdf/2310.03660.pdf)\] \[Abstract: While static [[0581 Tidal Love numbers|Love number]] vanish identically for Kerr black holes, we show that the corresponding dynamical tidal coefficients are generically non-zero and exhibit logarithmic behavior. The computational method employs a related but simpler scheme consistent with CFT descriptions, low-frequency regimes and post-Newtonian results. These coefficients are illustrated with a numerical examples.\] # Pook-Kolb, Zhao, Andersson, Krishnan, Yau ## Properties of Quasi-local mass in binary black hole mergers \[Links: [arXiv](https://arxiv.org/abs/2308.10906), [PDF](https://arxiv.org/pdf/2308.10906.pdf)\] \[Abstract:Identifying a general [[0595 Quasi-local energy|quasi-local notion of energy-momentum]] and angular momentum would be an important advance in general relativity with potentially important consequences for mathematical and astrophysical studies in general relativity. In this paper we study a promising approach to this problem first proposed by Wang and Yau in 2009 based on isometric embeddings of closed surfaces in Minkowski space. We study the properties of the Wang-Yau quasi-local mass in high accuracy numerical simulations of the head-on collisions of two non-spinning black holes within full general relativity. We discuss the behavior of the Wang-Yau quasi-local mass on constant expansion surfaces and we compare its behavior with the irreducible mass. We investigate the time evolution of the Wang-Yau Quasi-local mass in numerical examples. In addition we discuss mathematical subtleties in defining the Wang-Yau mass for marginally trapped surfaces.\] # Rabinovici, Sanchez-Garrido, Shir, Sonner ## A bulk manifestation of Krylov complexity \[Links: [arXiv](https://arxiv.org/abs/2305.04355), [PDF](https://arxiv.org/pdf/2305.04355.pdf)\] \[Abstract: There are various definitions of the concept of [[0204 Quantum complexity|complexity]] in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the [[0001 AdS-CFT|AdS/CFT dictionary]] for one such class of complexity, namely Krylov or K-complexity. For this purpose we work in the [[0503 Double-scaled SYK|double-scaled SYK model]] which is dual in a certain limit to [[0050 JT gravity|JT gravity]], a theory of gravity in AdS$_2$. In particular, states on the boundary have a clear geometrical definition in the bulk. We use this result to show that Krylov complexity of the infinite-temperature thermofield double state on the boundary of AdS$_2$ has a precise bulk description in JT gravity, namely the length of the two-sided wormhole. We do this by showing that the Krylov basis elements, which are eigenstates of the Krylov complexity operator, are mapped to length eigenstates in the bulk theory by subjecting K-complexity to the bulk-boundary map identifying the bulk/boundary Hilbert spaces. Our result makes extensive use of chord diagram techniques and identifies the Krylov basis of the boundary quantum system with fixed chord number states building the bulk gravitational Hilbert space.\] # Raeymaekers, Rossi ## Wormholes and surface defects in rational ensemble holography \[Links: [arXiv](https://arxiv.org/abs/2312.02276), [PDF](https://arxiv.org/pdf/2312.02276.pdf)\] \[Abstract: We study wormhole contributions to the bulk path integral in holographic models which are dual to ensembles of rational free boson conformal field theories. We focus on the path integral on a geometry connecting two toroidal boundaries, which should capture the variance of the ensemble distribution. We show that this requirement leads to a nontrivial set of constraints which generically picks out the uniform, maximum entropy, ensemble distribution. Furthermore, we show that the two-boundary path integral should receive contributions from 'exotic' wormholes, which arise from the inclusion of topological surface defects.\] # Rampp, Rather, Claeys ## The entanglement membrane in exactly solvable lattice models \[Links: [arXiv](https://arxiv.org/abs/2312.12509), [PDF](https://arxiv.org/pdf/2312.12509.pdf)\] \[Abstract: [[0433 Membrane theory of entanglement dynamics|Entanglement membrane theory]] is an effective coarse-grained description of [[0522 Entanglement dynamics|entanglement dynamics]] and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line tension. However, determining the entanglement line tension for microscopic models is in general exponentially difficult. We compute the entanglement line tension in a recently introduced class of exactly solvable yet chaotic unitary circuits, so-called generalized dual-unitary circuits, obtaining a non-trivial form that gives rise to a hierarchy of velocity scales with $v_E<v_B$. We find that these circuits saturate certain bounds on entanglement growth that are also saturated in [[0001 AdS-CFT|holographic]] models. Furthermore, we relate the entanglement line tension to temporal entanglement and correlation functions. We also find new methods of constructing generalized dual-unitary gates beyond qubits that display behavior unique to local dimension $\geq3$. Our results shed light on entanglement membrane theory in microscopic Floquet lattice models and enable us to perform non-trivial checks on the validity of its predictions by comparison to exact and numerical calculations.\] # Ren, Schreiber, Sharma, Wang ## All-order celestial OPE from on-shell recursion \[Links: [arXiv](https://arxiv.org/abs/2305.11851), [PDF](https://arxiv.org/pdf/2305.11851.pdf)\] \[Abstract: We determine tree level, all-order [[0114 Celestial OPE|celestial operator product expansions]] (OPEs) of gluons and gravitons in the [[0061 Maximally helicity violating amplitudes|maximally helicity violating (MHV)]] sector. We start by obtaining the all-order [[0078 Collinear limit|collinear]] expansions of MHV amplitudes using the [[0515 Inverse soft construction|inverse soft recursion relations]] that they satisfy. These collinear expansions are recast as celestial OPE expansions in bases of momentum as well as boost eigenstates. This shows that inverse soft recursion for MHV amplitudes is dual to OPE recursion in [[0010 Celestial holography|celestial conformal field theory]].\] ## Notations and definitions - use little group scaling to fix: $\lambda_i^\alpha=\left(\begin{array}{c}1 \\z_i\end{array}\right), \quad \tilde{\lambda}_i^{\dot{\alpha}}=\omega_i\left(\begin{array}{c}1 \\\bar{z}_i\end{array}\right)$ - here $\omega_i \in \mathbb{C}^*$ - [[0009 Soft theorems|soft]] expansion: - $O_{+}^a(z, \tilde{\lambda})=\sum_{r=0}^{\infty} J^a[r](z, \tilde{\lambda})$, where $r$ labels the order in $\omega$ - can also strip away the powers of $\omega$: $J^a[r](z, \bar{z}):=\frac{J^a[r](z, \tilde{\lambda})}{(\varepsilon \omega)^r}$ (here $\omega\in(0,\infty)$) - antiholomorphic expansion: - $J^a[r](z,\tilde\lambda) = \sum_{k=0}^r\frac{(\tilde\lambda^{\dot1})^k(\tilde\lambda^{\dot2})^{r-k}}{k!(r-k)!}\, J^a[k,r-k](z)$ - $r-k$ is the power of $\bar{z}$, which is just a label - holomorphic [[0078 Collinear limit|collinear]] expansion (soft current descendants): - $J^{a_1}_{-p}[r](\tilde\lambda_1)O^{a_2}_{s_2}(z_2,\tilde\lambda_2) \equiv \oint_{|z_{12}|=\varepsilon}\frac{d z_{1}}{2\pi i}\,\frac{1}{z_{12}^{p}}\,J^{a_1}[r](z_1,\tilde\lambda_1)\,O^{a_2}_{s_2}(z_2,\tilde\lambda_2)$ ## Comments - all-order gluon OPE agrees with a [[0497 Twistor string theory|twistor-string]] calculation in [[2022#Adamo, Bu, Casali, Sharma]] <!-- emails: Magnea2021, --> # Ribault, Tsiares ## On the Virasoro fusion kernel at $c=25$ \[Links: [arXiv](https://arxiv.org/abs/2310.09334), [PDF](https://arxiv.org/pdf/2310.09334.pdf)\] \[Abstract: We find a formula for the Virasoro [[0573 Crossing kernel|fusion kernel]] at $c=25$, in terms of the connection coefficients of the Painlevé VI differential equation. Our formula agrees numerically with previously known integral representations of the kernel. The derivation of our formula relies on a duality $c\to 26-c$ that is obeyed by the shift equations for the fusion and modular kernels. We conjecture that for $c<1$ the fusion and modular kernels are not smooth functions, but distributions.\] # Rodriguez, Santoni, Solomon, Temoche ## Love Numbers for Rotating Black Holes in Higher Dimensions \[Links: [arXiv](https://arxiv.org/abs/2304.03743), [PDF](https://arxiv.org/pdf/2304.03743.pdf)\] \[Abstract: We compute the [[0581 Tidal Love numbers|tidal Love numbers]] and static response coefficients associated to several rotating black holes in higher dimensions, including Myers-Perry black holes, black rings, and black strings. These coefficients exhibit a rich and complex structure as a function of the black hole parameters and multipoles. Our results agree in limiting cases with known and new expressions for various lower-dimensional black holes. In particular, we provide an alternative approach to the computation of the static response of Kerr black holes as a limiting case of the boosted black string.\] # Sachdev (Review) ## Quantum statistical mechanics of the Sachdev-Ye-Kitaev model and charged black holes \[Links: [arXiv](https://arxiv.org/abs/2304.13744), [PDF](https://arxiv.org/pdf/2304.13744.pdf)\] \[Abstract: This review is a contribution to a book dedicated to the memory of Michael E. Fisher. The first example of a quantum many body system not expected to have any quasiparticle excitations was the Wilson-Fisher conformal field theory. The absence of quasiparticles can be established in the compressible, metallic state of the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev model]] of fermions with random interactions. The solvability of the latter model has enabled numerous computations of the non-quasiparticle dynamics of [[0008 Quantum chaos|chaotic]] many-body states, such as those expected to describe quantum black holes. This chapter reviews thermodynamic properties of the SYK model, and describes how they have led to an understanding of the universal structure of the low energy density of states of charged black holes without low energy supersymmetry.\] # Saha ## w$_{1+\infty}$ and Carrollian Holography \[Links: [arXiv](https://arxiv.org/abs/2308.03673), [PDF](https://arxiv.org/pdf/2308.03673.pdf)\] \[Abstract: In a 1+2D [[0419 Carrollian CFT|Carrollian conformal field theory]], the [[0106 Ward identity|Ward identities]] of the two local fields $S^+_0$ and $S^+_1$, entirely built out of the Carrollian conformal stress-tensor, contain respectively up to the leading and the subleading positive helicity [[0009 Soft theorems|soft graviton theorems]] in the 1+3D asymptotically flat space-time. This work investigates how the subsubleading soft graviton theorem can be encoded into the Ward identity of a Carrollian conformal field $S^+_2$. The [[0030 Operator product expansion|operator product expansion]] (OPE) $S^+_2S^+_2$ is constructed using general Carrollian conformal symmetry principles and the OPE commutativity property, under the assumption that any time-independent, non-Identity field that is mutually local with $S^+_0,S^+_1,S^+_2$ has positive Carrollian scaling dimension. It is found that, for this OPE to be consistent, another local field $S^+_3$ must automatically exist in the theory. The presence of an infinite tower of local fields $S^+_{k\geq3}$ is then revealed iteratively as a consistency condition for the $S^+_2S^+_{k-1}$ OPE. The general $S^+_kS^+_l$ OPE is similarly obtained and the symmetry algebra manifest in this OPE is found to be the [[0069 Kac-Moody algebra|Kac-Moody algebra]] of the wedge sub-algebra of w$_{1+\infty}$. The Carrollian time-coordinate plays the central role in this purely holographic construction. The 2D Celestial conformally soft graviton primary $H^k(z,\bar{z})$ is realized to be contained in the Carrollian conformal primary $S_{1-k}^+(t,z,\bar{z})$. Finally, the existence of the infinite tower of fields $S^+_{k}$ is shown to be directly related to an infinity of positive helicity soft graviton theorems.\] ## Related topics - [[0328 w(1+infinity)]] # Shi, Vardhan, Liu ## Local dynamics and the structure of chaotic eigenstates \[Links: [arXiv](https://arxiv.org/abs/2306.08032), [PDF](https://arxiv.org/pdf/2306.08032.pdf)\] \[Abstract: We identify new universal properties of the energy eigenstates of [[0008 Quantum chaos|chaotic]] systems with local interactions, which distinguish them both from integrable systems and from non-local chaotic systems. We study the relation between the energy eigenstates of the full system and products of energy eigenstates of two extensive subsystems, using a family of spin chains in (1+1) dimensions as an illustration. The magnitudes of the coefficients relating the two bases have a simple universal form as a function of $\omega$, the energy difference between the full system eigenstate and the product of eigenstates. This form explains the exponential decay with time of the probability for a product of eigenstates to return to itself during thermalization. We also find certain new statistical properties of the coefficients. While it is generally expected that the coefficients are uncorrelated random variables, we point out that correlations implied by unitarity are important for understanding the transition probability between two products of eigenstates, and the evolution of operator expectation values during thermalization. Moreover, we find that there are additional correlations resulting from locality, which lead to a slower growth of the second [[0293 Renyi entropy|Renyi entropy]] than the one predicted by an uncorrelated random variable approximation.\] # Sleight, Taronna ## Celestial Holography Revisited \[Links: [arXiv](https://arxiv.org/abs/2301.01810), [PDF](https://arxiv.org/pdf/2301.01810.pdf)\] \[Abstract: We revisit the prescription commonly used to define holographic Celestial Correlators as an integral transform of flat space scattering amplitudes. We propose a new prescription according to which holographic Celestial Correlators are a [[0079 Mellin transform|Mellin transform]] of Minkowski time-ordered correlators extrapolated to the conformal boundary, which is analogous to the extrapolate definition of holographic correlators in [[0001 AdS-CFT|AdS/CFT]]. Our proposal is motivated by an ambiguity in the standard prescription for Celestial Correlators owing the presence of a divergent integral in the definition of [[0148 Conformal basis|conformal primary wave functions]]. We show that perturbative Celestial Correlators defined in this new way are manifestly recast in terms of corresponding [[0109 Witten diagrams|Witten diagrams]] in Euclidean anti-de Sitter space. We also discuss the possibility of using this definition of [[0516 Celestial correlators|Celestial Correlators]] in terms of bulk correlation functions to explore the non-perturbative properties of Celestial Correlators dual to Conformal Field Theories in Minkowski space.\] # Solanki, Bhattacharjee ## Soft Theorems and Memory Effects at Finite Temperatures \[Links: [arXiv](https://arxiv.org/abs/2308.02445), [PDF](https://arxiv.org/pdf/2308.02445.pdf)\] \[Abstract: We study the [[0009 Soft theorems|soft theorems]] for photons and gravitons at finite temperatures using the thermofield dynamics approach. The soft factors lose universality at finite temperatures as the soft amplitudes depend on the nature (or spin) of the particles participating in the scattering processes. However, at low temperatures, a universal behavior is observed in the cross-section of the soft processes. Further, we obtain the thermal contribution to the electromagnetic and gravitational memory effects and show that they are related to the soft factors consistently. The expected zero temperature results are obtained from the soft factors and memories. The thermal effects in soft theorems and memories seem to be sensitive to the spin of the particles involved in scattering.\] # Sorce (Feb, Notes) ## Notes on the type classification of von Neumann algebras \[Links: [arXiv](https://arxiv.org/abs/2302.01958), [PDF](https://arxiv.org/pdf/2302.01958.pdf)\] \[Abstract: These notes provide an explanation of the type classification of [[0415 Von Neumann algebra|von Neumann algebras]], which has made many appearances in recent work on entanglement in quantum field theory and quantum gravity. The goal is to bridge a gap in the literature between resources that are too technical for the non-expert reader, and resources that seek to explain the broad intuition of the theory without giving precise definitions. Reading these notes will provide you with: (i) an argument for why "factors" are the fundamental von Neumann algebras that one needs to study; (ii) an intuitive explanation of the type classification of factors in terms of renormalization schemes that turn unnormalizable positive operators into "effective density matrices;" (iii) a mathematical explanation of the different types of renormalization schemes in terms of the allowed traces on a factor; (iv) an intuitive characterization of type I and II factors in terms of their "standard forms;" and (v) a list of some interesting connections between type classification and modular theory, including the argument for why type III_1 factors are believed to be the relevant ones in quantum field theory. None of the material is new, but the pedagogy is different from other sources I have read; it is most similar in spirit to the recent work on gravity and the crossed product by Chandrasekaran, Longo, Penington, and Witten.\] # Sorce (Sep) ## An intuitive construction of modular flow \[Links: [arXiv](https://arxiv.org/abs/2309.16766), [PDF](https://arxiv.org/pdf/2309.16766.pdf)\] \[Abstract: The theory of [[0416 Modular Hamiltonian|modular flow]] has proved extremely useful for applying thermodynamic reasoning to out-of-equilibrium states in quantum field theory. However, the standard proofs of the fundamental theorems of modular flow use machinery from Fourier analysis on Banach spaces, and as such are not especially transparent to an audience of physicists. In this article, I present a construction of modular flow that differs from existing treatments. The main pedagogical contribution is that I start with thermal physics via the [[0521 KMS condition|KMS condition]], and derive the modular operator as the only operator that could generate a thermal arrow of time, rather than starting with the modular operator as the fundamental object of the theory. The main technical contribution is a new proof of the fundamental theorem stating that modular flow is a symmetry. The new proof circumvents the delicate issues of Fourier analysis that appear in previous treatments, but is still mathematically rigorous.\] # Stanford ## A Mirzakhani recursion for non-orientable surfaces \[Links: [arXiv](https://arxiv.org/abs/2303.04049), [PDF](https://arxiv.org/pdf/2303.04049)\] \[Abstract: We review [[0627 Mirzakhani recursion|Mirzakhani's recursion]] for the volumes of moduli spaces of orientable surfaces, using a perspective that generalizes to [[0624 Unorientable manifold|non-orientable]] surfaces. The non-orientable version leads to divergences when the recursion is iterated, from regions in moduli space with small crosscaps. However, the integral kernels of the recursion are well-defined and they map precisely onto the loop equations for a matrix integral with orthogonal symmetry class and classical density of eigenvalues proportional to $\sinh(2\pi\sqrt{E})$ for $E>0$. The recursion can be used to compute regularized volumes with a cutoff on the minimal size of a crosscap.\] # Stanford, Vardhan, Yao ## Scramblon loops \[Links: [arXiv](https://arxiv.org/abs/2311.12121), [PDF](https://arxiv.org/pdf/2311.12121.pdf)\] \[Abstract: In large $N$ chaotic quantum systems, the butterfly effect is mediated by a collective field mode known as the ''scramblon.'' We study self-interactions of the scramblon in variants of the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev model]]. In spatially extended versions of the model and for large spatial separation, fluctuations described by loop diagrams can invalidate the single-scramblon approximation well before its contribution to [[0482 Out-of-time-order correlator|out-of-time-order correlators]] becomes of order one. We find a qualitative difference between an incoherent regime at high temperaure (or in a Brownian version of the model) and a coherent regime at low temperature.\] # Susskind (Apr) ## A Paradox and its Resolution Illustrate Principles of de Sitter Holography \[Links: [arXiv](https://arxiv.org/abs/2304.00589), [PDF](https://arxiv.org/pdf/2304.00589.pdf)\] \[Abstract: Semiclassical gravity and the holographic description of the static patch of de Sitter space appear to disagree about properties of correlation functions. Certain holographic correlation functions are necessarily real whereas their semiclassical counterparts have both real and imaginary parts. The resolution of this apparent contradiction involves the fact that time-reversal is a gauge symmetry in de Sitter space -- a point made by Harlow and Ooguri -- and the need for an observer (or quantum reference frame) as advocated by [[2022#Chandrasekaran, Longo, Penington, Witten|Chandrasekaran, Longo, Penington, and Witten]].\] ## Puzzle - consider two bulk fields at $t$ and $-t$ - the correlators are not real: $\Im \langle\phi_1 \phi_2\rangle=\langle[\phi_1,\phi_2]\rangle$ - write $O(t)=[\phi(-t),\phi(t)]]$ - so $O(-t)=-O(t)$ - this is odd under time reversal, $T$, so must be zero - for any $O$, $\langle O\rangle=Tr (O\rho_{max})=Tr(O)$ in de Sitter - so it should be zero for the commutator - but the bulk computation gives a non-zero imaginary value ## Resolution - let time reversal be a gauge symmetry - define $\tilde{O}(t)$ in such a way that, - $\tilde{O}(t)|\text{forward}\rangle=O(t)|\text{forward}\rangle$ - $\tilde{O}(t)|\text{backward}\rangle=O(-t)|\text{backward}\rangle$ - then $T\tilde O(t)T=\tilde O(t)$ is time-reversal invariant - so that $\tilde O(t)\ne 0$ allowed - i.e., if you gauge fix the operator, it is allowed to have a non-zero value \[*Many thanks to Xi Dong for explaining some of the ideas in this paper at Gravity Lunch.*\] # Taylor, Zhu (Feb) ## Celestial Supersymmetry \[Links: [arXiv](https://arxiv.org/abs/2302.12830), [PDF](https://arxiv.org/pdf/2302.12830.pdf)\] \[Abstract: We discuss supersymmetric Yang-Mills theory coupled to dilatons in the framework of [[0010 Celestial holography|celestial holography]]. We show that in the presence of suitably chosen pointlike dilaton sources, the CCFT operators associated with the gauge supermultiplet acquire a simple, factorized form. They factorize into the holomorphic (super)current part and the exponential "light" operators of Liouville theory, in the infinite central charge limit. The current sector exhibits (1,0) supersymmetry, thus implementing spacetime supersymmetry in CCFT.\] ## Refs - [[0289 Celestial superamplitudes]] # Taylor, Zhu (Dec) ## w(1+infinity) Algebra with a Cosmological Constant and the Celestial Sphere \[Links: [arXiv](https://arxiv.org/abs/2312.00876), [PDF](https://arxiv.org/pdf/2312.00876.pdf)\] \[Abstract: It is shown that in the presence of a nonvanishing cosmological constant, Strominger's infinite-dimensional $\mathrm{w_{1+\infty}}$ [[0328 w(1+infinity)|algebra]] of soft graviton symmetries is modified in a simple way. The deformed algebra contains a subalgebra generating $SO(1,4)$ or $SO(2,3)$ symmetry groups of $\text{dS}_4$ or $\text{AdS}_4$, depending on the sign of the cosmological constant. The transformation properties of soft gauge symmetry currents under the deformed $\mathrm{w_{1+\infty}}$ are also discussed.\] # Tropper, Wang ## Lorentz Symmetry and IR Structure of The BFSS Matrix Model \[Links: [arXiv](https://arxiv.org/abs/2303.14200), [PDF](https://arxiv.org/pdf/2303.14200.pdf)\] \[Abstract: The [[0479 BFSS matrix model|BFSS matrix model]] relates flat space [[0517 M-theory|M-theory]] to a large $N$ limit of matrix quantum mechanics describing $N$ D0-branes. M-theory, being a theory of gravity in flat space, has a rich infrared structure that includes various [[0009 Soft theorems|soft theorems]] and an infinite set of conserved charges associated to [[0060 Asymptotic symmetry|asymptotic symmetries]]. In this work, we ask: to what extent is this infrared structure present in BFSS? We find that all the salient features concerning the infrared structure of M-theory carry over naturally to the quantum mechanics dual. Moreover, we demonstrate that the dual statement of the soft graviton theorem in the matrix model implies that D0-brane scattering amplitudes in BFSS enjoy the full 11d Lorentz symmetry of M-theory, a claim which has been long anticipated. We also offer several first-principle consistency checks for our findings, including a computation of the soft theorem which does not presuppose the BFSS duality and a non-trivial match between several known symmetries of M-theory and BFSS that appear naturally in this formalism. These calculations give non-perturbative evidence in support of the BFSS duality as a model of flat space holography.\] # Turiaci (News) ## New insights on near-extremal black holes \[Links: [arXiv](https://arxiv.org/abs/2307.10423), [PDF](https://arxiv.org/pdf/2307.10423.pdf)\] \[Abstract: We describe two puzzles that arise from a semiclassical treatment of near-extremal black hole thermodynamics. Both puzzles are resolved by realizing that quantum corrections become arbitrarily large at low temperatures, and we explain how the spectrum and dynamics of near-extremal black holes are modified. This analysis also implies that without low energy supersymmetry, such as in the real world, extremal black holes at exactly zero temperature do not exist since the classical picture breaks down completely. In the context of supergravity the analysis is modified; supersymmetric extremal black holes do exist and they are separated from the non-extremal spectrum by a gap power-law suppressed in the entropy. This justifies [[0248 Black hole microstates|black hole microstate counting]] performed in the 90's using string theory.\] ## Two puzzles 1. large ground state degeneracy because $S(T=0)\ne0$ which is inconsistent with Nernst's third law of thermodynamics - issued emphasised by [[2001#Page]] 2. thermal description breaks down below some temperature unless there is a gap power-law suppressed in entropy exists to remove the problematic states - raised by [[1991#Preskill, Schwarz, Shapere, Trivedi, Wilczek]] and elaborated in [[1998#Maldacena, Michelson, Strominger]] ## Resolutions - without SUSY or supergravity with $J\ne0$: - density of states continuously goes to zero at $E=0$ (i.e. extremal black holes do not exist) - with supergravity with $J=0$: - there is a large ground state degeneracy and a gap between the ground state and excited states - third law violated but ok: it's protected by SUSY - justified microstate counting # Turiaci, Witten ## $\mathcal{N}=2$ JT Supergravity and Matrix Models \[Links: [arXiv](https://arxiv.org/abs/2305.19438), [PDF](https://arxiv.org/pdf/2305.19438.pdf)\] \[Abstract: Generalizing previous results for $\mathcal{N}=0$ and $\mathcal{N}=1$, we analyze $\mathcal{N}=2$ [[0050 JT gravity|JT]] supergravity on asymptotically AdS${}_2$ spaces with arbitrary topology and show that this theory of gravity is [[0471 String-matrix duality|dual]], in a holographic sense, to a certain [[0197 Matrix model|random matrix ensemble]] in which supermultiplets of different $R$-charge are statistically independent and each is described by its own $\mathcal{N}=2$ random matrix ensemble. We also analyze the case with a time-reversal symmetry, either commuting or anticommuting with the $R$-charge. In order to compare supergravity to random matrix theory, we develop an $\mathcal{N}=2$ analog of the recursion relations for Weil-Petersson volumes originally discovered by Mirzakhani in the bosonic case.\] ## Refs - non-perturbative extension: [[2023#Johnson]] # Valenzuela, Zanelli ## The propagating modes of the massless Rarita--Schwinger system \[Links: [arXiv](https://arxiv.org/abs/2305.00106), [PDF](https://arxiv.org/pdf/2305.00106.pdf)\] \[Abstract: The counting of the degrees of freedom of the massless Rarita-Schwinger theory is revisited using covariant and non-covariant techniques. The Ogievetsky-Sokatchev spin-block projector approach shows that the gauge invariant part of the vector-spinor consists of spin-1/2 and spin-3/2 sectors. We corroborate this result by fixing the gauge with the standard gamma-traceless condition and exhibit a solution in which both spins propagate. We repeat the analysis in an alternative gauge which makes explicit the appearance of a dynamic spin-1/2 sector. We then carry out the constrained Hamiltonian analysis and observe that the elimination of the spin-1/2 sector results from assuming the Dirac conjecture as valid but this situation, described by the extended Hamiltonian, corresponds to a dynamical system different from the original one. Considering the total (unextended) Hamiltonian, which generates an evolution equivalent to the Lagrangian one, all the constraints can be solved by gauge fixing conditions corresponding to the freedom generated by the primary first-class constraints. Hence we conclude that the elimination of the spin-half mode in the study of the massless Rarita-Schwinger model relies on the validity of the Dirac conjecture. As a corollary, every supergravity would contain a spin-1/2 sector described by the standard Dirac action.\] # Vardhan, Wei, Zou ## Petz recovery from subsystems in conformal field theory \[Links: [arXiv](https://arxiv.org/abs/2307.14434), [PDF](https://arxiv.org/pdf/2307.14434.pdf)\] \[Abstract: We probe the [[0264 Multi-partite entanglement|multipartite entanglement]] structure of the vacuum state of a CFT in 1+1 dimensions, using recovery operations that attempt to reconstruct the density matrix in some region from its reduced density matrices on smaller subregions. We use an explicit recovery channel known as the twirled [[0413 Petz map|Petz map]], and study distance measures such as the fidelity, [[0199 Relative entropy|relative entropy]], and trace distance between the original state and the recovered state. One setup we study in detail involves three contiguous intervals $A$, $B$ and $C$ on a spatial slice, where we can view these quantities as measuring correlations between $A$ and $C$ that are not mediated by the region $B$ that lies between them. We show that each of the distance measures is both UV finite and independent of the operator content of the CFT, and hence depends only on the central charge and the cross-ratio of the intervals. We evaluate these universal quantities numerically using lattice simulations in critical spin chain models, and derive their analytic forms in the limit where $A$ and $C$ are close using the [[0030 Operator product expansion|OPE expansion]]. In the case where $A$ and $C$ are far apart, we find a surprising non-commutativity of the replica trick with the OPE limit. For all values of the cross-ratio, the fidelity is strictly better than a general information-theoretic lower bound in terms of the conditional mutual information. We also compare the [[0300 Mutual information|mutual information]] between various subsystems in the original and recovered states, which leads to a more qualitative understanding of the differences between them. Further, we introduce generalizations of the recovery operation to more than three adjacent intervals, for which the fidelity is again universal with respect to the operator content.\] # Wang, Zhang ## Fermionic Higher-form Symmetries \[Links: [arXiv](https://arxiv.org/abs/2303.12633), [PDF](https://arxiv.org/pdf/2303.12633.pdf)\] \[Abstract: In this paper, we explore a new type of global symmetries-the fermionic [[0205 Higher-form symmetry|higher-form symmetries]]. They are generated by topological operators with fermionic parameter, which act on fermionic extended objects. We present a set of field theory examples with fermionic higher-form symmetries, which are constructed from fermionic tensor fields. They include the free fermionic tensor theories, a new type of fermionic topological quantum field theories, as well as the exotic 6d (4,0) theory. We also discuss the gauging and breaking of such global symmetries and the relation to the no global symmetry swampland conjecture.\] # Wei, Zhou ## Tree and 1-loop fundamental BCJ relations from soft theorems \[Links: [arXiv](https://arxiv.org/abs/2305.04620), [PDF](https://arxiv.org/pdf/2305.04620.pdf)\] \[Abstract: We provide a new derivation of the fundamental [[0152 Colour-kinematics duality|BCJ relation]] among double color ordered tree amplitudes of ==bi-adjoint scalar theory==, based on the leading [[0009 Soft theorems|soft theorem]] for external scalars. Then, we generalize the fundamental BCJ relation to 1-loop Feynman integrands. We also use the fundamental BCJ relation to understand the Adler's zero for tree amplitudes of ==non-linear Sigma model and Born-Infeld theories==.\] # Winer, Swingle ## Reappearance of Thermalization Dynamics in the Late-Time Spectral Form Factor \[Links: [arXiv](https://arxiv.org/abs/2307.14415), [PDF](https://arxiv.org/pdf/2307.14415.pdf)\] \[Abstract: The [[0062 Spectral form factor|spectral form factor]] (SFF) is an important diagnostic of energy level repulsion in [[0579 Random matrix theory|random matrix theory]] (RMT) and [[0008 Quantum chaos|quantum chaos]]. The short-time behavior of the SFF as it approaches the RMT result acts as a diagnostic of the ergodicity of the system as it approaches the thermal state. In this work we observe that for systems ==without time-reversal symmetry==, there is a second break from the RMT result at late time around the Heisenberg time. Long after thermalization has taken hold, and after the SFF has agreed with the RMT result to high precision for a time of order the Heisenberg time, the SFF of a large system will briefly deviate from the RMT behavior in a way exactly determined by its early time thermalization properties. The conceptual reason for this second deviation is the Riemann-Siegel lookalike formula, a resummed expression for the spectral determinant relating late time behavior to early time spectral statistics. We use the lookalike formula to derive a precise expression for the late time SFF for semi-classical quantum chaotic systems, and then confirm our results numerically for more general systems.\] # Witten (Aug) ## A Background Independent Algebra in Quantum Gravity \[Links: [arXiv](https://arxiv.org/abs/2308.03663), [PDF](https://arxiv.org/pdf/2308.03663.pdf)\] \[Abstract: We propose an algebra of operators along an observer's worldline as a background-independent algebra in quantum gravity. In that context, it is natural to think of the Hartle-Hawking no boundary state as a universal state of maximum entropy, and to define entropy in terms of the relative entropy with this state. In the case that the only spacetimes considered correspond to de Sitter vacua with different values of the cosmological constant, this definition leads to sensible results.\] # Yan ## More on Torus Wormholes in 3d Gravity \[Links: [arXiv](https://arxiv.org/abs/2305.10494), [PDF](https://arxiv.org/pdf/2305.10494)\] \[Abstract: We study further the [[0073 AdS3-CFT2|duality]] between semiclassical AdS3 and formal CFT2 [[0154 Ensemble averaging|ensembles]]. First, we study torus wormholes (Maldacena-Maoz wormholes with two torus boundaries) with one insertion or two insertions on each boundary and find that they give non-decaying contribution to the product of two torus one-point or two-point functions at late-time. Second, we study the $\mathbb{Z}_2$ quotients of a torus wormhole such that the outcome has one boundary. We identify quotients that give non-decaying contributions to the torus two-point function at late-time. We comment on reflection (R) or time-reversal (T) symmetry v.s. the combination RT that is a symmetry of any relativistic field theory. RT symmetry itself implies that to the extent that a relativistic quantum field theory exhibits random matrix statistics it should be of the GOE type. We discuss related implications of these symmetries for wormholes.\] # Yan, Jepsen, Oz ## $p$-adic Holography from the Hyperbolic Fracton Model \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: We reveal a low-temperature duality between the hyperbolic lattice model featuring fractons and infinite decoupled copies of Zabrodin's [[0084 p-adic holography|p-adic]] model of AdS/CFT. The core of the duality is the subsystem symmetries of the hyperbolic [[0428 Fractons|fracton]] model, which always act on both the boundary and the bulk. These subsystem symmetries are associated with fractal trees embedded in the hyperbolic lattice, which have the same geometry as Zabrodin's model. The fracton model, rewritten as electrostatics theory on these trees, matches the equation of motion of Zabrodin's model. The duality extends from the action to lattice defects as p-adic black holes.\] # Yuan, Ge, Kim, Ji, Ahn ## Pole-skipping points in 2D gravity and SYK model \[Links: [arXiv](https://arxiv.org/abs/2303.04801), [PDF](https://arxiv.org/pdf/2303.04801.pdf)\] \[Abstract: We study the [[0179 Pole skipping|pole-skipping]] phenomenon of the boundary field theory dual to [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] with a minimally coupled massive scalar field. In contrast to the higher dimensional models, there is no momentum degree of freedom in (1+1)-dimensional bulk theory. Thus, we consider a scalar field mass as our degree of freedom for the pole-skipping phenomenon instead of momentum. The pole-skipping frequencies of the scalar field in 2D gravity are the same as higher dimensional cases: $\omega=-i2\pi Tn$ for positive integer $n$. At each of these frequencies, there is a corresponding pole-skipping mass, so the pole-skipping points exist in the $(\omega,m)$ space. We also compute the pole-skipping points of the [[0201 Sachdev-Ye-Kitaev model|SYK model]] in $(\omega, h)$ space where $h$ is the dimension of the bilinear primary operator. We find that there is a one-to-one correspondence of the pole skipping points between the JT gravity and the SYK model.\] # Zeng ## Twisted Holography and Celestial Holography from Boundary Chiral Algebra \[Links: [arXiv](https://arxiv.org/abs/2302.06693), [PDF](https://arxiv.org/pdf/2302.06693.pdf)\] \[Abstract: We study the [[0169 Kaluza-Klein|Kaluza-Klein]] reduction of various 6d holomorphic theories. The KK reduction is analyzed in the BV formalism, resulting in theories that come from the holomorphic topological twist of 3d $\mathcal{N} = 2$ supersymmetric field theories. Effective interactions of the KK theories at the classical level can be obtained at all orders using homotopy transfer theorem. We also analyze a deformation of the theories that comes from deforming the spacetime geometry to $SL_2(\mathbb{C})$ due to the brane back-reaction. We study the boundary chiral algebras for the various KK theories. Using [[0510 Koszul duality|Koszul duality]], we argue that by properly choosing a boundary condition, the boundary chiral algebra coincides with the universal defect chiral algebra of the original theory. This perspective provides a unified framework for accessing the chiral algebras that arise from both [[0130 Twisted holography|twisted holography]] and [[0010 Celestial holography|celestial holography]] programs.\] ## Refs - [[0384 4d-2d twistorial correspondence]]