# Aalsma, Faruk, van der Schaar, Visser, de Witte ## Late-Time Correlators and Complex Geodesics in de Sitter Space \[Links: [arXiv](https://arxiv.org/abs/2212.01394), [PDF](https://arxiv.org/pdf/2212.01394.pdf)\] \[Abstract: We study [[0103 Two-point functions|two-point correlation functions]] of a massive free scalar field in de Sitter space using the heat kernel formalism. Focusing on two operators in conjugate static patches we derive a geodesic approximation to the two-point correlator valid for large mass and at late times. This expression involves a sum over two complex conjugate geodesics that correctly reproduces the large-mass, late-time limit of the exact two-point function in the Bunch-Davies vacuum. The exponential decay of the late-time correlator is associated to the timelike part of the complex geodesics. We emphasize that the late-time exponential decay is in tension with the finite maximal entropy of empty de Sitter space, and we briefly discuss how non-perturbative corrections might resolve this paradox.\] ## Refs - simultaneous release [[2022#Chapman, Galante, Harris, Sheorey, Vegh]] # Adamo, Bu, Casali, Sharma ## All-order celestial OPE in the MHV sector \[Links: [arXiv](https://arxiv.org/abs/2211.17124), [PDF](https://arxiv.org/pdf/2211.17124.pdf)\] \[Abstract: On-shell kinematics for gluon scattering can be parametrized with points on the [[0022 Celestial sphere|celestial sphere]]; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an [[0030 Operator product expansion|operator product expansion]] (OPE)-like structure. While it is possible to obtain singular contributions to this [[0114 Celestial OPE|celestial OPE]], getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use [[0497 Twistor string theory|twistor string theory]] to describe the [[0061 Maximally helicity violating amplitudes|maximal helicity violating]] (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of [[0107 Soft gluon symmetry|soft gluon]] descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the [[0078 Collinear limit|collinear]] expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector.\] ## Refs - [[0114 Celestial OPE]] # Agon, Bueno, Andino, Lopez ## Aspects of $N$-partite information in conformal field theories \[Links: [arXiv](https://arxiv.org/abs/2209.14311), [PDF](https://arxiv.org/pdf/2209.14311)\] \[Abstract: We present several new results for the $N$[[0264 Multi-partite entanglement|-partite information]], $I_N$, of spatial regions in the ground state of $d$-dimensional conformal field theories. First, we show that $I_N$ can be written in terms of a single $N$-point function of twist operators. Using this, we argue that in the limit in which all mutual separations are much greater than the regions sizes, the $N$-partite information scales as $I_N \sim r^{-2N\Delta}$, where $r$ is the typical distance between pairs of regions and \Delta is the lowest primary scaling dimension. In the case of spherical entangling surfaces, we obtain a completely explicit formula for the $I_4$ in terms of 2-, 3- and 4-point functions of the lowest-dimensional primary. Then, we consider a three-dimensional scalar field in the lattice. We verify the predicted long-distance scaling and provide strong evidence that $I_N$ is always positive for general regions and arbitrary $N$ for that theory. For the $I_4$, we find excellent numerical agreement between our general formula and the lattice result for disk regions. We also perform lattice calculations of the [[0300 Mutual information|mutual information]] for more general regions and general separations both for a free scalar and a free fermion, and conjecture that, normalized by the corresponding disk entanglement entropy coefficients, the scalar result is always greater than the fermion one. Finally, we verify explicitly the equality between the $N$-partite information of bulk and boundary fields in holographic theories for spherical [[0007 RT surface|entangling surfaces]] in general dimensions.\] # Aharony, Chester, Sheaffer, Urbach ## Explicit holography for vector models at finite $N$, volume and temperature \[Links: [arXiv](https://arxiv.org/abs/2208.13607), [PDF](https://arxiv.org/pdf/2208.13607.pdf)\] \[Abstract: In previous work we constructed an explicit mapping between large $N$ vector models (free or critical) in $d$ dimensions and a non-local [[0421 Higher-spin gravity|high-spin gravity]] theory on AdS$_{d+1}$, such that the gravitational theory reproduces the field theory correlation functions order by order in $1/N$. In this paper we discuss three aspects of this mapping. First, our original mapping was not valid non-perturbatively in $1/N$, since it did not include non-local correlations between the gravity fields which appear at finite $N$. We show that by using a bi-local $G-\Sigma$ type formalism similar to the one used in the [[0201 Sachdev-Ye-Kitaev model|SYK]] model, we can construct an exact mapping to the bulk that is valid also at finite $N$. The theory in the bulk contains additional auxiliary fields which implement the finite $N$ constraints. Second, we discuss the generalization of our mapping to the field theory on $S^d$, and in particular how the sphere free energy matches exactly between the two sides, and how the mapping can be consistently regularized. Finally, we discuss the field theory at finite temperature, and show that the low-temperature phase of the vector models can be mapped to a high-spin gravity theory on thermal AdS space.\] ## Refs - based on earlier work [[AharonyChesterUrbach2020]][](https://arxiv.org/abs/2011.06328) - [[0421 Higher-spin gravity]] ## Summary - extension to finite $N$ - generalisation to $S^d$ - finite temperature # Ahmadain, Wall (a) ## Off-Shell Strings I: S-matrix and Action \[Links: [arXiv](https://arxiv.org/abs/2211.08607), [PDF](https://arxiv.org/pdf/2211.08607.pdf); Talks: [SFT](https://youtu.be/uexpP9cx1uw), [NYU](https://youtu.be/gQ63YnNg--c)\] \[Abstract: We explain why Tseytlin's [[0505 Off-shell strings|off-shell formulation of string theory]] is well-defined. Although quantizing strings on an off-shell background requires an arbitrary choice of Weyl frame, this choice is not physically significant since it can be absorbed into a field redefinition of the target space fields. The off-shell formalism is particularly subtle at tree-level, due to the treatment of the noncompact conformal Killing group $\mathrm{SL}(2,\mathbb{C})$ of the sphere. We prove that Tseytlin's sphere prescriptions recover the standard tree-level Lorentzian $S$-matrix, and show how to extract the stringy $i\varepsilon$ prescription from the UV cutoff on the worldsheet. We also demonstrate that the correct tree-level equations of motion are obtained to all orders in perturbation theory in $g_s$ and $\alpha^\prime$, and illuminate the close connection between the string action and the [[0351 Irreversibility theorems|c-theorem]].\] ## Refs - [[0505 Off-shell strings]] - part II: [[2022#Ahmadain, Wall (b)]] on entropy # Ahmadain, Wall (b) ## Off-Shell Strings II: Black Hole Entropy \[Links: [arXiv](https://arxiv.org/abs/2211.16448), [PDF](https://arxiv.org/pdf/2211.16448.pdf)\] \[Abstract: In 1994, [[1994#Susskind, Uglum|Susskind and Uglum]] argued that it is possible to derive the [[0004 Black hole entropy|Bekenstein-Hawking entropy]] $A/4G_N$ from string theory. In this article we explain the conceptual underpinnings of this argument, while elucidating its relationship to induced gravity and [[0220 ER=EPR|ER=EPR]]. Following an off-shell calculation by Tseytlin, we explicitly derive the classical closed string effective action from sphere diagrams at leading order in $\alpha^{\prime}$. We then show how to use this to obtain black hole entropy from the RG flow of the NLSM on conical manifolds. (We also briefly discuss the more problematic "open string picture" of Susskind and Uglum, in which strings end on the horizon.) We then compare these off-shell results with the rival "orbifold replica trick" using the on-shell $\mathbb{C}/Z_{N}$ background, which does not account for the leading order Bekenstein-Hawking entropy -- unless perhaps tachyons are allowed to condense on the orbifold. Possible connections to the [[0220 ER=EPR|ER=EPR]] conjecture are explored. Finally, we discuss prospects for various extensions, including prospects for deriving [[0145 Generalised area|holographic entanglement entropy]] in the bulk of AdS.\] ## Refs - [[0505 Off-shell strings]] - earlier [[2022#Ahmadain, Wall (a)]] # Ahn ## The ${\cal N}=4$ Supersymmetric Linear $W_{\infty}[λ]$ Algebra \[Links: [arXiv](https://arxiv.org/abs/2205.04024), [PDF](https://arxiv.org/pdf/2205.04024.pdf)\] \[Abstract: From the recently known ${\cal N}=2$ supersymmetric linear $W_{\infty}^{K,K}[\lambda]$ algebra where $K$ is the dimension of fundamental (or antifundamental) representation of bifundamental $\beta \, \gamma$ and $b \, c$ ghost system, we determine its ${\cal N}=4$ supersymmetric enhancement at $K=2$. We construct the ${\cal N}=4$ stress energy tensor, the first ${\cal N}=4$ multiplet and their [[0030 Operator product expansion|operator product expansions]] (OPEs) in terms of above bifundamentals. We show that the OPEs between the first ${\cal N}=4$ multiplet and itself are the same as the corresponding ones in the ${\cal N}=4$ coset $\frac{SU(N+2)}{SU(N)}$ model under the large $(N,k)$ 't Hooft-like limit with fixed $\lambda_{co} \equiv \frac{(N+1)}{(k+N+2)}$, up to two central terms. The two parameters are related to each other $\lambda =\frac{1}{2}\, \lambda_{co}$. We also provide other OPEs by considering the second, the third and the fourth ${\cal N}=4$ multiplets in the ${\cal N}=4$ supersymmetric linear $W_{\infty}[\lambda]$ algebra.\] # Akers, Engelhardt, Harlow, Penington, Vardhan ## The black hole interior from non-isometric codes and complexity \[Links: [arXiv](https://arxiv.org/abs/2207.06536), [PDF](https://arxiv.org/pdf/2207.06536.pdf)\] \[Abstract: [[0146 Quantum error correction|QEC]] has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of "non-isometric codes protected by computational complexity''. We show that many previous ideas, such as the existence of a large number of "[[0034 Null states|null states]]'', a breakdown of effective field theory for operations of exponential complexity, the [[0212 Quantum extremal surface|QES]] calculation of the Page curve, post-selection, "state-dependent/state-specific'' operator reconstruction, and the "simple entropy'' approach to [[0204 Quantum complexity|complexity]] coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.\] ## Refs - talks by #chrisakers and #nettaengelhardt at [[Rsc0045 Fundamental aspects of gravity conference London 2022]] - follow-ups - $S$-matrix: [[2022#Kim, Preskill]] - backward-forward map: [[2023#DeWolfe, Higginbotham]] ## Summary - a toy model for non-isometric codes modelling BH evaporation - obtains [[0212 Quantum extremal surface|QES]] from a "microscopic" (i.e., explicit) calculation of non-isometric codes - even though non-isometric, the code can be *approximately* invertible on the set of *sub-exponential* states ## A static model - it preserves the inner product even though not being an isometry # Alaee, Hung, Khuri ## The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets With Toroidal Infinity and Related Rigidity Results \[Links: [arXiv](https://arxiv.org/abs/2201.04327), [PDF](https://arxiv.org/pdf/2201.04327.pdf)\] \[Abstract: We establish the [[0116 Positive energy theorem|positive energy theorem]] and a [[0476 Penrose inequality|Penrose-type inequality]] for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped boundary, and satisfying the dominant [[0247 Energy conditions|energy condition]]. In the umbilic case, a rigidity statement is proven showing that the total energy vanishes precisely when the initial data manifold is isometric to a portion of the canonical slice of the associated Kottler spacetime. Furthermore, we provide a new proof of the recent rigidity theorems of Eichmair-Galloway-Mendes [10] in dimension 3, with weakened hypotheses in certain cases. These results are obtained through an analysis of the level sets of spacetime harmonic functions.\] ## Comments - requires that there is an "inner boundary" (trapped), so that the [[0567 AdS soliton|Horowitz-Myers]] solution is excluded from consideration - the "umbilic" case of $k=-g$ is appropriate for hyperboloidal initial data in asymptotically flat case but not in AdS # Alonso-Serrano, Liska ## Emergence of quadratic gravity from entanglement equilibrium \[Links: [arXiv](https://arxiv.org/abs/2212.03168), [PDF](https://arxiv.org/pdf/2212.03168.pdf)\] \[Abstract: In this work, we derive the linearised equations of [[0006 Higher-derivative gravity|quadratic gravity]] from entanglement equilibrium of local causal diamonds. Rather than starting from the [[0004 Black hole entropy|Wald entropy]] prescription (which depends on the gravitational Lagrangian), we employ a model independent approach based on the logarithmic corrections to horizon [[0301 Entanglement entropy|entanglement entropy]]. In this way, we are able to show the emergence of linearised quadratic gravity from entanglement equilibrium without using any a priori knowledge about gravitational dynamics. If the logarithmic correction to entropy has a negative sign, as predicted by replica trick calculations of entanglement entropy, we find that the quadratic gravity correction terms have the sign necessary to avoid tachyonic instabilities of the theory.\] # Altland, Post, Sonnor, van der Heijden, Verlinde ## Quantum chaos in 2D gravity \[Links: [arXiv](https://arxiv.org/abs/2204.07583), [PDF](https://arxiv.org/pdf/2204.07583.pdf)\] \[Abstract: We present a quantitative and fully non-perturbative description of the ergodic phase of [[0008 Quantum chaos|quantum chaos]] in the setting of two-dimensional gravity. To this end we describe the doubly non-perturbative completion of semiclassical 2D gravity in terms of its associated universe field theory. The guiding principle of our analysis is a flavor-matrix theory (fMT) description of the ergodic phase of holographic gravity, which exhibits $\mathrm{U}(n|n)$ causal symmetry breaking and restoration. [[0050 JT gravity|JT gravity]] and its 2D-gravity cousins alone do not realize an action principle with causal symmetry, however we demonstrate that their *universe field theory*, the [[0389 Kodaira-Spencer field theory|Kodaira-Spencer (KS) theory]] of gravity, does. After directly deriving the fMT from brane-antibrane correlators in KS theory, we show that causal symmetry breaking and restoration can be understood geometrically in terms of different (topological) [[0156 D-brane|D-brane]] vacua. We interpret our results in terms of an [[0399 Open-closed string duality|open-closed string duality]] between holomorphic [[0089 Chern-Simons theory|Chern-Simons theory]] and its closed-string equivalent, the KS theory of gravity. Emphasis will be put on relating these geometric principles to the characteristic spectral correlations of the quantum ergodic phase.\] # Amano, Blake, Cartwright, Kaminski, Thompson ## Chaos and pole-skipping in a simply spinning plasma \[Links: [arXiv](https://arxiv.org/abs/2211.00016), [PDF](https://arxiv.org/pdf/2211.00016.pdf)\] \[Abstract: We study the relationship between many-body [[0008 Quantum chaos|quantum chaos]] and energy dynamics in holographic quantum field theory states dual to the ==simply-spinning Myers-Perry-AdS$_5$ black hole==. The enhanced symmetry of such black holes allows us to provide a thorough examination of the phenomenon of pole-skipping, that is significantly simpler than a previous analysis of quantum field theory states dual to the Kerr-AdS$_4$ solution. In particular we give a general proof of [[0179 Pole skipping|pole-skipping]] in the [[0473 Retarded Green's function|retarded energy density Green's function]] of the dual quantum field theory whenever the spatial profile of energy fluctuations satisfies the [[0117 Shockwave|shockwave]] equation governing the form of the [[0482 Out-of-time-order correlator|OTOC]]. Furthermore, in the large black hole limit we are able to obtain a simple analytic expression for the OTOC for operator configurations on Hopf circles, and demonstrate that the associated [[0466 Lyapunov exponent|Lyapunov exponent]] and [[0167 Butterfly velocity|butterfly velocity]] are robustly related to the locations of a family of pole-skipping points in the energy response. Finally, we note that in contrast to previous studies, our results are valid for any value of rotation and we are able to numerically demonstrate that the dispersion relations of sound modes in the energy response explicitly pass through our pole-skipping locations.\] ## Geometry - in the past, there has been work on rotating BTZ and Kerr-AdS in the slowly rotating limit - here the geometry is the higher dimensional rotating BH - a co-rotating coordinate is defined to allow analytically continuation across the horizon (i.e. to get into Kruskal coordinates) - this co-rotating coordinate $\tilde \psi$ plays the role of $|x|$ in the planar case ## Butterfly velocity - can now be negative - the analogy is that boosting a fluid faster than the speed would lead to the sound "travelling backwards" - it seems that sometimes the local [[0466 Lyapunov exponent|Lyapunov exponent]] can exceed the bound - but the *average* still grows in a bounded way - there is a periodic function in the OTOC that makes the actual function oscillate around some average growth # Ananth, Pandey, Pant ## Soft factors and interaction vertices from light-cone actions \[Links: [arXiv](https://arxiv.org/abs/2212.13382), [PDF](https://arxiv.org/pdf/2212.13382.pdf)\] \[Abstract: Universal factors associated with the emission of a [[0009 Soft theorems|soft]] boson in gauge theories and gravity, formulated in the light-cone gauge, are presented. The inverse-soft method, for constructing higher-point amplitudes from lower-point ones, using these factors is reviewed. These ideas are then examined in (light-cone) superspace and applied to both the $\mathcal{N}=4$ super Yang-Mills and $\mathcal{N}=8$ supergravity theories. One highlight is a compact result for the quartic interaction vertex in $\mathcal{N}=8$ supergravity, a crucial ingredient for finiteness analyses.\] # Antonini, Bentsen, Cao, Harper, Jian, Swingle ## Holographic measurement and bulk teleportation \[Links: [arXiv](https://arxiv.org/abs/2209.12903), [PDF](https://arxiv.org/pdf/2209.12903.pdf)\] \[Abstract: [[0001 AdS-CFT|Holography]] has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual theory. In this paper, we describe how changes in the entanglement due to a local projective measurement (LPM) on a subregion $A$ of the boundary theory modify the bulk dual spacetime. We find that LPMs destroy portions of the bulk geometry, yielding post-measurement bulk spacetimes dual to the complementary unmeasured region $A^c$ that are cut off by end-of-the-world branes. Using a bulk calculation in AdS$_3$ and [[0054 Tensor network|tensor network]] models of holography, we show that the portions of the bulk geometry that are preserved after the measurement depend on the size of $A$ and the state we project onto. The post-measurement bulk dual to $A^c$ includes regions that were originally part of the entanglement wedge of $A$ prior to measurement. This suggests that LPMs performed on a boundary subregion $A$ teleport part of the bulk information originally encoded in $A$ into the complementary region $A^c$. In semiclassical holography an arbitrary amount of bulk information can be teleported in this way, while in tensor network models the teleported information is upper-bounded by the amount of entanglement shared between $A$ and $A^c$ due to finite-$N$ effects. When $A$ is the union of two disjoint subregions, the measurement triggers an entangled/disentangled phase transition between the remaining two unmeasured subregions, corresponding to a connected/disconnected phase transition in the bulk description. Our results shed new light on the effects of measurement on the entanglement structure of holographic theories and give insight on how bulk information can be manipulated from the boundary theory. They could also be extended to more general quantum systems and tested experimentally, and represent a first step towards a holographic description of [[0552 Measurement-induced phase transition|measurement-induced phase transitions]].\] # Antonini, Grado-White, Jian, Swingle ## Holographic measurement and quantum teleportation in the SYK thermofield double \[Links: [arXiv](https://arxiv.org/abs/2211.07658), [PDF](https://arxiv.org/pdf/2211.07658.pdf)\] \[Abstract: According to holography, entanglement is the building block of spacetime; therefore, drastic changes of entanglement will lead to interesting transitions in the dual spacetime. In this paper, we study the effect of projective measurements on the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev (SYK) model]]'s thermofield double state, dual to an eternal black hole in [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]]. We calculate the (Renyi-2) [[0300 Mutual information|mutual information]] between the two copies of the SYK model upon projective measurement of a subset of fermions in one copy. We propose a dual JT gravity model that can account for the change of entanglement due to measurement, and observe an entanglement wedge phase transition in the [[0301 Entanglement entropy|von Neumann entropy]]. The entanglement wedge for the unmeasured side changes from the region outside the horizon to include the entire time reversal invariant slice of the two-sided geometry as the number of measured Majorana fermions increases. Therefore, after the transition, the bulk information stored in the measured subsystem is not entirely lost upon projection in one copy of the SYK model, but rather teleported to the other copy. We further propose a decoding protocol to elucidate the teleportation interpretation, and connect our analysis to the physics of [[0083 Traversable wormhole|traversable wormholes]].\] ## Refs - [[0502 Bulk dual of measurement]] # Araujo-Regado ## Holographic Cosmology on Closed Slices in 2+1 Dimensions \[Links: [arXiv](https://arxiv.org/abs/2212.03219), [PDF](https://arxiv.org/pdf/2212.03219.pdf)\] \[Abstract: We apply the framework of [[0426 Cauchy slice holography|Cauchy Slice Holography]] to the quantization of gravity on closed slices with $\Lambda>0$ (with a focus on $2+1$ dimensions for concreteness). We obtain solutions to the [[0345 Wheeler-DeWitt (WdW) equation|Wheeler-DeWitt equation]] in a basis of CPT-dual branches. Each branch is a $T^2$-deformed CFT partition function with imaginary [[0033 Central charge|central charge]]. We compute explicit solutions in 2+1 dimensions in a [[0254 Minisuperspace|minisuperspace]] toy model of pure gravity. This analysis gives us evidence to conjecture a connection between the choice of superposition of branches and the choice of class of geometries to sum over in the gravitational path integral. We further argue that, in full quantum gravity on closed slices, bulk CPT symmetry is a sufficient condition for bulk unitarity, even if the Euclidean holographic field theory is not reflection-positive.\] ## Refs - [[0426 Cauchy slice holography]] - [[0254 Minisuperspace]] - precursor [[2022#Araujo-Regado, Khan, Wall]] # Araujo-Regado, Khan, Wall ## Cauchy Slice Holography: A New AdS/CFT Dictionary \[Links: [arXiv](https://arxiv.org/abs/2204.00591), [PDF](https://arxiv.org/pdf/2204.00591.pdf)\] \[Abstract: \] ## Summary - *makes* a CFT on a Cauchy slice by making a [[0170 TTbar]] deformation of a Euclidean CFT - *shows* equivalence between ADM and CFT Hamiltonians ## Matching of WdW WF and Partition function - deformation $\frac{d \mathcal{L}}{d \lambda}=\sqrt{g}\left[\left(T_{a b} T^{a b}-T^{2}\right)(\lambda)+\frac{c}{3 \lambda} R\right]$ - turns out that they satisfy WDW constraint equations (kind of by definition): $H Z_{T \bar{T}}\left[g_{a b}\right]=0, \quad D_{a} Z_{T \bar{T}}\left[g_{a b}\right]=0$ - so identify $Z_{T \bar{T}}\left[g_{a b}\right]=\Psi_{\text {WDW }}\left[g_{a b}\right]$ # Bah, Chen, Maldacena ## Estimating global charge violating amplitudes from wormholes \[Links: [arXiv](https://arxiv.org/abs/2212.08668), [PDF](https://arxiv.org/pdf/2212.08668.pdf)\] \[Abstract: We consider the scattering of high energy and ultra relativistic spherically symmetric shells in asymptotically AdS$_D$ spacetimes. We analyze an exclusive amplitude where a single spherically symmetric shell goes in and a single one comes out, such that the two have different [[0187 Global symmetries in QG|global symmetry]] charges of the effective gravity theory. We study a simple wormhole configuration that computes the square of the amplitude and analyze its properties.\] # Bah, Heidmann, Weck ## Schwarzschild-like Topological Solitons \[Links: [arXiv](https://arxiv.org/abs/2203.12625), [PDF](https://arxiv.org/pdf/2203.12625.pdf)\] \[Abstract: We construct the first class of topological solitons in gravity that are supported by internal electromagnetic flux with vanishing net charges. The solutions are obtained in a six-dimensional Einstein-Maxwell theory with a three-form flux, and admit an uplift to type IIB supergravity on $T^4$. They are asymptotic to a torus fibration over four-dimensional Minkowski spacetime. An interesting class corresponds to solitons with a BPS particle and its anti-BPS partner held apart by a vacuum bubble. In type IIB, they correspond to bound states of BPS and anti-BPS D1-D5 extremal black holes. These metrics are a particular limit of a larger class of axially symmetric metrics that we construct and that describe smooth horizonless topological solitons. They correspond to bound states of three non-BPS bubbles on a line. An important achievement is that the outer bubbles can carry arbitrary D1-D5 charges that we can tune to vanishing net charges. We discuss their properties and compare them to a four-dimensional Schwarzschild black hole of the same mass. We show that they have a long throat with a large redshift, and that they are ultra-compact with a characteristic size of 1.52 times the Schwarzschild radius.\] ## Summary - constructs topological solitons in gravity with vanishing net charges for the first time - in 6D Einstein-Maxwell with a three-form flux ## Set-up - a two-form potential $C^{(2)}$ ($F_3=dC^{(2)}$) - background $\mathbb{R}^{1,3} \times {T}^{2}$ ## Potential - non-trivial [[0060 Asymptotic symmetry]] on T2? # Balasubramanian, Lawrence, Magan, Sasieta (a) ## Microscopic origin of the entropy of black holes in general relativity \[Links: [arXiv](https://arxiv.org/abs/2212.02447), [PDF](https://arxiv.org/pdf/2212.02447.pdf)\] \[Abstract: We construct an infinite family of [[0248 Black hole microstates|microstates]] with geometric interiors for eternal black holes in [[0554 Einstein gravity|general relativity]] with negative cosmological constant in any dimension. Wormholes in the Euclidean [[0555 Gravitational path integral|path integral for gravity]] cause these states to have small, but non-zero, quantum mechanical overlaps that have a universal form. The overlaps have a dramatic consequence: the microstates span a Hilbert space of log dimension equal to the [[0004 Black hole entropy|Bekenstein-Hawking entropy]]. The semiclassical microstates we construct contain Einstein-Rosen bridges of arbitrary size behind their horizons. Our results imply that all these bridges can be interpreted as quantum superpositions of wormholes of size at most exponential in the entropy.\] ## Refs - [[0248 Black hole microstates]] - [[0004 Black hole entropy]] - astrophysical (flat space) version: [[2022#Balasubramanian, Lawrence, Magan, Sasieta (b)]] ## Computing the Hilbert space dimension 1. compute the inner products using the [[0555 Gravitational path integral|gravitational path integral]] 2. compute the rank of the inner product matrix 3. use the trick: introduce the resolvent # Balasubramanian, Lawrence, Magan, Sasieta (b) ## Microscopic origin of the entropy of astrophysical black holes \[Links: [arXiv](https://arxiv.org/abs/2212.08623), [PDF](https://arxiv.org/pdf/2212.08623.pdf)\] \[Abstract: We construct an infinite family of geometric microstates for black holes forming from collapse of dust shells in Minkowski spacetime. Quantum mechanical wormholes cause these states to have exponentially small, but universal, overlaps. We show that these overlaps imply that the microstates span a Hilbert space of log dimension equal to the event horizon area divided by four times the Newton constant, explaining the microscopic origin of the [[0004 Black hole entropy|Bekenstein-Hawking black hole entropy]].\] ## Refs - AdS version: [[2022#Balasubramanian, Lawrence, Magan, Sasieta (a)]] # Ball ## Celestial Locality and the Jacobi Identity \[Links: [arXiv](https://arxiv.org/abs/2211.09151), [PDF](https://arxiv.org/pdf/2211.09151.pdf)\] \[Abstract: We show the equivalence of several different tests of the [[0453 Jacobi identity or associativity of celestial OPE|Jacobi identity]] for celestial currents at tree level, in particular finding a simple, practical condition on hard momentum space 4-point amplitudes in any EFT. Along the way we clarify the role of the order of [[0009 Soft theorems|soft]] and [[0078 Collinear limit|collinear]] limits in obstructing Jacobi for soft insertions and we argue that, despite their current-algebra-like properties, soft insertions as formulated in this paper cannot be interpreted as local operators in [[0010 Celestial holography|celestial conformal field theory]].\] ## Nonlocal pole - when the pole for $z_i$ is not located at $z_j$ ($z_j$ being the location of any other inserted operator) # Banerjee, Pasterski ## Revisiting the Shadow Stress Tensor in Celestial CFT \[Links: [arXiv](https://arxiv.org/abs/2212.00257), [PDF](https://arxiv.org/pdf/2212.00257.pdf)\] \[Abstract: We revisit the standard construction of the celestial stress tensor as a [[0039 Shadow transform|shadow]] of the subleading conformally soft graviton. In its original formulation there is an obstruction to reproducing the expected $T T$ [[0030 Operator product expansion|OPE]] in the double [[0009 Soft theorems|soft]] limit. We propose a modification to the definition which circumvents this obstruction and then extend this change of basis beyond the [[0390 Conformally soft theorems|conformally soft]] and single helicity sectors. In the process we investigate how (non)-commutativity of double soft limits is tied to the decoupling of primary descendants, and how our choice of celestial basis determines which symmetries are manifest at the level of the OPE beyond the [[0061 Maximally helicity violating amplitudes|MHV]] sector.\] # Banerjee, Rahnuma, Singh ## Asymptotic Symmetry algebra of $\mathcal{N} = 8$ Supergravity \[Links: [arXiv](https://arxiv.org/abs/2212.12133), [PDF](https://arxiv.org/pdf/2212.12133.pdf)\] \[Abstract: The [[0060 Asymptotic symmetry|asymptotic symmetry]] algebra of $\mathcal{N}=1$ supergravity was recently constructed using the well-known [[0010 Celestial holography|2D celestial CFT]] (CCFT) technique in ArXiv: [2007.03785](https://arxiv.org/abs/2007.03785). In this paper, we extend the construction to the maximally supersymmetric four dimensional $\mathcal{N}=8$ supergravity theory in asymptotically flat spacetime and construct the extended asymptotic symmetry algebra, which we call $\mathcal{N}=8$ $\mathfrak{sbms}_4$. We use the celestial CFT technique to find the appropriate currents for extensions of $\mathcal{N}=8$ super-Poincaré and $\mathrm{SU}(8)_R$ $R$-symmetry current algebra on the celestial sphere $\mathcal{CS}^2$. We generalise the definition of shadow transformations and show that there is *no* infinite dimensional extension of the global $\mathrm{SU}(8)_R$ algebra in the theory.\] # Banihashemi, Jacobson ## Thermodynamic ensembles with cosmological horizons \[Links: [arXiv](https://arxiv.org/abs/2204.05324), [PDF](https://arxiv.org/pdf/2204.05324.pdf)\] \[Abstract: The entropy of a de Sitter horizon was derived long ago by Gibbons and Hawking via a gravitational partition function. Since there is no boundary at which to define the temperature or energy of the ensemble, the statistical foundation of their approach has remained obscure. To place the statistical ensemble on a firm footing we introduce an artificial "York boundary", with either canonical or microcanonical boundary conditions, as has been done previously for black hole ensembles. The partition function and the density of states are expressed as integrals over paths in the constrained, spherically reduced phase space of pure 3+1 dimensional gravity with a positive cosmological constant. Issues related to the domain and contour of integration are analyzed, and the adopted choices for those are justified as far as possible. The canonical ensemble includes a patch of spacetime without horizon, as well as configurations containing a black hole or a cosmological horizon. We study thermodynamic phases and (in)stability, and discuss an evolving reservoir model that can stabilize the cosmological horizon in the canonical ensemble. Finally, we explain how the Gibbons-Hawking partition function on the 4-sphere can be derived as a limit of well-defined thermodynamic ensembles and, from this viewpoint, why it computes the dimension of the Hilbert space of states within a cosmological horizon.\] ## Summary - *defines* rigorously a statistical ensemble in dS by introducing an artificial York boundary ## Motivation - original derivation by Hawking and Gibbons: [[GibbonsHawking1977]] # Banks, Draper, Zhang ## JT Gravity Coupled to Fermions \[Links: [arXiv](https://arxiv.org/abs/2205.07382), [PDF](https://arxiv.org/pdf/2205.07382.pdf)\] \[Abstract: We argue that two-dimensional dilaton gravity models can all be derived from an analog of Jacobson's covariant version of the first law of thermodynamics. We then specialize to the [[0050 JT gravity|JT gravity]] model and couple it to massless fermions. This model is exactly soluble in quantum field theory, and we present a new derivation of that result. The field theory model violates two principles one might want to impose on a quantum theory of gravity describing the near horizon region of an extremal charged black hole in four dimensions: finiteness of the entropy for finite causal diamonds, and the absence of global conservation laws. It preserves an infinite number of conservation laws that one would have expected to be violated, since the fermion state on each side of the AdS$_2$ wormhole is unavoidably thermal. We describe a cutoff version of the model, with extra interactions, which cures these difficulties. Our UV completion of the model depends on the AKK map of non-relativistic fermions in an inverted oscillator potential to Weyl fermions in Minkowski space. We argue that gauging the $Z_2$ symmetry of the oscillator model, using a density matrix with temperature that depends on the oscillator coordinates, and inserting chaotic interactions at (almost) infinite oscillator coordinate, we obtain a model with properties expected of quantum gravity in the near horizon region of an extremal charged black hole in four dimensions.\] # Bao, Cao, Zhu ## Deconfinement and error thresholds in holography \[Links: [arXiv](https://arxiv.org/abs/2202.04710), [PDF](https://arxiv.org/pdf/2202.04710.pdf)\] \[Abstract: We study the error threshold properties of holographic quantum error-correcting codes. We demonstrate that [[0122 Holographic CFT|holographic CFTs]] admit an algebraic threshold, which is related to the confinement-deconfinement phase transition. We then apply geometric intuition from holography and the [[0012 Hawking-Page transition|Hawking-Page phase transition]] to motivate the CFT result, and comment on potential extensions to other confining theories.\] ## Summary - *relates* an algebraic threshold for [[0146 Quantum error correction]] codes to [[0012 Hawking-Page transition]] ## Geometric intuition - with thermal AdS, the thermal noise has small backreaction so we expect the code to be only slightly modified from the original code - with a BH, it can be understood as the large backreaction due to $O(N^2)$ number of thermal particles, thus changing the code subspace, precluding the access of logical information like before --> above error threshold # Bartlett ## Three-dimensional TQFTs via string-nets and two-dimensional surgery \[Links: [arXiv](https://arxiv.org/abs/2206.13262), [PDF](https://arxiv.org/pdf/2206.13262)\] \[Abstract: If $C$ is a spherical fusion category, the string-net construction associates to each closed oriented surface $\Sigma$ the vector space $Z_\text{SN}(\Sigma)$ of linear combinations of $C$-labelled graphs on $\Sigma$ modulo local relations, in a way which is functorial with respect to orientation-preserving diffeomorphisms of surfaces. We show how to extend this assignment to a 3-dimensional topological quantum field theory (TQFT), by defining how the surgery generators in Juhász' presentation of the oriented 3-dimensional bordism category act on the string-net vector spaces. We show that the resulting TQFT, which is formulated completely in the two-dimensional graphical language of string-nets, is an alternative description of the Turaev-Viro state sum model.\] # Bekaert, Boulanger, Campoleoni, Chiodaroli, Francia, Grigoriev, Sezgin, Skvortsov (Review) ## Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry \[Links: [arXiv](https://arxiv.org/abs/2205.01567), [PDF](https://arxiv.org/pdf/2205.01567)\] \[Abstract: [[0421 Higher-spin gravity|Higher Spin Gravity]] refers to extensions of gravity including at least one field of spin greater than two. These extensions are expected to provide manageable models of quantum gravity thanks to the infinite-dimensional (higher spin) gauge symmetry constraining them. One of the key aspects of Higher Spin Gravity/Symmetry is the range and diversity of topics it embraces: (a) higher spin fields play a role in quantum gravity, AdS/CFT, string theory and are expected to have important consequences in cosmology and black hole physics; (b) higher spin symmetry finds applications in Conformal Field Theories, condensed matter systems and dualities therein; (c) these models often rely on tools developed in the study of the mathematical foundations of QFT or in pure mathematics: from deformation quantization and non-commutative geometry to conformal geometry, graded geometry (including BV-BRST quantization), and geometry of PDEs. Recent exciting applications also involve (d) modelling the coalescence of black hole binaries as scattering of massive [[0588 Higher-spin fields|higher spin particles]].\] # Belin, Myers, Ruan, Sarosi, Speranza ## Complexity Equals Anything II \[Links: [arXiv](https://arxiv.org/abs/2210.09647), [PDF](https://arxiv.org/pdf/2210.09647.pdf)\] \[Abstract: We expand on our results in [[2021#Belin, Myers, Ruan, Sarosi, Speranza]] to present a broad new class of gravitational observables in asymptotically Anti-de Sitter space living on general codimension-zero regions of the bulk spacetime. By taking distinct limits, these observables can reduce to well-studied holographic [[0204 Quantum complexity|complexity]] proposals, e.g., the volume of the maximal slice and the action or spacetime volume of the Wheeler-DeWitt patch. As with the codimension-one family found in [[2021#Belin, Myers, Ruan, Sarosi, Speranza]], these new observables display two key universal features for the thermofield double state: they grow linearly in time at late times and reproduce the switchback effect. Hence we argue that any member of this new class of observables is an equally viable candidate as a gravitational dual of complexity. Moreover, using the Peierls construction, we show that variations of the codimension-zero and codimension-one observables are encoded in the gravitational symplectic form on the semi-classical phase-space, which can then be mapped to the CFT.\] # Beneke, Hager, Schwienbacher ## Soft-collinear gravity with fermionic matter \[Links: [arXiv](https://arxiv.org/abs/2212.02525), [PDF](https://arxiv.org/pdf/2212.02525.pdf)\] \[Abstract: We extend the [[0509 Soft-collinear EFT|effective field theory]] for [[0009 Soft theorems|soft]] and [[0078 Collinear limit|collinear]] gravitons to interactions with fermionic matter fields. The full theory features a local Lorentz symmetry in addition to the usual diffeomorphisms, which requires incorporating the former into the soft-collinear gravity framework. The local Lorentz symmetry gives rise to Wilson lines in the effective theory that strongly resemble those in SCET for non-abelian gauge interactions, whereas the diffeomorphisms can be treated in the same fashion as in the case of scalar matter. The basic structure of soft-collinear gravity, which features a homogeneous soft background field, giving rise to a covariant derivative and multipole-expanded covariant Riemann-tensor interactions, remains unaltered and generalises in a natural way to fermion fields.\] ## Related - [[0509 Soft-collinear EFT]] # Benini, Copetti, Di Pietro ## Factorization and global symmetries in holography \[Links: [arXiv](https://arxiv.org/abs/2203.09537), [PDF](https://arxiv.org/pdf/2203.09537.pdf)\] \[Abstract: We consider toy models of holography arising from 3d [[0089 Chern-Simons theory|Chern-Simons theory]]. In this context a duality to an [[0154 Ensemble averaging|ensemble average]] over 2d CFTs has been recently proposed. We put forward an alternative approach in which, rather than summing over bulk geometries, one gauges a one-form global symmetry of the bulk theory. This accomplishes two tasks: it ensures that the bulk theory has [[0187 Global symmetries in QG|no global symmetries]], as expected for a theory of quantum gravity, and it makes the partition function on spacetimes with boundaries coincide with that of a modular-invariant 2d CFT on the boundary. In particular, on wormhole geometries one finds a factorized answer for the partition function. In the case of non-Abelian Chern-Simons theories, the relevant one-form symmetry is non-invertible, and its gauging corresponds to the condensation of a Lagrangian anyon.\] ## Properties of bulk theory after gauging the one-form global symmetry - Euclidean partition function equals 1 on any closed 3-manifold, independent of topology - with boundaries, the bulk partition function only depends on the boundary - the partition function of the bulk theory is defined to be the partition function on any fixed bulk 3-manifold, not a sum over them # Berenstein, Grabovsky, Li ## Aspects of Holography in Conical AdS3 \[Links: [arXiv](https://arxiv.org/abs/2205.02256), [PDF](https://arxiv.org/pdf/2205.02256.pdf)\] \[Abstract: We study the Feynman [[0103 Two-point functions|propagator]] of free scalar fields in AdS$_3$ with a conical defect. The propagator is built by solving the bulk equation of motion, summing over the modes of the field, and taking the boundary limit. We then perform several consistency checks. In the dual CFT, the operator responsible for the defect creates a highly excited state. We consider the exchange of the [[0032 Virasoro algebra|Virasoro]] identity block in the heavy-light limit to obtain an expression for the propagator sensitive to the mass of the defect. In AdS$_3/\mathbb{Z}_n$, we treat the propagator by the method of images and in the geodesic approximation. More generally, we argue that long-range correlations of the scalar are suppressed as the defect becomes more massive: we find a continuous phase transition in the correlator at the [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] threshold and examine its critical behavior. Finally, we apply our results to [[0007 RT surface|holographic entanglement entropy]] using an analogy between our scalars and replica twist fields.\] ## Refs - [[0002 3D gravity]] # Berkooz, Brukner, Ross, Watanabe ## Going beyond ER=EPR in SYK \[Links: [arXiv](https://arxiv.org/abs/2202.11381), [PDF](https://arxiv.org/pdf/2202.11381.pdf)\] \[Abstract: We discuss generalizations of the [[0574 Thermofield double|TFD]] to a density matrix on the doubled Hilbert space. We suggest that a semiclassical wormhole corresponds to a certain class of such density matrices, and specify how they are constructed. Different semi-classical profiles correspond to different non-overlapping density matrices. We show that this language allows for a finer criteria for when the wormhole is semiclassical, which goes beyond entanglement. Our main tool is the [[0201 Sachdev-Ye-Kitaev model|SYK]] model. We focus on the simplest class of such density matrices, in a scaling limit where the ER bridge is captured by chords going from one space to another, encoding correlations in the microscopic Hamiltonian. The length of the wormhole simply encodes the extent these correlations are eroded when flowing from one side to the other.\] ## Summary - *gives* a finer criterium for when a bulk wormhole is semiclassical than the original [[0220 ER=EPR|ER=EPR]] # Bhardwaj, Lippstreu, Ren, Spradlin, Srikant, Volovich ## Loop-level gluon OPEs in celestial holography \[Links: [arXiv](https://arxiv.org/abs/2208.14416), [PDF](https://arxiv.org/pdf/2208.14416.pdf)\] \[Abstract: We compute one-loop corrections to the [[0114 Celestial OPE|OPE]] of gluons in the [[0010 Celestial holography|celestial conformal field theory]] corresponding to Yang-Mills coupled to arbitrary matter. We exploit universal hard/soft factorization to derive an IR finite OPE for the hard gluon operators. This OPE involves logarithms and operators that resemble logarithmic partners of primary operators. We derive an exact all-loop OPE in a limit of the Higgs-regulated planar $\mathcal{N}=4$ super Yang-Mills theory.\] # Bhatkar, Jain ## Perturbative soft photon theorems in de Sitter spacetime \[Links: [arXiv](https://arxiv.org/abs/2212.14637), [PDF](https://arxiv.org/pdf/2212.14637.pdf)\] \[Abstract: We define a perturbative $S$-matrix in a local patch of de Sitter background in the limit when the curvature length scale ($\ell$) is large and study the '[[0009 Soft theorems|soft]]' behavior of the scalar QED amplitudes in de Sitter spacetime in generic dimensions. We obtain the leading and subleading perturbative corrections to flat space soft photon theorems in the large $\ell$ limit, and comment on the universality of these corrections. We compare our results with the electromagnetic memory tails obtained earlier in $d=4$ using classical radiation analysis.\] ## Refs - [[0009 Soft theorems]] # Bhattacharyya, Biswas, Dinda, Kundu ## The zeroth law of black hole thermodynamics in arbitrary higher derivative theories of gravity \[Links: [arXiv](https://arxiv.org/abs/2205.01648), [PDF](https://arxiv.org/pdf/2205.01648.pdf)\] \[Abstract: \] ## Refs - [[0127 Black hole thermodynamics]] # Bhattacharyya, Jethwani, Patra, Roy ## Reparametrization Symmetry of Local Entropy Production on a Dynamical Horizon \[Links: [arXiv](https://arxiv.org/abs/2204.08447), [PDF](https://arxiv.org/pdf/2204.08447.pdf)\] \[Abstract: Recently, it has been shown that for a dynamical black hole in any higher derivative theory of gravity, one could construct a spatial [[0004 Black hole entropy|entropy]] current, characterizing the in/outflow of entropy at every point on the horizon, as long as the dynamics of the amplitude is small enough. However, the construction is very much dependent on how we choose the spatial slicing of the horizon along its null generators. In this note, we have shown that though both the entropy density and the spatial entropy current change non-trivially under a reparametrization of the null generator, the net entropy production, which is given by the 'time' derivative of entropy density plus the divergence of the spatial current is invariant. We have explicitly verified this claim for the particular case of dynamical black holes Einstein-Gauss-Bonnet theory.\] # Biggs, Santos ## Black Tunnels and Hammocks \[Links: [arXiv](https://arxiv.org/abs/2207.14306), [PDF](https://arxiv.org/pdf/2207.14306.pdf)\] \[Abstract: \] ## Summary - [[0231 Bulk solutions for CFTs on non-trivial geometries]] where the boundary is a dS-Schwarzschild (i.e., both event and cosmological horizons) # Biswas, Dhivakar, Kundu ## Non-minimal coupling of scalar and gauge fields with gravity: an entropy current and linearized second law \[Links: [arXiv](https://arxiv.org/abs/2206.04538), [PDF](https://arxiv.org/pdf/2206.04538.pdf)\] \[Abstract: \] ## Summary - [[0005 Black hole second law]] for [[0338 Non-minimally coupled fields]] # Biswas, Semenoff ## Soft Scalars don’t decouple \[Links: [arXiv](https://arxiv.org/abs/2208.05023), [PDF](https://arxiv.org/pdf/2208.05023.pdf)\] \[Abstract: \] ## Summary - *shows* that hard and soft scalars do not decouple ## Theory - $\mathcal{L}=-i \bar{\psi}[\not \partial+m-g \phi] \psi-\frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi-V(\phi)$ # Bittermann, McLoughlin, Rosen ## On Causality Conditions in de Sitter Spacetime \[Links: [arXiv](https://arxiv.org/abs/2212.02559), [PDF](https://arxiv.org/pdf/2212.02559.pdf)\] \[Abstract: We carefully consider the Shapiro time delay due to black holes and shockwaves in de Sitter spacetime and study the implications for causality. We discuss how causality conditions of AdS and flat spacetime can be applied in de Sitter spacetime, using spatial shifts measured on the boundary to define "fastest null geodesics" and taking into account the "stretching" of the de Sitter Penrose diagram. We consider the propagation of a massless spin-1 field with an $RFF$ coupling in a de Sitter shockwave background as an illustrative example. We also briefly discuss connections to the ANEC.\] # Bittleston ## On the associativity of 1-loop corrections to the celestial operator product in gravity \[Links: [arXiv](https://arxiv.org/abs/2211.06417), [PDF](https://arxiv.org/pdf/2211.06417.pdf)\] \[Abstract: The question of whether the holomorphic [[0078 Collinear limit|collinear]] singularities of graviton amplitudes define a consistent chiral algebra has garnered much recent attention. We analyse a version of this question for ==infinitesimal perturbations around the [[0234 Self-dual gravity|self-dual sector of 4d Einstein gravity]]==. The singularities of tree amplitudes in such perturbations do form a consistent chiral algebra, however at 1-loop its operator products are corrected by the effective graviton vertex. We argue that this chiral algebra can be interpreted as the universal holomorphic surface defect in the [[0330 Twistor theory|twistor]] uplift of self-dual gravity, and show that the same correction is induced by an anomalous diagram in the bulk-defect system. The 1-loop holomorphic collinear singularities do not form a consistent chiral algebra. The failure of [[0453 Jacobi identity or associativity of celestial OPE|associativity]] can be traced to the existence of a recently discovered gravitational anomaly on twistor space. It can be restored by coupling to an unusual 4th-order gravitational axion, which cancels the anomaly by a [[0550 Green-Schwarz mechanism|Green-Schwarz mechanism]]. Alternatively, the anomaly vanishes in certain theories of self-dual gravity coupled to matter, including in ==self-dual supergravity==.\] # Blauvelt, Engelbrecht, Hinterbichler ## Shift Symmetries and AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/2211.02055), [PDF](https://arxiv.org/pdf/2211.02055.pdf)\] \[Abstract: \] ## Refs - [[0500 Shift symmetry]] # Blommaert, Iliesiu, Kruthoff ## Alpha states demystified: Towards microscopic models of AdS2 holography \[Links: [arXiv](https://arxiv.org/abs/2203.07384), [PDF](https://arxiv.org/pdf/2203.07384.pdf)\] \[Abstract: \] ## Refs - [[2021#Blommaert, Iliesiu, Kruthoff]] # Blommaert, Kruthoff, Yao ## An integrable road to a perturbative plateau \[Links: [arXiv](https://arxiv.org/abs/2208.13795), [PDF](https://arxiv.org/pdf/2208.13795.pdf)\] \[Abstract: As has been known since the 90s, there is an integrable structure underlying two-dimensional gravity theories. Recently, two-dimensional gravity theories have regained an enormous amount of attention, but now in relation with quantum chaos - superficially nothing like integrability. In this paper, we return to the roots and exploit the integrable structure underlying dilaton gravity theories to study a late time, large e^{S_\text{BH}} double scaled limit of the spectral form factor. In this limit, a novel cancellation due to the integrable structure ensures that at each genus g the spectral form factor grows like T^{2g+1}, and that the sum over genera converges, realising a perturbative approach to the late-time plateau. Along the way, we clarify various aspects of this integrable structure. In particular, we explain the central role played by ribbon graphs, we discuss intersection theory, and we explain what the relations with dilaton gravity and matrix models are from a more modern holographic perspective.\] # Bousso, Penington ## Entanglement Wedges for Gravitating Regions \[Links: [arXiv](https://arxiv.org/abs/2208.04993), [PDF](https://arxiv.org/pdf/2208.04993.pdf)\] \[Abstract: \] # Bousso, Shahbazi-Moghaddam (Jan) ## Singularity from entropy \[Links: [arXiv](https://arxiv.org/abs/2201.11132), [PDF](https://arxiv.org/pdf/2201.11132.pdf)\] \[Abstract: \] ## Refs - later [[#Bousso, Shahbazi-Moghaddam (Jun)]] ## Summary - *assuming* [[0171 Covariant entropy bound|Bousso bound]], *obtains* a [[0225 Singularity theorems|singularity theorem]] ## Key idea ![[BoussoShahbazi-Moghaddam2022_fig1.png|400]] In (a), entropy on red region must equal to entropy on blue region, so Bousso bound which bounds the entropy on L says B cannot be hyperentropic. Then if B is hyperentropic, L should close off at a singularity, like in (b). ## Assumptions 1. null curvature condition 2. [[0171 Covariant entropy bound|Bousso bound]] ## Comments - #raphaelbousso says #aronwall 's argument works only for two-sided BH and does not work for BH formed from collapse due to lack of *any* nice slice in the latter case # Bousso, Shahbazi-Moghaddam (Jun) ## Quantum singularities \[Links: [arXiv](https://arxiv.org/abs/2206.07001), [PDF](https://arxiv.org/pdf/2206.07001.pdf)\] \[Abstract: \] # Brown, Gowdy, Spence ## Celestial Twistor Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2212.01327), [PDF](https://arxiv.org/pdf/2212.01327.pdf)\] \[Abstract: We show how to formulate [[0010 Celestial holography|celestial]] [[0330 Twistor theory|twistor]] amplitudes in Yang-Mills (YM) and gravity. This is based on a refined holographic correspondence between the half-Fourier transform in split signature and the [[0412 Light transform|light transform]] in the boundary Lorentzian CFT. The resulting celestial twistor amplitudes are then equivalent to light transformed correlators on the [[0250 Celestial torus|celestial torus]]. Using an [[0506 Ambidextrous basis|ambidextrous basis]] of twistor and dual twistor variables, we derive formulae for the three and four point YM and gravity amplitudes. The four point amplitudes take a particularly simple form in terms of elementary functions, with a remarkable similarity between the YM and gravity expressions. We find celestial twistor [[0058 BCFW|BCFW]] recursion relations and show how these may be used to generate the four point YM amplitude, highlighting features that should enable the calculation of higher multiplicity light transformed correlators. Throughout our calculations we utilise the unique properties of the boundary structure of split signature, and in order to properly motivate and highlight these properties we first develop our methodology in Lorentzian signature. This also allows us to prove a correspondence between Fourier transforms and [[0039 Shadow transform|shadow transforms]].\] ## Refs - simultaneous release [[2022#Jorge-Diaz, Pasterski, Sharma]] # Bu, Casali ## The 4d/2d correspondence in twistor space and holomorphic Wilson lines \[Links: [arXiv](https://arxiv.org/abs/2208.06334), [PDF](https://arxiv.org/pdf/2208.06334.pdf)\] \[Abstract: We give an explicit realization of the 4d local operator / 2d conformal block correspondence of Costello and Paquette in the case of gauge theories. This is accomplished by lifting the 4d local operators to non-local operators in [[0330 Twistor theory|twistor space]] using a holomorphic generalization of the Wilson line. This procedure automatically constructs the 2d conformal blocks corresponding to the local operator. We interpret this lifting as effectively integrating out the 2d degrees of freedom living on the defect. We present some 2d chiral CFT representations of the defect algebra whose correlators reproduce the conformal blocks obtained by the lifting procedure.\] # Bu, Heuveline, Skinner ## Moyal deformations, $W_{1+\infty}$ and celestial holography \[Links: [arXiv](https://arxiv.org/abs/2208.13750), [PDF](https://arxiv.org/pdf/2208.13750.pdf)\] \[Abstract: We consider the [[0513 Moyal deformation|Moyal deformation]] of [[0234 Self-dual gravity|self-dual gravity]]. In the [[0148 Conformal basis|conformal primary basis]], holomorphic [[0078 Collinear limit|collinear limits]] of the amplitudes of this theory show that it enjoys a perturbatively exact symmetry algebra $LW_\wedge$ that generalises $Lw_\wedge$, the loop algebra of the wedge algebra of $w_{1+\infty}$, which appears in self-dual gravity.\] ## Refs - [[0328 w(1+infinity)]] - [[0358 W(1+infinity)]] - [[0513 Moyal deformation]] # Buchbinder, Stone ## Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins \[Links: [arXiv](https://arxiv.org/abs/2210.13135), [PDF](https://arxiv.org/pdf/2210.13135)\] \[Abstract: We analyse the general structure of the three-point functions involving conserved bosonic and fermionic higher-spin currents in [[0634 3d CFT|three-dimensional conformal field theory]]. Using the constraints of [[0028 Conformal symmetry|conformal symmetry]] and conservation equations, we use a computational formalism to analyse the general structure of $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$, where $J^{}_{s_{1}}$, $J'_{s_{2}}$ and $J''_{s_{3}}$ are conserved currents with spins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). The calculations are completely automated for any chosen spins and are limited only by computer power. We find that the correlation function is in general fixed up to two independent even structures, and one odd structure, subject to a set of triangle inequalities. We also analyse the structure of three-point functions involving [[0621 Higher-spin conserved currents in CFT|higher-spin currents]] and fundamental scalars and spinors.\] # Bzowski ## Wormholes, geons, and the illusion of the tensor product \[Links: [arXiv](https://arxiv.org/abs/2212.10652), [PDF](https://arxiv.org/pdf/2212.10652.pdf)\] \[Abstract: In this paper I argue that the Hilbert space of states of a holographic, traversable wormhole does not [[0514 Lorentzian factorisation problem|factorize]] into the tensor product of the boundary Hilbert spaces. After presenting the general argument I analyze two examples: the scalar sectors of the BTZ geon and the AdS$_2$ eternal wormhole. Utilizing real-time holography I derive the Hilbert spaces, identify the dual states and evaluate correlation functions. I show that the number of peculiarities associated with the wormhole and black hole physics emerges once the factorization is *a priori* assumed. This includes null states and null operators, highly entangled vacuum states and the cross-boundary interactions all emerging as avatars of non-factorization.\] ## Refs - [[0514 Lorentzian factorisation problem]] # Cao, Cheng, Swingle ## Large $N$ Matrix Quantum Mechanics as a Quantum Memory \[Links: [arXiv](https://arxiv.org/abs/2211.08448), [PDF](https://arxiv.org/pdf/2211.08448.pdf)\] \[Abstract: In this paper, we explore the possibility of building a [[0580 Quantum memory|quantum memory]] that is robust to thermal noise using large $N$ matrix quantum mechanics models. First, we investigate the gauged $SU(N)$ matrix harmonic oscillator and different ways to encode quantum information in it. By calculating the [[0300 Mutual information|mutual information]] between the system and a reference which purifies the encoded information, we identify a transition temperature, $T_c$, below which the encoded quantum information is protected from thermal noise for a memory time scaling as $N^2$. Conversely, for temperatures higher than $T_c$, the information is quickly destroyed by thermal noise. Second, we relax the requirement of gauge invariance and study a matrix harmonic oscillator model with only global symmetry. Finally, we further relax even the symmetry requirement and propose a model that consists of a large number $N^2$ of qubits, with interactions derived from an approximate $SU(N)$ symmetry. In both ungauged models, we find that the effects of gauging can be mimicked using an energy penalty to give a similar result for the memory time. The final qubit model also has the potential to be realized in the laboratory.\] ## Main theorem If a large $N$ system has a sparse low energy spectrum, couples to the bath uniformly, and is an approximately QEC code, then it has a memory time polynomial to $N$ at low enough temperatures. ## Models - full gauged (sec. 3) - first model: non-local logical operations required; $N^2$ life time at even high temperatures - second model: local; a large coupling between gauged oscillators; $N^2$ at low temperatures - (sec. 4): gauge constraint imposed only as an energy cost - (sec. 5): ungauged, and even global symmetry is approximate # Chandra, Collier, Hartman, Maloney ## Semiclassical 3D gravity as an average of large-$c$ CFTs \[Links: [arXiv](https://arxiv.org/abs/2203.06511), [PDF](https://arxiv.org/pdf/2203.06511.pdf); Talks: [Maloney](https://youtu.be/sCQot49-olw?feature=shared), [Collier](https://www.on.kitp.ucsb.edu/online/joint98/collier/)\] \[Abstract: A two-dimensional CFT dual to a semiclassical theory of gravity in three dimensions must have a large [[0033 Central charge|central charge]] $c$ and a sparse low energy spectrum. This constrains the [[0030 Operator product expansion|OPE]] coefficients and density of states of the CFT via the [[0036 Conformal bootstrap|conformal bootstrap]]. We define an [[0154 Ensemble averaging|ensemble]] of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce semiclassical [[0002 3D gravity|3D gravity]]. We analyze a wide variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell action of gravity agrees with the [[0154 Ensemble averaging|ensemble]]-averaged CFT at large $c$. The one-loop corrections also match in the cases where they have been computed. We also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger.\] ## Refs - [[0040 Eigenstate thermalisation hypothesis]] - [[0002 3D gravity]] ## Gravitational setup - 3D gravity with massive particles (defects) and multiple boundaries # Chandra, Hartman ## Coarse graining pure states in AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/2206.03414), [PDF](https://arxiv.org/pdf/2206.03414.pdf)\] \[Abstract: We construct new [[0278 Euclidean wormholes|Euclidean wormhole]] solutions in AdS(d+1) and discuss their role in UV-complete theories, without ensemble averaging. The geometries are interpreted as overlaps of GHZ-like entangled states, which arise naturally from coarse graining the density matrix of a pure state in the dual CFT. In several examples, including thin-shell collapsing black holes and pure black holes with an end-of-the-world brane behind the horizon, the coarse-graining map is found explicitly in CFT terms, and used to define a coarse-grained entropy that is equal to one quarter the area of a time-symmetric apparent horizon. Wormholes are used to derive the coarse-graining map and to study statistical properties of the quantum state. This reproduces aspects of the West Coast model of 2D gravity and the large-c ensemble of [[0002 3D gravity|3D gravity]], including a Page curve, in a higher-dimensional context with generic matter fields.\] ## Summary - constructs multi-boundary Euclidean wormholes in AdS in two models: - Einstein + matter - Einstein + EOW - interprets them as GHZ states, obtained from coarse-graining pure states - uses a [[2013#Lewkowycz, Maldacena]] procedure to obtain a [[0460 Coarse grained entropy]] ## The Euclidean solution - Euclidean AdS with multiple boundaries - no deformation to the CFT but with matter insertions ## The quantity - diagonal entropy [[BarankovPolkovnikov2008]] # Chandrasekaran, Longo, Penington, Witten ## An Algebra of Observables for de Sitter Space \[Links: [arXiv](https://arxiv.org/abs/2206.10780), [PDF](https://arxiv.org/pdf/2206.10780.pdf)\] \[Abstract: We describe an algebra of observables for a static patch in de Sitter space, with operators gravitationally dressed to the worldline of an observer. The algebra is a [[0415 Von Neumann algebra|von Neumann algebra]] of Type II$_1$. There is a natural notion of entropy for a state of such an algebra. There is a maximum entropy state, which corresponds to empty de Sitter space, and the entropy of any semiclassical state of the Type II$_1$ algebras agrees, up to an additive constant independent of the state, with the expected generalized entropy $S_{\text{gen}}=(A/4G_N)+S_{\text{out}}$. An arbitrary additive constant is present because of the renormalization that is involved in defining entropy for a Type II$_1$ algebra.\] # Chandrasekaran, Penington, Witten ## Large $N$ algebras and generalized entropy \[Links: [arXiv](https://arxiv.org/abs/2209.10454), [PDF](https://arxiv.org/pdf/2209.10454.pdf)\] \[Abstract: We construct a Type II$_\infty$ [[0415 Von Neumann algebra|von Neumann algebra]] that describes the large $N$ physics of single-trace operators in [[0001 AdS-CFT|AdS/CFT]] in the [[0462 Microcanonical ensemble|microcanonical ensemble]], where there is no need to include perturbative $1/N$ corrections. Using only the extrapolate dictionary, we show that the entropy of semiclassical states on this algebra is holographically dual to the generalized entropy of the black hole bifurcation surface. From a boundary perspective, this constitutes a derivation of a special case of the [[0212 Quantum extremal surface|QES]] prescription without any use of Euclidean gravity or replicas; from a purely bulk perspective, it is a derivation of the quantum-corrected Bekenstein-Hawking formula as the entropy of an explicit algebra in the $G \to 0$ limit of Lorentzian effective field theory quantum gravity. In a limit where a black hole is first allowed to equilibrate and then is later potentially re-excited, we show that the [[0082 Generalised second law|generalized second law]] is a direct consequence of the monotonicity of the entropy of algebras under trace-preserving inclusions. Finally, by considering excitations that are separated by more than a scrambling time we construct a "free product" von Neumann algebra that describes the semiclassical physics of long wormholes supported by [[0117 Shockwave|shocks]]. We compute [[0293 Renyi entropy|Rényi entropies]] for this algebra and show that they are equal to a sum over saddles associated to quantum extremal surfaces in the wormhole. Surprisingly, however, the saddles associated to "bulge" quantum extremal surfaces contribute with a negative sign.\] ## Summary - working in [[0462 Microcanonical ensemble|microcanonical ensemble]] where energy fluctuations are $O(1)$ # Chang, Ma ## Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2212.07025), [PDF](https://arxiv.org/pdf/2212.07025.pdf)\] \[Abstract: We study three-point celestial amplitudes in Minkowski space for massless scalars, photons, gluons, and gravitons. The corresponding scattering amplitudes in the plane wave basis vanish for generic momenta due to momentum conservation. However, the delta function for the momentum conservation has support in the soft and [[0078 Collinear limit|collinear]] regions, and contributes to the [[0079 Mellin transform|Mellin]] and [[0039 Shadow transform|shadow]] integrals that give non-zero celestial amplitudes. We show that the amplitudes with the incoming (outgoing) particles in the (shadow) conformal basis take the standard form of correlators in two-dimensional conformal field theory. In particular, the three-point celestial gluon amplitudes take the form of a three-point function of a spin-one current with two spin-one primary operators, which strongly supports the relation between soft spinning particles and conserved currents. Moreover, the three-point celestial amplitudes of one graviton and two massless scalars take the form of a correlation function involving a primary operator of conformal weight one and spin two, whose level-one descendent is the supertranslation current.\] # Chapman, Galante, Harris, Sheorey, Vegh ## Complex geodesics in de Sitter space \[Links: [arXiv](https://arxiv.org/abs/2212.01398), [PDF](https://arxiv.org/pdf/2212.01398.pdf)\] \[Abstract: The [[0103 Two-point functions|two-point function]] of a free massive scalar field on a fixed background can be evaluated in the large mass limit by using a semiclassical geodesic approximation. In de Sitter space, however, this poses a puzzle. Certain spacelike separated points are not connected by real geodesics despite the corresponding two-point function in the Bunch-Davies state being non-vanishing. We resolve this puzzle by considering complex geodesics after analytically continuing to the sphere. We compute one-loop corrections to the correlator and discuss the implications of our results to [[0251 dS-CFT|de Sitter holography]].\] ## Refs - simultaneous release [[2022#Aalsma, Faruk, van der Schaar, Visser, de Witte]] # Charalambous, Dubovsky, Ivanov ## Love symmetry \[Links: [arXiv](https://arxiv.org/abs/2209.02091), [PDF](https://arxiv.org/pdf/2209.02091.pdf)\] \[Abstract: Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (''Love'') $SL(2,\mathbb{R})$ symmetry in the suitably defined near zone approximation. We present a detailed study of this symmetry and show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the $SL(2,\mathbb{R})$ representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight $SL\left(2,\mathbb{R}\right)$ representations. It is this highest weight property that forces the static [[0581 Tidal Love numbers|Love numbers]] to vanish. We find that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. This relation is simplest for extremal charged spherically symmetric (Reissner-Nordström) solutions, where the Love symmetry exactly reduces to the isometry of the near horizon AdS$_2$ throat. For rotating (Kerr-Newman) black holes one is lead to consider an infinite-dimensional $SL\left(2,\mathbb{R}\right)\ltimes \hat U(1)_{\mathcal{V}}$ extension of the Love symmetry. It contains three physically distinct subalgebras: the Love algebra, the Starobinsky near zone algebra, and the near horizon algebra that becomes the Bardeen-Horowitz isometry in the extremal limit. We also discuss other aspects of the Love symmetry, such as the geometric meaning of its generators for spin weighted fields, connection to the no-hair theorems, non-renormalization of Love numbers, its relation to (non-extremal) [[0520 Kerr-CFT correspondence|Kerr/CFT correspondence]] and prospects of its existence in modified theories of gravity.\] # Chen ## Spectral form factor for free large $N$ gauge theory and strings \[Links: [arXiv](https://arxiv.org/abs/2202.04741), [PDF](https://arxiv.org/pdf/2202.04741.pdf)\] \[Abstract: We investigate the [[0062 Spectral form factor|spectral form factor]] in two different systems, free large $N$ gauge theories and highly excited string gas. In both cases, after a rapid decay of the spectral form factor at early time, new contributions come in, preventing the spectral form factor from ever becoming exponentially small. We consider $U(N)$ gauge theories with only adjoint matter and compute the spectral form factor using a matrix integral of the thermal holonomy $U$. The new saddles differ from the early time saddle by preserving certain subgroups of the center symmetry. For a gas of strings, the short time decay of the spectral form factor is governed by the continuous [[0439 Hagedorn transition|Hagedorn]] density of states, which can be associated to the thermal winding mode with winding number $\pm 1$. We show that the rise of the spectral form factor comes from other winding modes that also carry momentum along the time direction. We speculate on the existence of a family of classical solutions for these string modes, similar to the [[0323 Horowitz-Polchinski solution|Horowitz-Polchinski solution]]. We review a similar problem for black holes. In particular, we examine the Kontsevich-Segal criterion on complex black holes that contribute to the spectral form factor. In the canonical ensemble quantity $Z(\beta+it)$, the black hole becomes unallowed at $t\sim \mathcal{O}(\beta)$. A way to avoid this is to consider the microcanonical ensemble, where the black hole stays allowable.\] ## Summary - computes [[0062 Spectral form factor|spectral form factor]] for two systems: ==free large N gauge theories== and ==highly excited string gas== - uses **geometry** to do the computation (so that the discreteness is not manifest) - finds new geometries to prevent $\left|Y_{E, \Delta}(t)\right|^{2}$ from becoming exponentially small - speculates on BHs ## What are "geometries" - for large $N$ gauge theories: - different eigenvalue distributions of the thermal holonomy - for string gass: - [[0323 Horowitz-Polchinski solution|Horowitz-Polchinski solution]] ## String gas - decaying contribution: [[0323 Horowitz-Polchinski solution]] - new contribution: winding modes that carry some other quantum numbers - free string partition function at complex temperature (computed in [[DeoJainTan1989]][](https://www.sciencedirect.com/science/article/abs/pii/0370269389900245?via%3Dihub)) ## Black holes - for the canonical quantity $Z(\beta+it)$, the BH is always subdominant (against thermal AdS) before it is unallowed. So there is no problem. - for the microcanonical quantity $\left|Y_{E, \Delta}(t)\right|^{2}$, the thermal AdS does not contribute at high $E$, and the BH is allowable even for large $t$ - there is no replacement saddles at large $t$, so there is a puzzle (as the spectral form factor continues to drop) # Cheung, Helset, Parra-Martinez ## Geometry-Kinematics Duality \[Links: [arXiv](https://arxiv.org/abs/2111.03045), [PDF](https://arxiv.org/pdf/2111.03045.pdf)\] \[Abstract: \] ## Summary - generalises [[0152 Colour-kinematics duality]] - write [[0009 Soft theorems]] as a geometric covariant derivative # Costello, Paquette (Jan) ## Celestial holography meets twisted holography: 4d amplitudes from chiral correlators \[Links: [arXiv](https://arxiv.org/abs/2201.02595), [PDF](https://arxiv.org/pdf/2201.02595.pdf)\] \[Abstract: We propose a new program for computing a certain integrand of scattering amplitudes of four-dimensional gauge theories which we call the form factor integrand, starting from 6d holomorphic theories on [[0330 Twistor theory|twistor space]]. We show that the form factor integrands can be expressed as sums of products of 1.) correlators of a 2d chiral algebra, related to the algebra of asymptotic symmetries uncovered recently in the celestial holography program, and 2.) [[0030 Operator product expansion|OPE]] coefficients of a 4d non-unitary CFT. We prove that [[0031 Conformal block|conformal blocks]] of the chiral algebras are in one-to-one correspondence with local operators in 4d. We use this bijection to recover the [[0072 Parke-Taylor n-gluon tree amplitude|Parke-Taylor formula]], the [[0352 CSW relations|CSW formula]], and certain one-loop scattering amplitudes. Along the way, we explain and derive various aspects of celestial holography, incorporating techniques from the [[0130 Twisted holography|twisted holography]] program such as [[0510 Koszul duality|Koszul duality]]. This perspective allows us to easily and efficiently recover the infinite-dimensional chiral algebras of asymptotic symmetries recently extracted from scattering amplitudes of massless gluons and gravitons in the [[0010 Celestial holography|celestial]] basis. We also compute some simple one-loop corrections to the chiral algebras and derive the three-dimensional bulk theories for which these 2d algebras furnish an algebra of boundary local operators.\] ## Refs - [[0384 4d-2d twistorial correspondence]] ## Concrete example - a concrete example that comes from a local theory on twistor space: [[0136 Self-dual Yang-Mills|SDYM]] with $SU(3)$ group with the axion field to cancel the anomaly - anomaly free => all correlation functions and [[0030 Operator product expansion|OPE]] coefficients are rational functions - then deform by $g_{Y M}^2 \operatorname{tr}\left(B^2\right)$ - perturbatively equivalent to [[0071 Yang-Mills|YM]] + axion field # Costello, Paquette (Apr) ## On the associativity of one-loop corrections to the celestial OPE \[Links: [arXiv](https://arxiv.org/abs/2204.05301), [PDF](https://arxiv.org/pdf/2204.05301.pdf)\] \[Abstract: There has been recent interest in the question of whether QCD [[0078 Collinear limit|collinear singularities]] can be viewed as the [[0030 Operator product expansion|OPE]] of a two-dimensional CFT. We analyze a version of this question for the self-dual limit of pure gauge theory (incorporating states of both helicities). We show that the known one-loop collinear singulaties do not form an [[0453 Jacobi identity or associativity of celestial OPE|associative]] chiral algebra. The failure of associativity can be traced to a novel gauge anomaly on [[0330 Twistor theory|twistor space]]. We find that associativity can be restored for certain gauge groups if we introduce an unusual axion, which cancels the twistor space anomaly by a [[0550 Green-Schwarz mechanism|Green-Schwarz mechanism]]. Alternatively, associativity can be restored for some gauge groups with carefully chosen matter.\] # Costello, Paquette, Sharma ## Top-down holography in an asymptotically flat spacetime \[Links: [arXiv](https://arxiv.org/abs/2208.14233), [PDF](https://arxiv.org/pdf/2208.14233.pdf)\] \[Abstract: We propose a holographic duality for a four dimensional WZW model with target manifold $\mathrm{SO}(8)$, coupled to scalar-flat Kähler gravity on an asymptotically flat, four dimensional background known as the Burns metric. The holographic dual is a two dimensional chiral algebra built out of gauged beta-gamma systems with $\mathrm{SO}(8)$ flavor. We test the duality by matching two-point correlators of soft gluon currents with two-point gluon amplitudes, and their leading [[0030 Operator product expansion|OPE coefficients]] with [[0078 Collinear limit|collinear limits]] of three-point gluon amplitudes.\] # Cotler, Jensen ## A precision test of averaging in AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/2205.12968), [PDF](https://arxiv.org/pdf/2205.12968.pdf)\] \[Abstract: We reconsider the role of wormholes in the [[0001 AdS-CFT|AdS/CFT]] correspondence. We focus on Euclidean wormholes that connect two asymptotically AdS or hyperbolic regions with $\mathbb{S}^1 \times \mathbb{S}^{d-1}$ boundary. There is no solution to Einstein's equations of this sort, as the wormholes possess a modulus that runs to infinity. To find on-shell wormholes we must stabilize this modulus, which we can do by fixing the total energy on the two boundaries. Such a wormhole gives the saddle point approximation to a non-standard problem in quantum gravity, where we fix two asymptotic boundaries and constrain the common energy. Crucially the dual quantity does not factorize even when the bulk is dual to a single CFT, on account of the fixed energy constraint. From this quantity we extract a smeared version of the microcanonical [[0062 Spectral form factor|spectral form factor]]. For a [[0008 Quantum chaos|chaotic]] theory this quantity is self-averaging, i.e. well-approximated by averaging over energy windows, or over coupling constants. We go on to give a precision test involving the microcanonical spectral form factor where the two replicas have slightly different coupling constants. In chaotic theories this form factor is known to smoothly decay at a rate universally predicted in terms of one replica physics, provided that there is an average either over a window or over couplings. We compute the expected decay rate for holographic theories, and the form factor from a wormhole, and the two exactly agree for a wide range of two-derivative effective field theories in AdS. This gives a precision test of averaging in [[0001 AdS-CFT|AdS/CFT]]. Our results interpret a number of confusing facts about wormholes and [[0249 Factorisation problem|factorization]] in AdS and suggest that we should regard gravitational effective field theory as a mesoscopic description, analogous to semiclassical mesoscopic descriptions of quantum chaotic systems.\] ## Refs - [[0249 Factorisation problem]] - [[0154 Ensemble averaging]] - [[0062 Spectral form factor]] # Cotler, Strominger ## The Universe as a Quantum Encoder \[Links: [arXiv](https://arxiv.org/abs/2201.11658), [PDF](https://arxiv.org/pdf/2201.11658.pdf)\] \[Abstract: \] # David, Kumar ## Thermal one point functions, large $d$ and interior geometry of black holes \[Links: [arXiv](https://arxiv.org/abs/2212.07758), [PDF](https://arxiv.org/pdf/2212.07758.pdf)\] \[Abstract: We study thermal one point functions of massive scalars in AdS$_{d+1}$ black holes. These are induced by coupling the scalar to either the Weyl tensor squared or the [[0425 Gauss-Bonnet gravity|Gauss-Bonnet]] term. [[2020#Grinberg, Maldacena|Grinberg and Maldacena]] argued that the one point functions sourced by the Weyl tensor exponentiate in the limit of large scalar masses and they contain information of the black hole geometry behind the horizon. We observe that the one point functions behave identically in this limit for either of the couplings mentioned earlier. We show that in an appropriate large $d$ limit, the one point function for the charged black hole in AdS$_{d+1}$ can be obtained exactly. These black holes in general contain an inner horizon. We show that the one point function exponentiates and contains the information of both the proper time between the outer horizon to the inner horizon as well as the proper length from the inner horizon to the singularity. We also show that Gauss-Bonnet coupling induced one point functions in AdS$_{d+1}$ black holes with hyperbolic horizons behave as anticipated by Grinberg-Maldacena. Finally, we study the one point functions in the background of rotating [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black holes induced by the cubic coupling of scalars.\] # Davies, Reall ## Dynamical Black Hole Entropy in Effective Field Theory \[Links: [arXiv](https://arxiv.org/abs/2212.09777), [PDF](https://arxiv.org/pdf/2212.09777.pdf)\] \[Abstract: In recent work, [[2022#Hollands, Kovacs, Reall|Hollands, Kovács and Reall]] have built on previous work of [[2015#Wall (Essay)|Wall]] to provide a definition of dynamical [[0004 Black hole entropy|black hole entropy]] for gravitational effective field theories (EFTs). This entropy satisfies a [[0005 Black hole second law|second law of black hole mechanics]] to quadratic order in perturbations around a stationary black hole. We determine the explicit form of this entropy for the EFT of 4d vacuum gravity including terms in the action with up to 6 derivatives. An open question concerns the gauge invariance of this definition of black hole entropy. We show that gauge invariance holds for the EFT of vacuum gravity with up to 6 derivatives but demonstrate that it can fail when 8 derivative terms are included. We determine an entropy for [[0425 Gauss-Bonnet gravity|Einstein-Gauss-Bonnet]] theory by treating it as an EFT with vanishing 6 derivative terms.\] ## Summary - examples with non-trivial HKR terms - need 6-derivatives in the action - gauge invariance of HKR - 6-derivatives: indeed gauge-invariant - 8-derivatives: *not* gauge-invariant - [[0425 Gauss-Bonnet gravity|GB gravity]] as an example ## Results for GB - it can be considered as a self-contained theory rather than an $N=4$ truncation of an EFT, so it makes sense to calculate to higher orders in the length scale $l$ - at $O(l^2$): agrees with Wall - at $O(l^4)$ (i.e. $K^4$): see eq.52 - only powers of four $Ks, no derivatives of $K$ such as $\partial_z\partial_\bar{z}K$ - reduces to 0 when $d=4$ (GB being topological): using properties of 2-by-2 matrices (footnote 12) - at $O(l^6)$: not displayed, very lengthy, non-gauge invariant - n.b. still at most four $Ks (since $K\bar K\sim \epsilon$, but they will have further derivatives) # Doi, Harper, Mollabashi, Takayanagi, Taki ## Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy \[Links: [arXiv](https://arxiv.org/abs/2210.09457), [PDF](https://arxiv.org/pdf/2210.09457)\] \[Abstract: We study [[0007 RT surface|holographic entanglement entropy]] in dS/CFT and introduce [[0606 Timelike entanglement|time-like entanglement entropy]] in CFTs. Both of them take complex values in general and are related with each other via an analytical continuation. We argue that they are correctly understood as [[0052 Pseudo-entropy|pseudo entropy]]. We find that the imaginary part of pseudo entropy implies an emergence of time in dS/CFT.\] # Dong, Wang, Weng, Wu ## A tale of two butterflies: an exact equivalence in higher-derivative gravity \[Links: [arXiv](https://arxiv.org/abs/2203.06189), [pdf](https://arxiv.org/pdf/2203.06189.pdf), [JHEP](https://link.springer.com/article/10.1007/JHEP10(2022)009)\] \[Abstract: We prove the equivalence of two holographic computations of the [[0167 Butterfly velocity|butterfly velocity]] in [[0006 Higher-derivative gravity|higher-derivative theories]] with Lagrangian built from arbitrary contractions of curvature tensors. The butterfly velocity characterizes the speed at which local perturbations grow in [[0008 Quantum chaos|chaotic]] many-body systems and can be extracted from the [[0482 Out-of-time-order correlator|out-of-time-order correlator]]. This leads to a holographic computation in which the butterfly velocity is determined from a localized shockwave on the horizon of a dual black hole. A second holographic computation uses [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]] to define a notion of operator size and determines the butterfly velocity from certain extremal surfaces. By direct computation, we show that these two butterfly velocities match precisely in the aforementioned class of gravitational theories. We also present evidence showing that this equivalence holds in all gravitational theories. Along the way, we prove a number of general results on [[0117 Shockwave|shockwave]] spacetimes.\] ## Introduction The [[0167 Butterfly velocity|butterfly velocity]], whose name comes from the butterfly effect, is a quantity that characteristic how chaotic a system is. The [butterfly effect](https://en.wikipedia.org/wiki/Butterfly_effect) is the phenomenon that, in certain systems, i.e., [[0008 Quantum chaos|chaotic systems]], a small change in the initial conditions leads to drastic variations in the outcome. In [[0001 AdS-CFT|holography]], there are various ways to compute the butterfly velocity for a thermal state on the boundary from bulk knowledge. In this paper we study two of them: via [[0007 RT surface|entanglement surface]] and via [[0117 Shockwave|shockwaves]]. It turns out that the butterfly velocity depends on the bulk theory non-trivially. This means that both methods will receive corrections in the presence of [[0006 Higher-derivative gravity|higher-derivative]] terms in the Lagrangian. We show via direct computations that the corrections are the same for $f$(Riemann) gravity with these two methods, thereby suggesting that the two methods are equivalent in general. ## Significance One way to understand the equivalence is that there is some non-trivial connection between [[0145 Generalised area|holographic entanglement]] and bulk gravitational dynamics. Such a connection is not unheard of: in what is known as the "[[0302 Gravity from entanglement|Gravity from Entanglement]]" program, the bulk equation of motion is supposedly contained in the [[0145 Generalised area|holographic entropy]] formula. This is a manifestation of that, but it remains an open question to show how the connection comes about more generally. The success of the entanglement wedge method in computing the butterfly velocity also serves as a good quantitative check for [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]], manifested here by the capability of the boundary region to capture the falling operator in the bulk. ## Follow-ups - a proposal in the discussion about comparing with a third butterfly velocity, defined via [[0179 Pole skipping|pole skipping]], is studied in [[2022#Wang, Wang]] # Donnay, Esmaeili, Heissenberg ## $p$-Forms on the Celestial Sphere \[Links: [arXiv](https://arxiv.org/abs/2212.03060), [PDF](https://arxiv.org/pdf/2212.03060.pdf)\] \[Abstract: We construct a basis of [[0148 Conformal basis|conformal primary wavefunctions]] (CPWs) for $p$-form fields in any dimension, calculating their scalar products and exhibiting the change of basis between conventional plane wave and CPW mode expansions. We also perform the analysis of the associated [[0039 Shadow transform|shadow transforms]]. For each family of $p$-form CPWs, we observe the existence of pure gauge wavefunctions of conformal dimension $\Delta = p$, while shadow $p$-forms of this weight are only pure gauge in the critical spacetime dimension value $D = 2p + 2$. We then provide a systematic technique to obtain the large-$r$ asymptotic limit near $\mathscr{I}$ based on the method of regions, which naturally takes into account the presence of both ordinary and contact terms on the [[0022 Celestial sphere|celestial sphere]]. In $D = 4$, this allows us to reformulate in a conformal primary language the links between scalars and dual two-forms.\] ## Refs - [[0148 Conformal basis]] # Donnay, Pasterski, Puhm ## Goldilocks Modes and the Three Scattering Bases \[Links: [arXiv](https://arxiv.org/abs/2202.11127), [PDF](https://arxiv.org/pdf/2202.11127.pdf)\] \[Abstract: We consider massless scattering from the point of view of the position, momentum, and celestial bases. In these three languages different properties of physical processes become manifest or obscured. Within the soft sector, they highlight distinct aspects of the infrared triangle: quantum field theory soft theorems arise in the limit of vanishing energy $\omega$, [[0287 Memory effect|memory effects]] are described via shifts of fields at the boundary along the null time coordinate u, and celestial symmetry algebras are realized via currents that appear at special values of the conformal dimension $\Delta$. We focus on the subleading [[0009 Soft theorems|soft theorems]] at $\Delta=1-s$ for gauge theory ($s=1$) and gravity ($s=2$) and explore how to translate the infrared triangle to the celestial basis. We resolve an existing tension between proposed overleading gauge transformations as examined in the position basis and the 'Goldstone-like' modes where we expect celestial symmetry generators to appear. In the process we elucidate various order-of-limits issues implicit in the celestial formalism. We then generalize our construction to the tower of $w_{1+\infty}$ generators in celestial CFT, which probe further subleading-in-$\omega$ soft behavior and are related to subleading-in-$r$ vacuum transitions that measure higher multipole moments of scatterers. In the end we see that the celestial basis is 'just right' for identifying the symmetry structure.\] ## Refs - [[0328 w(1+infinity)]] - [[0010 Celestial holography]] # Donnelly, Freidel, Moosavian, Speranza ## Matrix Quantization of Gravitational Edge Modes \[Links: [arXiv](https://arxiv.org/abs/2212.09120), [PDF](https://arxiv.org/pdf/2212.09120.pdf)\] \[Abstract: Gravitational subsystems with boundaries carry the action of an infinite-dimensional symmetry algebra, with potentially profound implications for the quantum theory of gravity. We initiate an investigation into the quantization of this corner symmetry algebra for the phase space of gravity localized to a region bounded by a 2-dimensional sphere. Starting with the observation that the algebra $\mathfrak{sdiff}(S^2)$ of area-preserving diffeomorphisms of the 2-sphere admits a deformation to the finite-dimensional algebra $\mathfrak{su}(N)$, we derive novel finite-$N$ deformations for two important subalgebras of the gravitational corner symmetry algebra. Specifically, we find that the area-preserving hydrodynamical algebra $\mathfrak{sdiff}(S^2)\oplus_{\mathcal{L}}\mathbb{R}^{S^2}$ arises as the large-$N$ limit of $\mathfrak{sl}(N,\mathbb C)\oplus\mathbb{R}$ and that the full area-preserving corner symmetry algebra $\mathfrak{sdiff}(S^2)\oplus_{\mathcal{L}}\mathfrak{sl}(2,\mathbb{R})^{S^2}$ is the large-$N$ limit of the pseudo-unitary group $\mathfrak{su}(N,N)$. We find matching conditions for the Casimir elements of the deformed and continuum algebras and show how these determine the value of the deformation parameter $N$ as well as the representation of the deformed algebra associated with a quantization of the local gravitational phase space. Additionally, we present a number of novel results related to the various algebras appearing, including a detailed analysis of the asymptotic expansion of the $\mathfrak{su}(N)$ structure constants, as well as an explicit computation of the full $\mathfrak{diff}(S^2)$ structure constants in the spherical harmonic basis. A consequence of our work is the definition of an area operator which is compatible with the deformation of the area-preserving corner symmetry at finite $N$.\] ## Refs - [[0044 Extended phase space]] # Eberhardt ## Off-shell Partition Functions in 3d Gravity \[Links: [arXiv](https://arxiv.org/abs/2204.09789), [PDF](https://arxiv.org/pdf/2204.09789)\] \[Abstract: We explore [[0002 3D gravity|three-dimensional gravity]] with negative cosmological constant via canonical quantization. We focus on chiral gravity which is related to a single copy of $\mathrm{PSL}(2,\mathbb{R})$ [[0089 Chern-Simons theory|Chern-Simons theory]] and is simpler to treat in canonical quantization. Its phase space for an initial value surface $\Sigma$ is given by the appropriate moduli space of Riemann surfaces. We use geometric quantization to compute partition functions of chiral gravity on three-manifolds of the form $\Sigma \times \mathrm{S}^1$, where $\Sigma$ can have asymptotic boundaries. Most of these topologies do not admit a classical solution and are thus not amenable to a direct semiclassical path integral computation. We use an index theorem that expresses the partition function as an integral of characteristic classes over phase space. In the presence of $n$ asymptotic boundaries, we use techniques from equivariant cohomology to localize the integral to a finite-dimensional integral over $\overline{\mathcal{M}}_{g,n}$, which we evaluate in low genus cases. Higher genus partition functions quickly become complicated since they depend in an oscillatory way on Newton's constant. There is a precise sense in which one can isolate the non-oscillatory part which we call the fake partition function. We establish that there is a topological recursion that computes the fake partition functions for arbitrary Riemann surfaces $\Sigma$. There is a scaling limit in which the model reduces to [[0050 JT gravity|JT gravity]] and our methods give a novel way to compute JT partition functions via equivariant localization.\] # Erdmenger, Hess, Matthaiakakis, Meyer ## Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity \[Links: [arXiv](https://arxiv.org/abs/2211.02064), [PDF](https://arxiv.org/pdf/2211.02064.pdf)\] \[Abstract: Motivated by establishing [[0209 Holographic renormalisation|holographic renormalization]] for gravitational theories with non-metricity and torsion, we present a new and efficient general method for calculating [[0138 Variational principle|Gibbons-Hawking-York (GHY)]] terms. Our method consists of linearizing any nonlinearity in curvature, torsion or non-metricity by introducing suitable Lagrange multipliers. Moreover, we use a split formalism for differential forms, writing them in $(n-1)+1$ dimensions. The boundary terms of the action are manifest in this formalism by means of Stokes' theorem, such that the compensating GHY term for the Dirichlet problem may be read off directly. We observe that only those terms in the Lagrangian that contain curvature contribute to the GHY term. Terms polynomial solely in torsion and non-metricity do not require any GHY term compensation for the variational problem to be well-defined. We test our method by confirming existing results for Einstein-Hilbert and four-dimensional Chern-Simons modified gravity. Moreover, we obtain new results for Lovelock-Chern-Simons and metric-affine gravity. For all four examples, our new method and results contribute to a new approach towards a systematic hydrodynamic expansion for spin and hypermomentum currents within [[0001 AdS-CFT|AdS/CFT]].\] # Fan, Fotopoulos, Stieberger, Taylor, Zhu ## Elements of Celestial Conformal Field Theory \[Links: [arXiv](https://arxiv.org/abs/2202.08288), [PDF](https://arxiv.org/pdf/2202.08288.pdf)\] \[Abstract: \] - uses dilaton field to deal with singularity # Faulkner, Li ## Asymptotically isometric codes for holography \[Links: [arXiv](https://arxiv.org/abs/2211.12439), [PDF](https://arxiv.org/pdf/2211.12439.pdf)\] \[Abstract: The holographic principle suggests that the low energy effective field theory of gravity, as used to describe perturbative quantum fields about some background has far too many states. It is then natural that any [[0146 Quantum error correction|quantum error correcting code]] with such a quantum field theory as the code subspace is not isometric. We discuss how this framework can naturally arise in an algebraic QFT treatment of a family of CFT with a large-$N$ limit described by the single trace sector. We show that an isometric code can be recovered in the $N \rightarrow \infty$ limit when acting on fixed states in the code Hilbert space. Asymptotically isometric codes come equipped with the notion of simple operators and nets of causal wedges. While the causal wedges are additive, they need not satisfy Haag duality, thus leading to the possibility of non-trivial [[0219 Entanglement wedge reconstruction|entanglement wedge reconstructions]]. Codes with complementary recovery are defined as having extensions to Haag dual nets, where entanglement wedges are well defined for all causal boundary regions. We prove an asymptotic version of the information disturbance trade-off theorem and use this to show that boundary theory causality is maintained by net extensions. We give a characterization of the existence of an entanglement wedge extension via the asymptotic equality of bulk and boundary [[0199 Relative entropy|relative entropy]] or [[0416 Modular Hamiltonian|modular flow]]. While these codes are asymptotically exact, at fixed $N$ they can have large errors on states that do not survive the large-$N$ limit. This allows us to fix well known issues that arise when modeling gravity as an exact codes, while maintaining the nice features expected of gravity, including, among other things, the emergence of non-trivial [[0415 Von Neumann algebra|von Neumann algebras]] of various types.\] ## Refs - talk at [[Rsc0048 MURI 2022|MURI 2022]] ## Why [[0484 Type III-1 von Neumann algebra|type III-1]]? - many reasons ## Immediate concerns - holographic bounds preclude many QFT states - $S_{EE}$ is $A/4$ finite, so maybe not type III-1? - previous attempts had trouble with ADH feature that is absent and the expected approximate nature ## Resolution - incorporate the large-$N$ limit into holographic codes - ... ## Asymptotic isometric codes - take a sequence of CFTs labelled by $N$, so a sequence of Hilbert spaces, $K_N$ - # Fernandes, Carrilho, Clifton, Mulryne ## The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review \[Links: [arXiv](https://arxiv.org/abs/2202.13908), [PDF](https://arxiv.org/pdf/2202.13908.pdf)\] \[Abstract: We review the topic of 4D [[0425 Gauss-Bonnet gravity|Einstein-Gauss-Bonnet gravity]], which has been the subject of considerable interest over the past two years. Our review begins with a general introduction to Lovelock's theorem, and the subject of Gauss-Bonnet terms in the action for gravity. These areas are of fundamental importance for understanding modified theories of gravity, and inform our subsequent discussion of recent attempts to include the effects of a Gauss-Bonnet term in four space-time dimensions by re-scaling the appropriate coupling parameter. We discuss the mathematical complexities involved in implementing this idea, and review recent attempts at constructing well-defined, self-consistent theories that enact it. We then move on to consider the gravitational physics that results from these theories, in the context of black holes, cosmology, and weak-field gravity. We show that 4D Einstein-Gauss-Bonnet gravity exhibits a number of interesting phenomena in each of these areas.\] ## Refs - [[0006 Higher-derivative gravity]] - [[0425 Gauss-Bonnet gravity]] # Figueras, Franca, Gu, Andrade ## The endpoint of the Gregory-Laflamme instability of black strings revisited \[Links: [arXiv](https://arxiv.org/abs/2210.13501), [PDF](https://arxiv.org/pdf/2210.13501.pdf)\] \[Abstract: We reproduce and extend the previous studies of Lehner and Pretorius of the endpoint of the [[0442 Gregory-Laflamme instability|Gregory-Laflamme instability]] of [[0232 Black string|black strings]] in five space-time dimensions. We consider unstable black strings of fixed thickness and different lengths, and in all cases we confirm that at the intermediate stages of the evolution the horizon can be interpreted as a quasistationary self-similar sequence of black strings connecting spherical black holes on different scales. However, we do not find any evidence for a global timescale relating subsequent generations. The endpoint of the instability is the pinch off of the horizon in finite asymptotic time, thus confirming the violation of the [[0221 Weak cosmic censorship|weak cosmic censorship conjecture]] around black string spacetimes.\] ## Refs - talk at KITP on 27 Oct 2022 ## Summary - independently reproducing a famous numerical evolution by [[LehnerPretorius2010]] # Folkestad ## The Penrose Inequality as a Constraint on the Low Energy Limit of Quantum Gravity \[Links: [arXiv](https://arxiv.org/abs/2209.00013), [PDF](https://arxiv.org/pdf/2209.00013.pdf)\] \[Abstract: We construct [[0310 Initial data in AdS|initial data]] violating the AdS [[0476 Penrose inequality|Penrose inequality]] using scalars with various potentials. Since the Penrose inequality can be derived from basic entries in the [[0001 AdS-CFT|AdS/CFT]] dictionary, we argue that it is a new [[0184 Swampland|swampland condition]], ruling out holographic UV completion for theories that violate it. We produce exclusion plots on scalar couplings violating the inequality, and we find no violations for top-down potentials. In the special case where the dominant energy condition holds, we use GR techniques to prove the AdS Penrose inequality in all dimensions greater than two, assuming spherical, planar, or hyperbolic symmetry. However, our violations show that this result cannot be generically true with only the null energy condition, and we give an analytic sufficient condition for violation of the Penrose inequality, constraining couplings and the exponential behavior of scalar potentials.\] ## Summary - obtains conditions on the potential $V(\phi)$ of a scalar field $\phi$ from Penrose inequality from holography, i.e., if the equality does not hold, it cannot be holographic - uses numerics to test inequality in various theories with millions of initial data for the scalar field - existence of superpotential seems to guarantee Penrose inequality ## Setup - theories: $ \frac{1}{8 \pi G_N} \int \mathrm{d}^{d+1} x \sqrt{-g}\left[\frac{1}{2} R+\frac{d(d-1)}{2 L^2}-\frac{1}{2}|\nabla \phi|^2-V(\phi)\right] $ - (for the proof) works at moment of time symmetry: MOTS = minimal surface ## Subtleties - need to first find the most entropic solution in the microcanonical ensemble; but with symmetrical symmetry - [[2022#Xiao, Yang]]: the only static spherically symmetric BH that can dominate the [[0462 Microcanonical ensemble|microcanonical ensemble]] is AdS-Schwarzschild - assumes no spontaneous time-translation symmetry breaking for the most entropy saddles - the most entropy saddle could break spatial homogeneity; in this case can use a different ensemble where the energy density is fixed on the boundary (to be homogeneous) ## Proof of Penrose inequality The idea is to construct a function that monotonically increases from the marginally trapped surface to infinity and show that this function evaluates to the desired function of area at the trapped surface and to the mass at infinity. # Folkestad, Dhumuntarao ## Maximal Entangling Rates from Holography \[Links: [arXiv](https://arxiv.org/abs/2211.07654), [PDF](https://arxiv.org/pdf/2211.07654.pdf)\] \[Abstract: We prove novel speed limits on the growth of entanglement, equal time correlators, and spacelike Wilson loops in spatially uniform time-evolving states in strongly coupled CFTs with holographic duals. These bounds can also be viewed as quantum weak energy conditions. Several of the speed limits are valid for regions of arbitrary size and with multiple connected components, and our findings imply new bounds on the effective [[0327 Entanglement velocity|entanglement velocity]] of small subregions. In 2d CFT, our results prove a conjecture by Liu and Suh for a large class of states. Key to our findings is a momentum-entanglement correspondence, showing that [[0522 Entanglement dynamics|entanglement growth]] is computed by the momentum crossing the [[0007 RT surface|HRT]] surface. In our setup, we prove a number of general features of boundary-anchored extremal surfaces, such as a sharp bound on the smallest radius that a surface can probe, and that the tips of extremal surfaces cannot lie in trapped regions. Our methods rely on novel global GR techniques, including a delicate interplay between Lorentzian and Riemannian Hawking masses. While our proofs assume the dominant [[0247 Energy conditions|energy condition]] in the bulk, we provide numerical evidence that our bounds are true under less restrictive assumptions.\] # Freidel, Pranzetti, Raclariu ## A discrete basis for celestial holography \[Links: [arXiv](https://arxiv.org/abs/2212.12469), [PDF](https://arxiv.org/pdf/2212.12469.pdf)\] \[Abstract: [[0010 Celestial holography|Celestial holography]] provides a reformulation of scattering amplitudes in four dimensional asymptotically flat spacetimes in terms of conformal correlators of operators on the two dimensional [[0022 Celestial sphere|celestial sphere]] in a basis of boost eigenstates. A basis of massless particle states has previously been identified in terms of conformal primary wavefunctions labeled by a boost weight $\Delta=1+i\lambda$ with $\lambda\in \mathbb{R}$. Here we show that a *discrete* orthogonal and complete basis exists for $\Delta\in\mathbb{Z}$. This new basis consists of a tower of discrete memory and Goldstone observables, which are conjugate to each other and allow to reconstruct gravitational signals belonging to the Schwartz space. We show how generalized dressed states involving the whole tower of Goldstone operators can be constructed and evaluate the higher spin Goldstone 2-point functions. Finally, we recast the tower of higher spin charges providing a representation of the $\rm{w}_{1+\infty}$ loop algebra (in the same helicity sector) in terms of the new discrete basis.\] ## Main results - for a special class of sufficiently localised gravity signals, conformal primary wavefunctions with discrete conformal weights form a complete basis ## Refs - [[0148 Conformal basis]] - [[0328 w(1+infinity)]] # Geng, Karch, Perez-Pardavila, Raju, Randall, Riojas, Shashi ## Jackiw-Teitelboim Gravity from the Karch-Randall Braneworld \[Links: [arXiv](https://arxiv.org/abs/2206.04695), [PDF](https://arxiv.org/pdf/2206.04695.pdf)\] \[Abstract: \] ## Summary - [[0050 JT gravity]] from [[0452 Karch-Randall braneworld]] - radion plays the role of dilaton - resolves a would-be classical puzzle of [[0219 Entanglement wedge reconstruction]] by including quantum fluctuations of the radion/dilaton # Giombi, Komatsu, Offertaler ## Chaos and the reparametrization mode on the AdS$_2$ string \[Links: [arXiv](https://arxiv.org/abs/2212.14842), [PDF](https://arxiv.org/pdf/2212.14842.pdf)\] \[Abstract: We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS$_2$ geometry. In the out-of-time-order configuration, the correlators display a [[0466 Lyapunov exponent|Lyapunov]] growth that saturates the [[0474 Chaos bound|chaos bound]]. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the [[0482 Out-of-time-order correlator|out-of-time-order correlator]] (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in [[0050 JT gravity|JT gravity]]. The result can be understood as coming from high energy scattering near the horizon of a AdS$_2$ black hole, and is essentially controlled by the flat space worldsheet $S$-matrix. While previous works on the AdS$_2$ string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to $SL(2,\mathbb{R})$ invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in ${\cal N}=4$ SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling.\] # Gopakumar, Mazenc ## Deriving the Simplest Gauge-String Duality -- I: Open-Closed-Open Triality \[Links: [arXiv](https://arxiv.org/abs/2212.05999), [PDF](https://arxiv.org/pdf/2212.05999)\] \[Abstract: We lay out an approach to derive the closed string [[0471 String-matrix duality|dual]] to the simplest possible gauge theory, a single hermitian [[0197 Matrix model|matrix integral]], in the conventional 't Hooft large $N$ limit. In this first installment of three papers, we propose and verify an explicit correspondence with a (mirror) pair of closed topological string theories. On the A-model side, this is a supersymmetric $SL(2, \mathbb{R})_1/U(1)$ Kazama-Suzuki coset (with background momentum modes turned on). The mirror B-model description is in terms of a Landau-Ginzburg theory with superpotential $W(Z)=\frac{1}{Z}+t_2Z$ and its deformations. We arrive at these duals through an "open-closed-open triality". This is the notion that two open string descriptions ought to exist for the same closed string theory depending on how closed strings manifest themselves from open string modes. Applying this idea to the hermitian matrix model gives an exact mapping to the Imbimbo-Mukhi matrix model. The latter model is known to capture the physical correlators of the c=1 string theory at self-dual radius, which, in turn, has the equivalent topological string descriptions given above. This enables us to establish the equality of correlators, to all genus, between single trace operators in our original matrix model and those of the dual closed strings. Finally, we comment on how this simplest of dualities might be fruitfully viewed in terms of an embedding into the full [[0001 AdS-CFT|AdS/CFT]] correspondence.\] # Grewal, Law, Parmentier ## Black Hole Horizon Edge Partition Functions \[Links: [arXiv](https://arxiv.org/abs/2211.16644), [PDF](https://arxiv.org/pdf/2211.16644.pdf)\] \[Abstract: We extend a formula for 1-loop black hole determinants by [[2009#Denef, Hartnoll, Sachdev|Denef, Hartnoll, and Sachdev (DHS)]] to spinning fields on any ($d+ 1$)-dimensional static spherically symmetric black hole. By carefully analyzing the regularity condition imposed on the Euclidean eigenfunctions, we reveal an unambiguous bulk-edge split in the 1-loop Euclidean partition function for tensor fields of arbitrary integer spin: the bulk part captures the “renormalized” thermal canonical partition function recently discussed in [[2022#Law, Parmentier|1]]; the edge part is related to [[0325 Quasi-normal modes|quasinormal modes (QNMs)]] that fail to analytically continue to a subset of Euclidean modes with enhanced fall-offs near the origin. Since the edge part takes the form of a path integral on $S^{d−1 }$, this suggests that these are associated with degrees of freedom living on the bifurcation surface in the Lorentzian twosided black hole geometry. For massive higher spin on static [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] and massive vector on Nariai black holes, we find that the edge partition function is related to the QNMs with lowest overtone numbers.\] ## Refs - earlier work [[2022#Law, Parmentier]] - important precursor: [[2009#Denef, Hartnoll, Sachdev]] # Guerrieri, Murali, Penedones, Vieira ## Where is M-theory in the space of scattering amplitudes? \[Links: [arXiv](https://arxiv.org/abs/2212.00151), [PDF](https://arxiv.org/pdf/2212.00151.pdf)\] \[Abstract: We use the $S$-matrix bootstrap to carve out the space of [[0035 Unitarity of CFT|unitary]], [[0120 Analyticity constraints|analytic]], [[0021 Crossing symmetry|crossing symmetric]] and supersymmetric graviton scattering amplitudes in nine, ten and eleven dimensions. We extend and improve the numerical methods of our previous work in ten dimensions. A key new tool employed here is unitarity in the [[0022 Celestial sphere|celestial sphere]]. In all dimensions, we find that the minimal allowed value of the Wilson coefficient $\alpha$, controlling the leading correction to maximal supergravity, is very close but not equal to the minimal value realized in Superstring theory or [[0517 M-theory|M-theory]]. This small difference may be related to inelastic effects that are not well described by our numerical extremal amplitudes. Although $\alpha$ has a unique value in [[0517 M-theory|M-theory]], we found no evidence of an upper bound on $\alpha$ in 11D.\] # Guevara ## Towards Gravity From a Color Symmetry \[Links: [arXiv](https://arxiv.org/abs/2209.00696), [PDF](https://arxiv.org/pdf/2209.00696.pdf)\] \[Abstract: Using tools from [[0152 Colour-kinematics duality|color-kinematics duality]] we propose a holographic construction of gravitational amplitudes, based on a 2d [[0069 Kac-Moody algebra|Kac-Moody]] theory on the [[0022 Celestial sphere|celestial sphere]]. In the $N\to\infty$ limit the gauge group corresponds to [[0328 w(1+infinity)|w(1+infinity)]], due to the $U(N)$ generators enjoying a simple quantum group structure, which is in turn inherited from a twistor fiber over the celestial sphere. We show how four-dimensional momentum-space is emergent in this picture, which connects directly to the so-called kinematic algebra of the tree-level S-Matrix. On the other hand, the framework can be embedded within a [[0010 Celestial holography|celestial CFT]] to make contact with [[0063 Symmetry of CCFT|holographic symmetry algebras]] previously observed in the soft expansion. [[0069 Kac-Moody algebra|Kac-Moody]] currents play the role of a graviton to all orders in such expansion, and also lead to a natural notion of Goldstone modes for [[0328 w(1+infinity)|w(1+infinity)]]. Focusing on [[0061 Maximally helicity violating amplitudes|MHV]] amplitudes, main examples are a [[0058 BCFW|BCFW]] type recursion relation and holomorphic three-point amplitudes.\] ## Refs - talk at Amplitudes 22: [YouTube](https://www.youtube.com/watch?v=7JIBQVKPYMc&t=28431s&ab_channel=Amplitudes2022) ## Summary - large N limit of $SU(N)$ provides a classical realisation of [[0328 w(1+infinity)|w(1+infinity)]] as a colour algebra of matrices ## A recursive formula for MHV from OPE $\begin{aligned}\left\langle G^\lambda(z) G^{\lambda_1}\left(z_1\right) \cdots G^{\lambda_n}\left(z_n\right)\right\rangle &=\frac{1}{2 \pi i} \oint \frac{d w}{w-z}\left\langle G^\lambda(w) G^{\lambda_1}\left(z_1\right) \cdots G^{\lambda_n}\left(z_n\right)\right\rangle \\ &=\sum_i \frac{\left[\lambda \lambda_i\right]}{z-z_i} e^{\left[\lambda \frac{\partial}{\partial \lambda_i}\right]}\left\langle G^{\lambda_1}\left(z_1\right) \cdots G^{\lambda_i}\left(z_i\right) \cdots G^{\lambda_n}\left(z_n\right)\right\rangle+\mathcal{A}_{\infty}(z) \end{aligned}$ ## Relation to conformal primary basis (Appendix I) - soft expansion - $a_{+2}^{\dagger}(\omega, z, \bar{z})=\sum_{k=0}^{\infty} \omega^{k-1} H_{1-k}(z, \bar{z})$ - rewriting soft currents - $H_{4-2 p}(z, \bar{z})=\frac{1}{(2 p-2) !} \sum_{n=1-p}^{p-1}\left(\begin{array}{c}2 p-2 \\ p-n-1\end{array}\right) w_n^p(z) \bar{z}^{p-1-n}$ - a natural spin-$p$ representation of $SL(2,\mathbb{R})$: - $w_n^p=\mathbf{W}_{+\cdots+-\cdots-}^{2 p-2}$ - number of pluses = $p-n-1$ - number of minuses = $p+n-1$ - write in spinor $|\hat{\lambda}]=\left(\begin{array}{ll}1 & \bar{z}\end{array}\right)$: - $H_{4-2 p=1-k}(z, \bar{z})=\frac{1}{(2 p-2) !} \mathbf{W}_{\alpha_1 \cdots \alpha_{2 p-2}}^{2 p-2}(z) \hat{\lambda}^{\alpha_1} \cdots \hat{\lambda}^{\alpha_{2 p-2}}$ - use little group scaling: - $|\eta\rangle=\sqrt{\omega}(1 \quad z), |\lambda]=\sqrt{\omega}(1 \quad \bar{z})$ - becomes $\left.|\eta\rangle=\left(\begin{array}{ll}1 & z\end{array}\right), |\lambda\right]=\omega(1 \quad \bar{z})=\omega |\hat{\lambda}]$ - write in terms of $|\lambda]$ - $\mathbf{G}^{\lambda=\omega \hat{\lambda}}(z)=\sum_{k=0}^{\infty} \frac{1}{(k+1) !} \mathbf{W}_{\alpha_1 \cdots \alpha_{k+1}}^{k+1}(z) \lambda^{\alpha_1} \cdots \lambda^{\alpha_{k+1}}$ - relation to [[0412 Light transform|light transform]] - $H_{4-2 p}(z, \eta)=\frac{1}{\Gamma(2 p-1)} \oint \frac{[\lambda d \lambda]}{2 \pi i}[\lambda \eta]^{2 p-2} \mathbb{L}\left[H_{4-2 p}\right](z, \lambda), p>0$ - so $\mathbf{W}_{\alpha_1 \cdots \alpha_{2 p-2}}^{2 p-2}=\oint \frac{[\lambda d \lambda]}{2 \pi i} \lambda_{\alpha_1} \ldots \lambda_{\alpha_{2 p-2}} \mathbb{L}\left[H_{4-2 p}\right](z, \lambda)$ - which is a Penrose transform - using $[\lambda d \lambda]=d \bar{z}$ - get $w_n^p(z)=\oint \frac{d \bar{z}}{2 \pi i} \bar{z}^{p-n-1} \mathbb{L}\left[H_{2 p-2}\right](z, \bar{z})$ # Hartman, Jiang, Sgarlata, Tajdini # Focusing bounds for CFT correlators and the $S$-matrix \[Links: [arXiv](https://arxiv.org/abs/2212.01942), [PDF](https://arxiv.org/pdf/2212.01942.pdf)\] \[Abstract: The focusing theorem in General Relativity underlies causality, [[0225 Singularity theorems|singularity theorems]], entropy inequalities, and more. In AdS/CFT, we show that focusing in the bulk leads to a bound on CFT $n$-point functions that is generally stronger than causality. Causality is related to the [[0417 Averaged null energy condition|averaged null energy condition (ANEC)]] on the boundary, while focusing is related to the [[0417 Averaged null energy condition|ANEC]] in the bulk. The bound is derived by translating the Einstein equations into a relation between bulk and boundary light-ray operators. We also discuss the consequences of focusing for the flat space $S$-matrix, which satisfies a similar inequality, and give a new derivation of bounds on higher derivative operators in effective field theories. The string theory $S$-matrix and CFT correlators in conformal Regge theory also satisfy the focusing bound, even though in these cases it cannot be derived from the standard focusing theorem.\] ## Summary - bulk focusing => a focusing bound for CFT $n$-point functions or flat space scattering amplitude - string theory: satisfies focusing bound too, but not from bulk focusing ## The focusing bound - the bound states $\vec{\partial}^2 \Delta v \leq 0$, where $\Delta v$ is the time delay for probe particles passing through a shockwave - $S$-matrix version: - relate the phase to the time delay by $\Delta v(\vec{x})=2 \frac{\partial}{\partial E} \operatorname{Re} \delta(s, \vec{x})$ - since $s=4 E\left|P_u\right|$, the bound becomes $\partial_s \vec{\partial}^2 \operatorname{Re} \delta(s, \vec{x}) \leq 0$ ## Higher derivatives - write $G_{\mu \nu}^{(1)}=8 \pi G_N T_{\mu \nu}^{\text {total }}$, where the LHS is the linearised Einstein tensor, while the RHS contains both the matter stress tensor and graviton stress tensor - the graviton stress pseudo-tensor is quadratic in the metric because only second-order theories are considered here like in [[2014#Camanho, Edelstein, Maldacena, Zhiboedov]] \[*I am grateful to Tom and Amir for answering some of my questions.*\] # Harrison, Maloney, Numasawa ## Liouville Theory and the Weil-Petersson Geometry of Moduli Space \[Links: [arXiv](https://arxiv.org/abs/2210.08098), [PDF](https://arxiv.org/pdf/2210.08098.pdf)\] \[Abstract: [[0562 Liouville theory|Liouville theory]] describes the dynamics of surfaces with constant negative curvature and can be used to study the [[0617 Weil-Petersson volume|Weil-Petersson]] geometry of the moduli space of Riemann surfaces. This leads to an efficient algorithm to compute the Weil--Petersson metric to arbitrary accuracy using Zamolodchikov's recursion relation for conformal blocks. For example, we compute the metric on $\mathcal M_{0,4}$ numerically to high accuracy by considering Liouville theory on a sphere with four punctures. We numerically compute the eigenvalues of the Weil-Petersson Laplacian, and find evidence that the obey the statistics of a [[0579 Random matrix theory|random matrix]] in the Gaussian Orthogonal Ensemble.\] # Hartnoll ## Wheeler-DeWitt states of the AdS-Schwarzschild interior \[Links: [arXiv](https://arxiv.org/abs/2208.04348), [PDF](https://arxiv.org/pdf/2208.04348.pdf)\] \[Abstract: \] ## Summary - uses [[0227 Hamilton-Jacobi]] theory: no explicit *time* coordinate; this rewrites the metric in terms of just Hamilton-Jacobi quantities without time, but can recover the full metric by substituting back - works with a [[0254 Minisuperspace]] metric ansatz so that the Lagrangian simplifies - the [[0345 Wheeler-DeWitt (WdW) equation|WDW wavefunction]] evolves outwards to the partition function of the Lorentzian CFT on the boundary - in particular, the Gaussian wavepacket evolves into a micro canonical partition function with an energy window ## Assumptions - Einstein gravity in 4D - a specific ansatz for minisuperspace metric - $\mathbb{Z}_2$ symmetric between two asymptotic boundaries ## Where does time go - can choose what to use as the clock, e.g. $k$ or $g_{tt}$ - with $g_{tt}$ as the clock, it goes to the boundary as $g_{tt}\to - \infty$ and goes to the singularity of BH as it goes to positive infinity # Headrick, Hubeny ## Covariant bit threads \[Links: [arXiv](https://arxiv.org/abs/2208.10507), [PDF](https://arxiv.org/pdf/2208.10507)\] \[Abstract: We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant [[0007 RT surface|holographic entanglement entropy]] formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to $D(A)$ (the boundary causal domain of the region $A$ whose entropy we are calculating) and minimizing over the hypersurface; (2) a max $V$-flow formula, in which we maximize the flux through $D(A)$ of a divergenceless bulk 1-form $V$ subject to an upper bound on its norm that is non-local in time; and (3) a min $U$-flow formula, in which we minimize the flux over a bulk Cauchy slice of a divergenceless timelike 1-form $U$ subject to a lower bound on its norm that is non-local in space. The two flow formulas define convex programs and are related to each other by Lagrange duality. For each program, the optimal configurations dynamically find the HRT surface and the entanglement wedges of $A$ and its complement. The $V$-flow formula is the covariant version of the Freedman-Headrick [[0211 Bit thread|bit thread]] reformulation of the [[0007 RT surface|Ryu-Takayanagi formula]]. We also introduce a measure-theoretic concept of a "thread distribution", and explain how Riemannian flows, $V$-flows, and $U$-flows can be expressed in terms of thread distributions.\] # Heller, Serantes, Spalinski, Withers ## Rigorous bounds on transport from causality \[Links: [arXiv](https://arxiv.org/abs/2212.07434), [PDF](https://arxiv.org/pdf/2212.07434.pdf)\] \[Abstract: We use causality to derive a number of simple and universal constraints on dispersion relations, which describe the location of singularities of retarded two-point functions in relativistic quantum field theories. We prove that all causal dissipative dispersion relations have a finite radius of convergence. We then give bounds on all transport coefficients in units of this radius, including an upper bound on diffusivity.\] # Hollands (Lectures) ## GGI Lectures on Entropy, Operator Algebras and Black Holes \[Links: [arXiv](https://arxiv.org/abs/2209.05132), [PDF](https://arxiv.org/pdf/2209.05132.pdf)\] ## 1. Hawking, Unruh, Bisognano-Wichmann ## 2. Entropy and relative entropy - think the entropy as "averaged surprise" - [[0199 Relative entropy|relative entropy]] ## 3. Quantum channels and DPI - **Data processing inequality**: the distinguishability of two states cannot increase when passed through a channel - *cyclic*: $\operatorname{span}\{L(a)|\sqrt{\rho}\rangle: a \in \mathcal{A}\}=\mathscr{H}$ - *separating*: $L(a)|\sqrt{\rho}\rangle=0 \Longrightarrow a=0$ # Hollands, Kovacs, Reall ## BH second law in EFT \[Links: [arXiv](https://arxiv.org/abs/2205.15341), [PDF](https://arxiv.org/pdf/2205.15341.pdf)\] \[Abstract: We investigate the [[0005 Black hole second law|second law of black hole mechanics]] in gravitational theories with [[0006 Higher-derivative gravity|higher derivative terms]] in the action. [[2015#Wall (Essay)|Wall]] has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. We show that this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. We also address some outstanding issues with Wall's method, in particular, its gauge invariance and its relation to the Iyer-Wald entropy.\] ## Summary - extends [[2015#Wall (Essay)]] to second order in perturbation - proves the claim that the vanishing-boost-weight part is the same as the [[1993#Wald|Wald entropy]] - shows that Wall's entropy is gauge invariant at linear level, and in fact can make it fully gauge invariant by choosing terms at higher orders - the usual GR strategy does not work ## Refs - [[0005 Black hole second law]] - follow-up [[2022#Davies, Reall]] ## Main results The generalisation of the Wall's formula $ E_{v v}=\partial_{v}\left[\frac{1}{\sqrt{\mu}} \partial_{v}\left(\sqrt{\mu} s^{v}\right)+D_{A} s^{A}\right]+\ldots $ is$\partial_{v}\left[\frac{1}{\sqrt{\mu}} \partial_{v}\left(\sqrt{\mu} S^{v}\right)+D_{A} S^{A}\right]=-\big(K^{A B}+X^{A B}\big)\big(K_{A B}+X_{A B}\big)-D_{A} Y^{A}+\mathcal{O}\left(\ell^{N}\right)$The key is that the RHS contains a square which is positive definite. The other term vanishes upon variation and integration. ## Comments - does not seem to produce [[1993#Jacobson, Myers|JM entropy]] for [[0425 Gauss-Bonnet gravity|GB]] gravity at higher orders # Horn ## Asymptotic symmetries in Bondi gauge and the sub-subleading soft graviton theorem \[Links: [arXiv](https://arxiv.org/abs/2212.02566), [PDF](https://arxiv.org/pdf/2212.02566.pdf)\] \[Abstract: We investigate [[0060 Asymptotic symmetry|asymptotic symmetries]] which preserve the Bondi gauge conditions but do not preserve the asymptotic falloff conditions for the metric near the null boundary, and their connection to [[0009 Soft theorems|soft graviton theorems]] for scattering amplitudes. These include generalized superrotation symmetries parameterized by a smooth vector field $Y^{A}$ obeying $D_{A}Y^{A} = 0$, for which we show that the associated conserved charge can be derived by applying the Noether procedure to the Einstein-Katz action. We also discuss the connection between asymptotic symmetries and the conserved charge associated with the sub-subleading soft theorem, and we find that in Bondi gauge this charge is generated by the combination of a diffeomorphism together with an extra transformation of the metric.\] # Horowitz, Kolanowski, Santos (Oct) ## Almost all extremal black holes in AdS are singular \[Links: [arXiv](https://arxiv.org/abs/2210.02473), [PDF](https://arxiv.org/pdf/2210.02473.pdf)\] \[Abstract: We investigate the geometry near the horizon of a generic, four-dimensional extremal black hole. When the cosmological constant is negative, we show that (in almost all cases) tidal forces diverge as one crosses the horizon, and this singularity is stronger for larger black holes. In particular, this applies to generic nonspherical black holes, such as those satisfying inhomogeneous boundary conditions. Nevertheless, all scalar curvature invariants remain finite. Moreover, we show that nonextremal black holes have tidal forces that diverge in the extremal limit. Holographically, this singularity is reflected in anomalous scaling of the specific heat with temperature. Similar (albeit weaker) effects are present when the cosmological constant is positive, but not when it vanishes.\] # Horowitz, Leung, Queimada, Zhao ## Bouncing inside the horizon and scrambling delays \[Links: [arXiv](https://arxiv.org/abs/2207.10679), [PDF](https://arxiv.org/pdf/2207.10679.pdf)\] \[Abstract: \] ## Summary - charged matter has a delay before scrambling starts - uses two arguments - quantum circuit - the [[0482 Out-of-time-order correlator|OTOC]] has a delay before it monotonically decreases # Horowitz, Wang, Ye ## An infinity of black holes \[Links: [arXiv](https://arxiv.org/abs/2206.08944), [PDF](https://arxiv.org/pdf/2206.08944.pdf), [CQG](https://iopscience.iop.org/article/10.1088/1361-6382/ac994b)\] \[Abstract: In general relativity (without matter), there is typically a one parameter family of static, maximally symmetric black hole solutions labelled by their mass. We show that there are situations with many more black holes. We study [[0231 Bulk solutions for CFTs on non-trivial geometries|asymptotically anti-de Sitter solutions]] in six and seven dimensions having a conformal boundary which is a product of spheres cross time. We show that the number of families of static, maximally symmetric black holes depends on the ratio, $\lambda$, of the radii of the boundary spheres. As $\lambda$ approaches a critical value, $\lambda_{c}$, the number of such families becomes infinite. In each family, we can take the size of the black hole to zero, obtaining an infinite number of static, maximally symmetric non-black hole solutions. We discuss several applications of these results, including [[0012 Hawking-Page transition|Hawking-Page phase transitions]] and the phase diagram of dual field theories on a product of spheres, new [[0116 Positive energy theorem|positive energy conjectures]], and more.\] ## Summary - studies [[0403 Bulk dual of CFT on dS|bulk dual]] of CFT on $S^1\times S^2\times S^2$ and $S^1\times S^2\times S^3$, where one of the spheres can be analytically continued to de Sitter - the lowest energy solution depends on the ratio between sphere radii - one-parameter family of [[0012 Hawking-Page transition|Hawking-Page phase transition]]; overall a three-phase phase diagram - demonstrates an extreme form of [[0455 Black hole uniqueness theorems|black hole non-uniqueness]] - discusses [[0025 Operator-state correspondence|operator-state correspondence]] for CFTs on non-trivial topologies ## Relevant topics - [[0403 Bulk dual of CFT on dS]] - [[0116 Positive energy theorem]] - [[0455 Black hole uniqueness theorems]] # Huang, Remmen ## UV-Complete Gravity Amplitudes and the Triple Product \[Links: [arXiv](https://arxiv.org/abs/2203.00696), [PDF](https://arxiv.org/pdf/2203.00696.pdf)\] \[Abstract: \] ## Summary - constructs UV complete amplitudes in a bootstrap way - finds infinitely many amplitudes that are finite in the UV by breaking a rule: accumulation point - exchanges an infinite tower of massive higher-spin states ## Why tree-level completion - at tree-level, the Einstein gravity is UV divergent: $\sim R^2/m_{pl}^2$ (breaks down at Planck scale) - as shown via $\hbar$ counting in [[CheungRemmen2016]][](https://arxiv.org/abs/1608.02942), any theory that perturbatively unitarises Einstein-Hilbert graviton scattering must do so at tree level ## The triple product - $\mathcal{M}=\kappa^{2} \mathbb{R}^{4} \mathcal{A}(s) \mathcal{A}(t) \mathcal{A}(u)$ - there is some $\mathcal{A}$ from type-II string, but they generalise it to $\mathcal{A}(s)=\frac{1}{s}+\sum_{n=1}^{\infty} \frac{g_{n}^{2}}{-s+m_{n}^{2}}$ for arbitrary $\sum_n g_n^2=1$ and $m_n$ - this goes to 0 at large $s$ ## Requirement for unitarity - needs to compute partial waves on various massless and massive residues - e.g. residue for the massless pole: $\mathcal{R}_{0}=\lim _{s \rightarrow 0}(-s) \mathcal{A}(s) \mathcal{A}(t) \mathcal{A}(u)$ - and residue for massive poles $\mathcal{R}_{n}=\lim _{s \rightarrow m_{n}^{2}}\left(-s+m_{n}^{2}\right) \mathcal{A}(s) \mathcal{A}(t) \mathcal{A}(u)$ - they are all positive ## Causality - Shapiro time delay vanishes at leading order if $\sum g_n^2=1$ is satisfied and there causal - if the sum is not imposed, still cause but with a non-vanishing delay ## Trying to find it in String Theory - [[0348 Ambitwistor strings|twistor string]] <!-- ## Refs - talk given by #grantremmen on 10 May 2022 ---> # Hu, Pasterski (Aug) ## Celestial Recursion \[Links: [arXiv](https://arxiv.org/abs/2208.11635), [PDF](https://arxiv.org/pdf/2208.11635.pdf)\] \[Abstract: We examine the [[0058 BCFW|BCFW recursion relations]] for celestial amplitudes and how they inform the celestial bootstrap program. We start by recasting the celestial incarnation of the BCFW shift as a generalization of the action of familiar asymptotic symmetries on hard particles, before focusing on two limits: $z\to \infty$ and $z\to 0$. We then discuss how the celestial CFT data encodes the large-$z$ behavior determining which shifts are allowed, while the infinitesimal limit is tied to the celestial bootstrap program via the BG equations that constrain the MHV sector. The extension to super-BCFW is also presented. We close by remarking on several open questions for future study.\] ## Summary - [[0058 BCFW|BCFW]] is an energy dependent generalisation of the superrotation [[0060 Asymptotic symmetry|AS]] - can read off when a given BCFW shift is allowed from celestial data - BCFW implies an infinite number of PDE that exponentiate the BG equations # Hu, Pasterski (Nov) ## Celestial Conformal Colliders \[Links: [arXiv](https://arxiv.org/abs/2211.14287), [PDF](https://arxiv.org/pdf/2211.14287.pdf)\] \[Abstract: We start by observing that the [[0450 Light-ray operators|light-ray operators]] featured in the [[0493 Conformal collider bounds|conformal collider]] literature are celestial primaries. This allows us to rephrase the corresponding 4D CFT correlators as probing a [[0390 Conformally soft theorems|conformally soft]] matter sector of the 2D [[0010 Celestial holography|celestial CFT]] (CCFT). To demonstrate the utility of this perspective we show how the recent [[0328 w(1+infinity)|w]]$_{1+\infty}$ symmetry observed in [[0010 Celestial holography|CCFT]] suggests a natural extension of the conformal collider operators.\] # Hui, Joyce, Penco, Santoni, Solomon ## Near-Zone Symmetries of Kerr Black Holes \[Links: [arXiv](https://arxiv.org/abs/2203.08832), [PDF](https://arxiv.org/pdf/2203.08832.pdf)\] \[Abstract: We study the near-zone symmetries of a massless scalar field on four-dimensional black hole backgrounds. We provide a geometric understanding that unifies various recently discovered symmetries as part of an $SO(4,2)$ group. Of these, a subset are exact symmetries of the static sector and give rise to the ladder symmetries responsible for the vanishing of [[0581 Tidal Love numbers|Love numbers]]. In the Kerr case, we compare different near-zone approximations in the literature, and focus on the implementation that retains the symmetries of the static limit. We also describe the relation to spin-1 and 2 perturbations.\] # Iliesiu, Murthy, Turiaci (a) ## Revisiting the Logarithmic Corrections to the Black Hole Entropy \[Links: [arXiv](https://arxiv.org/abs/2209.13602), [PDF](https://arxiv.org/pdf/2209.13602.pdf)\] \[Abstract: Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In this paper, we show that, by using supersymmetric localization, the gravitational path integral for $\frac{1}8$-BPS black holes in $\mathcal{N}=8$ supergravity reproduces the index obtained in the string theory construction of such black holes, including all non-perturbatively suppressed geometries. A more refined argument then shows that, not only the black hole index, but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges, also matches this string theory index. To achieve such a match we compute the one-loop determinant arising in the localization calculation for all $\mathcal{N}=2$ supergravity supermultiplets in the $\mathcal{N}=8$ gravity supermultiplet. Furthermore, we carefully account for the contribution of boundary zero-modes, that can be seen as arising from the zero-temperature limit of the $\mathcal{N}=4$ super-Schwarzian, and show that performing the exact path integral over such modes provides a critical contribution needed for the match to be achieved. A discussion about the importance of such zero-modes in the wider context of all extremal black holes is presented in a companion paper.\] # Iliesiu, Murthy, Turiaci (b) ## Black hole microstate counting from the gravitational path integral \[Links: [arXiv](https://arxiv.org/abs/2209.13602), [PDF](https://arxiv.org/pdf/2209.13602.pdf)\] \[Abstract: \] # Jafferis, Kolchmeyer, Mukhametzhanov, Sonner (Short) ## Matrix models for eigenstate thermalization \[Links: [arXiv](https://arxiv.org/abs/2209.02130), [PDF](https://arxiv.org/pdf/2209.02130.pdf)\] \[Abstract: We develop a class of matrix models which implement and formalize the '[[0040 Eigenstate thermalisation hypothesis|eigenstate thermalization hypothesis]]' (ETH) and point out that in general these models must contain non-Gaussian corrections, already in order to correctly capture thermal mean-field theory, or to capture non-trivial [[0482 Out-of-time-order correlator|OTOCs]] as well as their higher-order generalizations. We develop the framework of these '[[0587 ETH matrix model|ETH matrix models]]', and put it in the context of recent studies in statistical physics incorporating higher statistical moments into the ETH ansatz. We then use the 'ETH matrix model' in order to develop a matrix-integral description of [[0050 JT gravity|JT gravity]] coupled to a single scalar field in the bulk. This particular example takes the form of a double-scaled ETH matrix model with non-Gaussian couplings matching disk correlators and the density of states of the gravitational theory. Having defined the model from the disk data, we present evidence that the model correctly captures the JT+matter theory with multiple boundaries, and conjecturally at higher genus. This is a shorter companion paper to the work [[2022#Jafferis, Kolchmeyer, Mukhametzhanov, Sonner (Long)|(1)]], serving both as a guide to the much more extensive material presented there, as well as developing its underpinning in statistical physics.\] # Jafferis, Kolchmeyer, Mukhametzhanov, Sonner (Long) ## JT gravity with matter, generalized ETH, and Random Matrices \[Links: [arXiv](https://arxiv.org/abs/2209.02131), [PDF](https://arxiv.org/pdf/2209.02131.pdf)\] \[Abstract: We present evidence for a duality between [[0050 JT gravity|Jackiw-Teitelboim gravity]] minimally coupled to a free massive scalar field and a single-trace two-matrix model. One matrix is the Hamiltonian $H$ of a holographic disorder-averaged quantum mechanics, while the other matrix is the light operator $\cal O$ dual to the bulk scalar field. The single-boundary observables of interest are thermal correlation functions of $\cal O$. We study the matching of the genus zero one- and two-boundary expectation values in the matrix model to the disk and cylinder Euclidean path integrals. The non-Gaussian statistics of the matrix elements of $\cal O$ correspond to a generalization of the ETH ansatz. We describe multiple ways to construct double-scaled matrix models that reproduce the gravitational disk correlators. One method involves imposing an operator equation obeyed by $H$ and $\cal O$ as a constraint on the two matrices. Separately, we design a model that reproduces certain [[0503 Double-scaled SYK|double-scaled SYK]] correlators that may be scaled once more to obtain the disk correlators. We show that in any single-trace, two-matrix model, the genus zero two-boundary expectation value, with up to one $\cal O$ insertion on each boundary, can be computed directly from all of the genus zero one-boundary correlators. Applied to the models of interest, we find that these cylinder observables depend on the details of the double-scaling limit. To the extent we have checked, it is possible to reproduce the gravitational double-trumpet, which is UV divergent, from a systematic classification of matrix model 't Hooft diagrams. The UV divergence indicates that the matrix integral saddle of interest is perturbatively unstable. A non-perturbative treatment of the matrix models discussed in this work is left for future investigations.\] # Jafferis, Zlokapa, Lykken, Kolchmeyer, Davis, Lauk, Neven, Spiropulu ## Traversable wormhole dynamics on a quantum processor \[Links: [Nature](https://www.nature.com/articles/s41586-022-05424-3)\] \[Abstract: The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The [[0001 AdS-CFT|anti-de Sitter (AdS)/conformal field theory correspondence or duality]] is the principal example of holography. The [[0201 Sachdev-Ye-Kitaev model|Sachdev–Ye–Kitaev]] (SYK) model of $N \gg 1$ Majorana fermions has features suggesting the existence of a gravitational dual in AdS$_2$, and is a new realization of holography. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured [[0220 ER=EPR|ER=EPR]] relation between entanglement and spacetime geometry through the [[0083 Traversable wormhole|traversable wormhole]] mechanism as implemented in the SYK model. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.\] ## Refs - comment by [[2023#Kobrin, Schuster, Yao]], reply to the comment in [[2023#Jafferis, Zlokapa, Lykken, Kolchmeyer, Davis, Lauk, Neven, Spiropulu]] ## Model - obtained by machine learning - unperturbed learned Hamiltonian: $\begin{aligned} H_0= & -0.36 \psi^1 \psi^2 \psi^4 \psi^5+0.19 \psi^1 \psi^3 \psi^4 \psi^7 -0.71 \psi^1 \psi^3 \psi^5 \psi^6\\&+0.22 \psi^2 \psi^3 \psi^4 \psi^6 +0.49 \psi^2 \psi^3 \psi^5 \psi^7\end{aligned}$ - perturbation: $H_1=0.3 \psi^1 \psi^2 \psi^3 \psi^5$ # Jorge-Diaz, Pasterski, Sharma ## Celestial amplitudes in an ambidextrous basis \[Links: [arXiv](https://arxiv.org/abs/2212.00962), [PDF](https://arxiv.org/pdf/2212.00962.pdf)\] \[Abstract: We start by constructing a conformally covariant improvement of the celestial [[0412 Light transform|light transform]] which keeps track of the mixing between incoming and outgoing states under finite Lorentz transformations in $\mathbb{R}^{2,2}$. We then compute generic 2, 3 and 4-point celestial amplitudes for massless external states in the [[0506 Ambidextrous basis|ambidextrous basis]] prepared by composing this $\mathrm{SL}(2,\mathbb{R})$ intertwiner with the usual celestial map between momentum and boost eigenstates. The results are non-distributional in the celestial coordinates $(z,\bar{z})$ and conformally covariant in all scattering channels. Finally, we focus on the tree level 4-gluon amplitude where we present a streamlined route to the ambidextrous correlator based on Grassmannian formulae and examine its alpha space representation. In the process, we gain insights into the operator dictionary and CFT data of the holographic dual.\] # Kapec, Law, Narayanan ## Soft Scalars and the Geometry of the Space of Celestial CFTs \[Links: [arXiv](https://arxiv.org/abs/2205.10935), [PDF](https://arxiv.org/pdf/2205.10935.pdf)\] \[Abstract: Known examples of the holographic dictionary in asymptotically Anti-de Sitter spacetimes equate moduli spaces of bulk vacua with conformal manifolds in the dual quantum field theory. We demonstrate that the same identification holds for gravity in asymptotically flat spacetimes in any dimension, in accord with expectations derived from the [[0010 Celestial holography|celestial conformal field theory]] (CCFT) formalism. Soft limits of moduli scalars described by the sigma model are universal, and relate to parallel transport of $S$-matrix observables over the moduli space of bulk vacua. The leading "soft moduli operator" is the [[0039 Shadow transform|shadow transform]] of a dimension $\Delta=d$ marginal operator $M(x)$. The universal form of the soft limit guarantees that $M(x)$ acts as a marginal deformation in the CCFT$_d$, and coherent states of the soft scalars correspond to finite deformations along the conformal manifold. This manifold typically has curvature, which is captured by the antisymmetric double-soft theorem and which reflects the Berry curvature in CCFT$_d$. We also compute the [[0079 Mellin transform|Mellin-transformed]] four-point function in the sigma model and compare to a formula of Kutasov for the curvature of the conformal manifold.\] # Kaplan, Marolf ## The action of HRT-areas as operators in semiclassical gravity \[Links: [arXiv](https://arxiv.org/abs/2203.04270), [PDF](https://arxiv.org/pdf/2203.04270.pdf)\] \[Abstract: \] ## Summary - shows that the HRT operator boosts the entanglement wedge on one side of the HRT surface relative to the entanglement wedge on the other side in ==Einstein gravity minimally coupled to matter==; more precisely, the HRT area flow is a [[0483 Boundary-condition-preserving kink transformation|BC-preserving kink transformation]] - computes the commutator between operators in Einstein gravity with semi-classical approximation, where the commutators are [[0360 Poisson bracket|Poisson brackets]] or [[0150 Peierls bracket|Peierls brackets]] # Karch, Sun, Uhlemann ## Double holography in string theory \[Links: [arXiv](https://arxiv.org/abs/2206.11292), [PDF](https://arxiv.org/pdf/2206.11292.pdf)\] \[Abstract: We develop the notion of [[0544 Double holography|double holography]] in Type IIB string theory realizations of braneworld models. The Type IIB setups are based on the [[0181 AdS-BCFT|holographic duals]] of 4d [[0548 Boundary CFT|BCFTs]] comprising 4d $\mathcal N=4$ SYM on a half space coupled to 3d $\mathcal N=4$ SCFTs on the boundary. Based on the concrete BCFTs and their brane construction, we provide microscopic realizations of the intermediate holographic description, obtained by dualizing only the 3d degrees of freedom. Triggered by recent observations in bottom-up models, we discuss the causal structures in the full BCFT duals and intermediate descriptions. This confirms qualitative features found in the bottom-up models but suggests a refinement of their interpretation.\] # Katona, Lucietti ## Supersymmetric black holes with a single axial symmetry in five dimensions \[Links: [arXiv](https://arxiv.org/abs/2206.11782), [PDF](https://arxiv.org/pdf/2206.11782.pdf)\] \[Abstract: We present a classification of asymptotically flat, supersymmetric black hole and soliton solutions of five-dimensional minimal [[0332 Supergravity|supergravity]] that admit a single axial symmetry which 'commutes' with the [[0359 Supersymmetry|supersymmetry]]. This includes the first examples of five-dimensional black hole solutions with exactly one axial Killing field that are smooth on and outside the horizon. The solutions have similar properties to the previously studied class with biaxial symmetry, in particular, they have a Gibbons-Hawking base and the harmonic functions must be of multi-centred type with the centres corresponding to the connected components of the horizon or fixed points of the axial symmetry. We find a large moduli space of black hole and soliton spacetimes with non-contractible 2-cycles and the horizon topologies are $S^3$, $S^1\times S^2$ and lens spaces $L(p,1)$.\] ## Comments - uses the definition of [[1996#Fatibene, Ferraris, Francaviglia, Godina (Aug)]] for the [[0527 Lie derivative of spinor fields|Lie derivative of spinors]] # Kehagias, Perrone, Riotto ## Quasinormal Modes and Love Numbers of Kerr Black Holes from AdS$_2$ Black Holes \[Links: [arXiv](https://arxiv.org/abs/2211.02384), [PDF](https://arxiv.org/pdf/2211.02384.pdf)\] \[Abstract: We show that the linear perturbations of any spin field in the near-zone limit of the Kerr black hole are identical to those of an AdS$_2$ black hole which enjoys the same basic properties of the Kerr black hole. Thanks to this identification, we calculate the spectrum of the [[0325 Quasi-normal modes|quasinormal modes]] and the [[0581 Tidal Love numbers|Love numbers]] of Kerr black holes using an AdS$_2$/CFT$_1$ correspondence and a group theoretical approach.\] # Khuri, Kopinski ## Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS \[Links: [arXiv](https://arxiv.org/abs/2209.01234), [PDF](https://arxiv.org/pdf/2209.01234.pdf)\] \[Abstract: We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an application of this result, we verify the [[0476 Penrose inequality|Penrose inequality]] for certain perturbations of Schwarzschild Anti-de Sitter black hole initial data.\] # Kim, Preskill ## Complementarity and the unitarity of the black hole $S$-matrix \[Links: [arXiv](https://arxiv.org/abs/2212.00194), [PDF](https://arxiv.org/pdf/2212.00194.pdf)\] \[Abstract: Recently, [[2022#Akers, Engelhardt, Harlow, Penington, Vardhan|Akers et al.]] proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole $S$-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the $S$-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the $S$-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the $S$-matrix of an evaporating black hole has polynomial computational complexity.\] ## Refs - talk at [[Rsc0048 MURI 2022|MURI 2022]] ## Set up - the observer is in the asymptotic region (far away from BH) - throw a robot into the BH (not the observer) ## Conclusions - unitarity is preserved in a non-trivial way # Kudler-Flam, Kusuki ## On Quantum Information Before the Page Time \[Links: [arXiv](https://arxiv.org/abs/2212.06839), [PDF](https://arxiv.org/pdf/2212.06839.pdf)\] \[Abstract: While recent progress in the [[0131 Information paradox|black hole information problem]] has shown that the entropy of Hawking radiation follows a unitary Page curve, the quantum state of Hawking radiation prior the Page time is still treated as purely thermal, containing no information about the microstructure of the black hole. We demonstrate that there is significant quantum information regarding the quantum state of the black hole in the Hawking radiation prior to the Page time. By computing of the quantum fidelity in a 2D boundary conformal field theory ([[0181 AdS-BCFT|BCFT]]) model of black hole evaporation, we demonstrate that an observer outside of an evaporating black hole may distinguish different black holes via measurements of the Hawking radiation at $any$ time during the evaporation process, albeit with an exponentially large number of measurements. Furthermore, our results are universal, applicable to general BCFTs including those with large central charge and rational BCFTs. The techniques we develop for computing the fidelity are more generally applicable to excited states in CFT. As such, we are able to characterize more general aspects of thermalization in 2D conformal field theory.\] # Kudler-Flam, Rath (Mar) ## Large and Small Corrections to the JLMS Formula from Replica Wormholes \[Links: [arXiv](https://arxiv.org/abs/2203.11954), [PDF](https://arxiv.org/pdf/2203.11954.pdf)\] \[Abstract: \] ## Refs - [[0048 JLMS]] # Law, Parmentier ## Black hole scattering and partition functions \[Links: [arXiv](https://arxiv.org/abs/2207.07024), [PDF](https://arxiv.org/pdf/2207.07024.pdf)\] \[Abstract: When computing the ideal gas thermal canonical partition function for a scalar outside a black hole horizon, one encounters the divergent single-particle density of states (DOS) due to the continuous nature of the normal mode spectrum. Recasting the Lorentzian field equation into an effective 1D scattering problem, we argue that the scattering phases encode non-trivial information about the DOS and can be extracted by “renormalizing” the DOS with respect to a reference. This defines a renormalized free energy up to an arbitrary additive constant. Interestingly, we discover that the 1-loop Euclidean path integral, as computed by the [[2009#Denef, Hartnoll, Sachdev|Denef-Hartnoll-Sachdev formula]], fixes the reference free energy to be that on a Rindler-like region, and the renormalized DOS captures the quasinormal modes for the scalar. We support these claims with the examples of scalars on static [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]], Nariai black holes and the de Sitter static patch. For black holes in asymptotically flat space, the renormalized DOS is captured by the phase of the transmission coefficient whose magnitude squared is the greybody factor. We comment on possible connections with recent works from an algebraic point of view.\] ## Refs - follow-up [[2022#Grewal, Law, Parmentier]] ## Summary - Lorentzian analogue of Euclidean path integral computing 1-loop free energy ## Euclidean path integral - including the 1-loop contribution from a scalar gives$Z_{\mathrm{PI}}\left(m^2\right)=\int \mathcal{D} \phi e^{-\frac{1}{2} \int(\nabla \phi)^2+m^2 \phi^2}=\frac{1}{\operatorname{det}\left(-\nabla^2+m^2\right)^{1 / 2}}$ ## Setup - static spherically symmetric metric - non-zero temperature ## Lorentzian - naively expect we can just do a trace on the exterior of a BH - if the spectrum of $\hat H$ is discrete, easier; but the spectrum is continuous! - confusing - in particular, the density of states (of single particle) is $\rho(\omega)=\infty$ - hints from de Sitter - periodically identify the static patch of dS -> get a sphere where calculation can be done - observation 1: QNM character and single-particle DOS. - if we replace DOS with the one we have for a discrete DOS, found that $Z_{PI}=\tilde{Z}_{bulk}$ for scalars and spinors - observation 2: horizon edge partition function - for non-zero spins, it is not that simple! - the difference is a factor that is related to the bifurcate sphere (so they are called edge modes) - $Z_{PI}=\tilde{Z}_{bulk}/Z_{edge}$ ## Scattering problem - a scattering problem from past horizon to future horizon - can add a cut-off (with e.g. Dirichlet BC) at some finite radius; call it a brick wall - now we are computing normal modes (not QNM) - get infinity as cut-off is removed - compare with a reference situation with e.g. no potential - then get finite result! - can have various choices of $\tilde{Z}_{bulk}$ (the one earlier is a specific choice) ## What is special about Euclidean PI - it pick up a special reference: Rindler wedge ## Bulk-edge split - question: how to split it in general - for non-zero spins, the partition function is not $\tilde{Z}_{bulk}$ ## Remarks - non-perturbative formulation? - [[0415 Von Neumann algebra]]: divergence related to Type III etc - [[0019 Covariant phase space]]? - near horizon [[0459 Soft hair|soft]] physics? - boundary perspective in AdS/CFT? ## My questions - is it important that the spinning fields are gauged (e.g. Maxwell and gravity)? - i.e. are the edge modes coming from gauge symmetry or not - my A: not related to the usual edge modes # Leutheusser, Liu ## Subalgebra-subregion duality: emergence of space and time in holography \[Links: [arXiv](https://arxiv.org/abs/2212.13266), [PDF](https://arxiv.org/pdf/2212.13266.pdf)\] \[Abstract: In [[0001 AdS-CFT|holographic duality]], a higher dimensional quantum gravity system emerges from a lower dimensional conformal field theory (CFT) with a large number of degrees of freedom. We propose a formulation of duality for a general causally complete bulk spacetime region, called subalgebra-subregion duality, which provides a framework to describe how geometric notions in the gravity system, such as spacetime subregions, different notions of times, and causal structure, emerge from the dual CFT. Subalgebra-subregion duality generalizes and brings new insights into subregion-subregion duality (or equivalently [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]]). It provides a mathematically precise definition of subregion-subregion duality and gives an independent definition of entanglement wedges without using entropy. Geometric properties of entanglement wedges, including those that play a crucial role in interpreting the bulk as a [[0146 Quantum error correction|quantum error correcting code]], can be understood from the duality as the geometrization of the additivity anomaly of certain algebras. Using general boundary subalgebras rather than those associated with geometric subregions makes it possible to find duals for general bulk spacetime regions, including those not touching the boundary. Applying subalgebra-subregion duality to a boundary state describing a single-sided black hole also provides a precise way to define mirror operators.\] # Levine, Shaghoulian ## Encoding beyond cosmological horizons in dS JT gravity \[Links: [arXiv](https://arxiv.org/abs/2204.08503), [PDF](https://arxiv.org/pdf/2204.08503.pdf)\] \[Abstract: \] ## Summary - *presents* a paradox related to No-cloning theorem when two observers can encode the same information beyond each of their horizons - *resolves* the paradox in controlled examples using path integrals ## The resolution - whether or not the geometry in Bob’s distinct inflating region is taken to be frozen or not can have a drastic effect on Alice’s ability to reconstruct operators in Bob’s region (and vice versa for Bob) - for most “natural” choices of state on the two asymptotic regions, the *dominant* saddle in the semi-classical path integral is one where Alice and Bob’s regions exist in their own, *disconnected* spacetimes - => no overlap in their accessible regions - => no cloning - **on the other hand**, if we want to dominant saddle to host both Bob and Alice in the same region, one needs to change the path integral prescription (by acting with an operator) which *entangles* the two asymptotic regions # Lin ## The bulk Hilbert space of double scaled SYK \[Links: [arXiv](https://arxiv.org/abs/2208.07032), [PDF](https://arxiv.org/pdf/2208.07032.pdf)\] \[Abstract: The emergence of the bulk Hilbert space is a mysterious concept in holography. In [[2018#Berkooz, Isachenkov, Narovlansky, Torrents|arXiv:1811.02584]], the [[0201 Sachdev-Ye-Kitaev model|SYK]] model was solved in the double scaling limit by summing chord diagrams. Here, we explicitly construct the bulk Hilbert space of [[0503 Double-scaled SYK|double scaled SYK]] by slicing open these chord diagrams; this Hilbert space resembles that of a lattice field theory where the length of the lattice is dynamical and determined by the chord number. Under a calculable bulk-to-boundary map, states of fixed chord number map to particular entangled 2-sided states with a corresponding size. This [[0026 Bulk reconstruction|bulk reconstruction]] is well-defined even when quantum gravity effects are important. Acting on the double scaled Hilbert space is a Type II$_1$ [[0415 Von Neumann algebra|algebra]] of observables, which includes the Hamiltonian and matter operators. In the appropriate quantum Schwarzian limit, we also identify the JT gravitational algebra including the physical $\rm{SL}(2,\mathbb{R})$ symmetry generators, and obtain explicit representations of the algebra using chord diagram techniques.\] # Lin, Maldacena, Rozenberg, Shan (a) ## Holography for people with no time \[Links: [arXiv](https://arxiv.org/abs/2207.00407), [PDF](https://arxiv.org/pdf/2207.00407)\] \[Abstract: We study the gravitational description of extremal supersymmetric black holes. We point out that the AdS$_2$ near horizon geometry can be used to compute interesting observables, such as correlation functions of operators. In this limit, the Hamiltonian is zero and correlation functions are time independent. We discuss some possible implications for the gravity description of black hole microstates. We also compare with numerical results in a supersymmetric version of [[0201 Sachdev-Ye-Kitaev model|SYK]]. These results can also be interpreted as providing a construction of wormholes joining two extremal black holes. This is the short version of a longer and more technical companion paper [arXiv:2207.00408](https://arxiv.org/abs/2207.00408).\] # Lin, Maldacena, Rozenberg, Shan (b) ## Looking at supersymmetric black holes for a very long time \[Links: [arXiv](https://arxiv.org/abs/2207.00408), [PDF](https://arxiv.org/pdf/2207.00408)\] \[Abstract: We study correlation functions for extremal supersymmetric black holes. It is necessary to take into account the strongly coupled nature of the boundary supergraviton mode. We consider the case with ${\cal N}=2$ supercharges which is the minimal amount of supersymmetry needed to give a large ground state degeneracy, separated from the continuum. Using the exact solution for this theory we derive formulas for the two point function and we also give integral expressions for any n-point correlator. These correlators are time independent at large times and approach constant values that depend on the masses and couplings of the bulk theory. We also explain that in the non-supersymmetric case, the correlators develop a universal time dependence at long times. This paper is the longer companion paper of [arXiv:2207.00407](https://arxiv.org/abs/2207.00407).\] # Lin, Ning, Chen ## Weak Cosmic Censorship and Second Law of Black Hole Thermodynamics \[Links: [arXiv](https://arxiv.org/abs/2211.17225), [PDF](https://arxiv.org/pdf/2211.17225.pdf)\] \[Abstract: Infalling matter may destroy a black hole and expose the naked singularity. Thus, Penrose proposed the [[0221 Weak cosmic censorship|weak cosmic censorship conjecture]] to avoid such a possibility. On the other hand, if the black hole is not destroyed by infalling matter, from the [[0005 Black hole second law|second law of black hole thermodynamics]], the black hole entropy should increase due to the information carried by the infalling matter. In this work, we demonstrate by examples of perturbative near-extremal black holes in [[0006 Higher-derivative gravity|higher derivative gravity theories]], that the second law implies weak cosmic censorship. We also compare our proposal to the one developed by [[2017#Sorce, Wald|Sorce and Wald]] based on the first law of black hole thermodynamics, and show that the latter fails to yield weak cosmic censorship in such cases. Finally, we give a proof of our proposal for generic gravity theories.\] ## Comment - by second law, they mean [[0409 Physical process version of the first law|physical process version of the first law]] - mathematically, it is no different from the standard first law ## Summary - a connection between [[0409 Physical process version of the first law|physical process version of the first law]] and [[0221 Weak cosmic censorship|weak cosmic censorship]] demonstrated using [[0006 Higher-derivative gravity|HDG]] ## Intuition - for RN black hole, $\Delta r_{+}=\Delta m+\Delta W(m, q) /(2 \sqrt{W(m, q)})$, so $\Delta W>0$ ensures $\Delta r_+>0$ - n.b. the converse is not clear in this example ## Condition for no violation of WCC - a black hole (i.e. no naked singularity) is defined by the inequality $W(m,q)\ge0$ for some function $W$ that depends on the theory - [[0221 Weak cosmic censorship|WCC]] is defined to hold if $W(m+\Delta m, q+\Delta q) \geq 0$ for all physically allowed $\Delta m$ and $\Delta q$ # Lin, Yang ## Double copy for tree-level form factors I: foundations \[Links: [arXiv](https://arxiv.org/abs/2211.01386), [PDF](https://arxiv.org/pdf/2211.01386.pdf)\] \[Abstract: The [[0067 Double copy|double-copy]] construction for [[0566 Form factors|form factors]] was reported in our previous work, in which a novel mechanism of turning spurious poles in Yang-Mills theory into physical poles in gravity is observed. This paper is the first of a series of two papers providing the details as well as various generalizations on the double-copy construction of tree-level form factors. In this paper, we establish the generic formalism by focusing on the form factor of ${\rm tr}(\phi^2)$ in the Yang-Mills-scalar theory. A thorough discussion is given on the emergence of the "spurious"-type poles and various related properties. We also discuss two generalizations: the Higgs amplitudes in QCD, and the ${\rm tr}(\phi^2)$ form factors with multiple external scalar states.\] ## Refs - part II: [[2023#Lin, Yang]] # Loganayagam, Rangamani, Virrueta ## Holographic thermal correlators: A tale of Fuchsian ODEs and integration contours \[Links: [arXiv](https://arxiv.org/abs/Holographic thermal correlators: A tale of Fuchsian ODEs and integration contours), [PDF](https://arxiv.org/pdf/Holographic thermal correlators: A tale of Fuchsian ODEs and integration contours.pdf)\] \[Abstract: We analyze real-time thermal correlation functions of conserved currents in holographic field theories using the [[0440 grSK geometry|grSK geometry]], which provides a contour prescription for their evaluation. We demonstrate its efficacy, arguing that there are situations involving components of conserved currents, or derivative interactions, where such a prescription is, in fact, essential. To this end, we first undertake a careful analysis of the linearized wave equations in AdS black hole backgrounds and identify the ramification points of the solutions as a function of (complexified) frequency and momentum. All the equations we study are Fuchsian with only regular singular points that for the most part are associated with the geometric features of the background. Special features, e.g., the appearance of apparent singular points at the horizon, whence outgoing solutions end up being analytic, arise at higher codimension loci in parameter space. Using the grSK geometry, we demonstrate that these apparent singularities do not correspond to any interesting physical features in higher-point functions. We also argue that the [[0042 Schwinger-Keldysh techniques|Schwinger-Keldysh]] collapse and KMS conditions, implemented by the grSK geometry, continue to hold even in the presence of such singularities. For charged black holes above a critical charge, the energy density operator does not possess an exponentially growing mode, associated with '[[0179 Pole skipping|pole-skipping]]' (from one such apparent singularity). Our analysis suggests that the connection between the scrambling physics of black holes and energy transport has, at best, a limited domain of validity.\] # Maiellaro, Marino, Illuminati ## Squashed entanglement: order parameter for topological superconductors \[Links: [arXiv](https://arxiv.org/abs/2201.12035), [PDF](https://arxiv.org/pdf/2201.12035.pdf)\] \[Abstract: \] ## Refs - [[0158 Topological order]] # Marolf, Santos (Feb, a) ## The Canonical Ensemble Reloaded: The Complex-Stability of Euclidean quantum gravity for Black Holes in a Box \[Links: [arXiv](https://arxiv.org/abs/2202.11786), [PDF](https://arxiv.org/pdf/2202.11786.pdf)\] \[Abstract: We revisit the stability of black hole saddles for the Euclidean path integral describing the canonical partition function $Z(\beta)$ for gravity inside a spherical reflecting cavity. The boundary condition at the cavity wall couples the transverse-traceless (TT) and pure-trace modes that are traditionally used to describe fluctuations about Euclidean Schwarzschild black holes in infinite-volume asymptotically flat and asymototically AdS spacetimes. This coupling obstructs the familiar Gibbons-Hawking-Perry treatment of the conformal factor problem, as Wick rotation of the pure-trace modes would require that the TT modes be rotated as well. The coupling also leads to complex eigenvalues for the Ł operator. We nevertheless find that the Ł operator can be diagonalized in the space of coupled modes. This observation allows the eigenmodes to define a natural generalization of the pure-trace Wick-rotation recipe used in infinite volume, with the result that a mode with eigenvalue $\lambda$ is stable when ${\rm Re}\,\lambda > 0$. In any cavity, and with any cosmological constant $\Lambda \le 0$, we show this recipe to reproduce the expectation from black hole thermodynamics that large Euclidean black holes define stable saddles while the saddles defined by small Euclidean black holes are unstable.\] ## Related - [[0446 Conformal factor problem]] - [[0443 Gubser-Mitra conjecture|correlated stability conjecture]] # Marolf, Santos (Feb, b) ## Stability of the microcanonical ensemble in Euclidean Quantum Gravity \[Links: [arXiv](https://arxiv.org/abs/2202.12360), [PDF](https://arxiv.org/pdf/2202.12360.pdf)\] \[Abstract: This work resolves a longstanding tension between the physically-expected stability of the [[0462 Microcanonical ensemble|microcanonical ensemble]] for gravitating systems and the fact that the known negative mode of the asymptotically flat Schwarzschild black hole decays too rapidly at infinity to affect the [[0487 ADM mass|ADM energy]] boundary term at infinity. The key to our study is that we fix an appropriate *off-shell* notion of energy, which we obtain by constructing the microcanonical partition function as an integral transform of the canonical partition function. After applying the rule-of-thumb for Wick rotations from our recent companion paper to deal with the conformal mode problem of Euclidean gravity, we find a positive definite action for linear perturbations about any Euclidean Schwarzchild (-AdS) black hole. Most of our work is done in a cavity with reflecting boundary conditions, but the cavity wall can be removed by taking an appropriate limit.\] ## Refs - canonical ensemble: [[2022#Marolf, Santos (Feb, a)]] ## Summary - uses a notion of *off-shell energy* to establish the positive-definiteness of the action upon linear perturbations of the Euclidean BH ## Tension - in flat space, the negative mode decays at infinity and does not contribute to the [[0487 ADM mass|ADM energy]] boundary term; therefore, fixing the boundary cannot remove the negative mode. ## Microscopic path integral - define $Z_{\text {micro }}\left(E_0\right)=e^{\beta_0 E} \int_{T \in \mathbb{R}} \mathrm{d} T \int \mathcal{D} \mathrm{g}_{R, \beta_0+i T} f_{E_0}(T) e^{-I[g]}$where$ f_{E_0}(T)=e^{-i E_0 T} e^{-\sigma^2 T^2 / 2 G}=e^{-i e_0 T / G} e^{-\sigma^2 T^2 / 2 G} $ - then do the $T$ integral first - key feature: restriction to static metrics implies that the action is linear in $\beta$ # Mars, Sanchez-Perez ## Double Null Data and the Characteristic Problem in General Relativity \[Links: [arXiv](https://arxiv.org/abs/2205.15267), [PDF](https://arxiv.org/pdf/2205.15267.pdf)\] \[Abstract: General hypersurfaces of any causal character can be studied abstractly using the hypersurface data formalism. In the null case, we write down all tangential components of the ambient Ricci tensor in terms of the abstract data. Using this formalism, we formulate and solve in a completely abstract way the characteristic Cauchy problem of the Einstein vacuum field equations. The initial data is detached from any spacetime notion, and it is fully diffeomorphism and gauge covariant. The results of this paper put the characteristic problem on a similar footing as the standard Cauchy problem in General Relativity.\] # Mason ## Gravity from holomorphic discs and celestial $Lw_{1+\infty}$ symmetries \[Links: [arXiv](https://arxiv.org/abs/2212.10895), [PDF](https://arxiv.org/pdf/2212.10895.pdf)\] \[Abstract: In split signature, global twistor constructions for conformally [[0234 Self-dual gravity|self-dual (SD) gravity]] and [[0136 Self-dual Yang-Mills|Yang-Mills]] construct solutions from twistor data that can be expressed in terms of free functions without gauge freedom. This is developed for asymptotically flat SD gravity to give a fully nonlinear encoding of the asymptotic gravitational data in terms of a real homogeneous generating function h on the real twistor space. The recently discovered $Lw_{1+\infty}$ celestial symmetries, when real, act locally as passive Poisson diffeomorphisms on the real twistor space. The twistor data, $h$, generates an imaginary such Poisson transformation that then generates the gravitational field by shifting the real slice of the twistor space. The twistor chiral sigma models, whose correlators yield the Einstein gravity tree-level $S$-matrix, are reformulated as theories of holomorphic discs in twistor space whose boundaries lie on the deformed real slice determined by $h$. The real $Lw_{1+\infty}$ symmetries act on the corresponding formula for the $S$-matrix geometrically with vanishing Noether currents, but imaginary generators yield graviton vertex operators that generate gravitons in the perturbative expansion. A generating function for the all plus 1-loop amplitude, the analogous framework for Yang-Mills, possible interpretations in Lorentz signature and similar open string formulations of [[0497 Twistor string theory|twistor]] and [[0348 Ambitwistor strings|ambitwistor]] strings in 4d in split signature, are briefly discussed.\] # Matsuo ## Fluid model of black hole/string transition \[Links: [arXiv](https://arxiv.org/abs/2205.15976), [PDF](https://arxiv.org/pdf/2205.15976.pdf)\] \[Abstract: \] ## Summary - shows that the stress tensor of [[0323 Horowitz-Polchinski solution]] approximately takes the form of a perfect fluid - solves for the spacetime solution in the fluid model # Maxfield, Wang ## Gravitating spinning strings in AdS3 \[Links: [arXiv](https://arxiv.org/abs/2203.02492), [PDF](https://arxiv.org/pdf/2203.02492.pdf)\] \[Abstract: \] # May ## Complexity and entanglement in non-local computation and holography \[Links: [arXiv](https://arxiv.org/abs/2204.00908), [PDF](https://arxiv.org/pdf/2204.00908.pdf)\] \[Abstract: \] ## Summary - *asks* how the existence of the boundary description, and in particular the finite entanglement available there, constrains computation in the bulk # May, Sorce, Yoshida ## The connected wedge theorem and its consequences \[Links: [arXiv](https://arxiv.org/abs/2210.00018), [PDF](https://arxiv.org/pdf/2210.00018.pdf)\] \[Abstract: In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the $n$-to-$n$ connected wedge theorem, which considers $n$ input and $n$ output locations at the boundary of an asymptotically AdS$_{2+1}$ spacetime described by [[0001 AdS-CFT|AdS/CFT]]. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of $n$ associated regions in the boundary will have extensive-in-$N$ [[0300 Mutual information|mutual information]] across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The $n$-to-$n$ connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-$N$ entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting. Our theorem generalizes the 2-to-2 connected wedge theorem proven in [arXiv:1912.05649](https://arxiv.org/abs/1912.05649). We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions.\] # Mazloumi, Stieberger ## Intersections of Twisted Forms: New theories and Double copies \[Links: [arXiv](https://arxiv.org/abs/2212.12535), [PDF](https://arxiv.org/pdf/2212.12535.pdf)\] \[Abstract: Tree–level scattering amplitudes of particles have a geometrical description in terms of intersection numbers of pairs of twisted differential forms on the moduli space of Riemann spheres with punctures. We customize a catalog of twisted differential forms containing both already known and new differential forms. By pairing elements from this list intersection numbers of various theories can be furnished to compute their scattering amplitudes. Some of the latter are familiar through their CHY description, but others are unknown. Likewise, certain pairings give rise to various known and novel [[0067 Double copy|double–copy]] constructions of spin– two theories. This way we find double copy constructions for many theories, including higher derivative gravity, (partial massless) bimetric gravity and some more exotic theories. Furthermore, we present a derivation of amplitude relations in intersection theory.\] # Melton, Narayanan, Strominger ## Deforming Soft Algebras for Gauge Theory \[Links: [arXiv](https://arxiv.org/abs/2212.08643), [PDF](https://arxiv.org/pdf/2212.08643.pdf)\] \[Abstract: Symmetry algebras deriving from towers of [[0009 Soft theorems|soft theorems]] can be deformed by a short list of higher-dimension Wilsonian corrections to the effective action. We study the simplest of these deformations in gauge theory arising from a massless complex scalar coupled to $F^2$. The soft gauge symmetry '$s$-algebra', compactly realized as a higher-spin current algebra acting on the [[0022 Celestial sphere|celestial sphere]], is deformed and enlarged to an associative algebra containing soft scalar generators. This deformed soft algebra is found to be non-abelian even in abelian gauge theory. A two-parameter family of central extensions of the $s$-subalgebra are generated by shifting and decoupling the scalar generators. It is shown that these central extensions can also be generated by expanding around a certain non-trivial but Lorentz invariant [[0117 Shockwave|shockwave]] type background for the scalar field.\] ## Action $S=\int d^4 x\left(-\partial^\mu \phi \partial_\mu \bar{\phi}-\frac{1}{4} \operatorname{Tr} F_{\mu \nu} F^{\mu \nu}-\frac{\mu}{4}\left(\phi \operatorname{Tr} F_{\mu \nu}^{+} F^{+\mu \nu}+\bar{\phi} \operatorname{Tr} F_{\mu \nu}^{-} F^{-\mu \nu}\right)\right)$ # Mertens, Simon, Wong ## A proposal for 3d quantum gravity and its bulk factorization \[Links: [arXiv](https://arxiv.org/abs/2210.14196), [PDF](https://arxiv.org/pdf/2210.14196.pdf)\] \[Abstract: Recent progress in [[0001 AdS-CFT|AdS/CFT]] has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT. This theory can be viewed as a q-deformation and dimensional uplift of [[0050 JT gravity|JT gravity]]. Using this model, we show that the [[0004 Black hole entropy|Bekenstein-Hawking entropy]] of a two-sided black hole equals the bulk [[0301 Entanglement entropy|entanglement entropy]] of gravitational [[0556 Edge mode|edge modes]]. In the conventional Chern-Simons description, these black holes correspond to Wilson lines in representations of $PSL(2,\mathbb{R})\otimes PSL(2,\mathbb{R})$. We show that the correct calculation of gravitational entropy suggests we should interpret the bulk theory as an extended topological quantum field theory associated to the quantum semi-group $SL^+_{q}(2,\mathbb{R})\otimes SL^+_{q}(2,\mathbb{R})$. Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.\] # Mertens, Turiaci (Review) ## Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity \[Links: [arXiv](https://arxiv.org/abs/2210.10846), [PDF](https://arxiv.org/pdf/2210.10846.pdf)\] \[Abstract: We review recent developments in [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]]. This is a simple solvable model of quantum gravity in two dimensions (that arises e.g. from the s-wave sector of higher dimensional gravity systems with spherical symmetry). Due to its solvability, it has proven to be a fruitful toy model to analyze important questions such as the relation between black holes and [[0008 Quantum chaos|chaos]], the role of wormholes in black hole physics and holography, and the way in which [[0131 Information paradox|information]] that falls into a black hole can be recovered.\] # Milekhin, Popov ## Measurement-induced phase transition in teleportation and wormholes \[Links: [arXiv](https://arxiv.org/abs/2210.03083), [PDF](https://arxiv.org/pdf/2210.03083.pdf)\] \[Abstract: We demonstrate that some quantum teleportation protocols exhibit measurement induced phase transitions in [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev model]]. Namely, [[2017#Kitaev, Yoshida|Kitaev-Yoshida]] and [[2016#Gao, Jafferis, Wall|Gao-Jafferis-Wall]] protocols have a phase transition if we apply them at a large projection rate or at a large coupling rate respectively. It is well-known that at small rates they allow teleportation to happen only within a small time-window. We show that at large rates, the system goes into a new steady state, where the teleportation can be performed at any moment. In dual [[0050 JT gravity|Jackiw-Teitelboim gravity]] these phase transitions correspond to the formation of an eternal traversable wormhole. In the Kitaev-Yoshida case this novel type of wormhole is supported by continuous projections.\] # Milekhin, Tajdini ## Bra-ket wormholes and Casimir entropy \[Links: [arXiv](https://arxiv.org/abs/2212.08246), [PDF](https://arxiv.org/pdf/2212.08246.pdf)\] \[Abstract: [[0216 Bra-ket wormholes|Bra-ket wormholes]] are non-trivial saddles in Euclidean gravity. They have to be sustained by negative Casimir energy of matter fields inside the throat. However, Casimir energy is very sensitive to boundary conditions and in presence of gauge symmetries one has to integrate over all possible boundary conditions for the matter fields, as they are a part of bra-ket wormhole moduli. For non-Abelian gauge groups the corresponding measure for the boundary conditions, which we call Casimir entropy, is non-trivial and it competes with the Casimir energy. We find that for large gauge groups this significantly affects the bra-ket wormhole action and modifies the phase diagram. Despite that, we do not find any violations of [[0218 Strong subadditivity|strong subadditivity]] in the setup proposed by [[2020#Chen, Gorbenko, Maldacena|Chen, Gorbenko and Maldacena]].\] ## Summary - after taking into account of [[0216 Bra-ket wormholes|bra-ket wormholes]] phase diagram modified but [[0218 Strong subadditivity|strong subadditivity]] still holds - some saddles only exist after taking into account of Casimir energy: otherwise they just collapse ## Setup - long wormholes so only Casimir energy contributes # Miller, Strominger, Tropper, Wang ## Soft Gravitons in the BFSS Matrix Model \[Links: [arXiv](https://arxiv.org/abs/2208.14547), [PDF](https://arxiv.org/pdf/2208.14547.pdf)\] \[Abstract: [[0479 BFSS matrix model|BFSS]] proposed that asymptotically flat [[0517 M-theory|M-theory]] is dual to a large $N$ limit of the matrix quantum mechanics describing $N$ nonrelativistic D0-branes. Recent insights on the soft symmetries of any quantum theory of gravity in asymptotically flat space are applied to the BFSS matrix model. It is shown that soft gravitons are realized by submatrices whose rank is held fixed in the large $N$ M-theory limit, rather than the usual linear scaling with N for hard gravitons. The soft expansion is identified with the large $N$ expansion and the [[0009 Soft theorems|soft theorem]] becomes a universal formula for the quantum mechanical scattering of such submatrix excitations. This formula is shown to be the Ward identity of large type IIA $U(1)_{RR}$ asymptotic gauge symmetry in the matrix model, whose asymptotic boundaries are at future and past timelike infinity.\] # Miyaji, Murdia ## Holographic BCFT with a Defect on the End-of-the-World Brane \[Links: [arXiv](https://arxiv.org/abs/2208.13783), [PDF](https://arxiv.org/pdf/2208.13783)\] \[Abstract: In this paper, we propose a new gravity dual for a 2d [[0548 Boundary CFT|BCFT]] with two conformal boundaries by introducing a defect that connects the two End-of-the-World branes. We demonstrate that the BCFT dual to this bulk model exhibits a richer lowest spectrum. The corresponding lowest energy eigenvalue can continuously interpolate between $-\frac{\pi c}{24\Delta x}$ and $0$ where $\Delta x$ is the distance between the boundaries. This range was inaccessible to the conventional [[0181 AdS-BCFT|AdS/BCFT]] model with distinct boundary conditions. We compute the [[0007 RT surface|holographic entanglement entropy]] and find that it exhibits three different phases, one of which breaks the time reflection symmetry. We also construct a wormhole saddle, analogous to a 3d [[0206 Replica wormholes|replica wormhole]], which connects different boundaries through the AdS bulk. This saddle is present only if the BCFT is non-unitary and is always subdominant compared to the disconnected saddle.\] # Mizera, Pasterski ## Celestial Geometry \[Links: [arXiv](https://arxiv.org/abs/2204.02505), [PDF](https://arxiv.org/pdf/2204.02505.pdf)\] \[Abstract: [[0010 Celestial holography|Celestial holography]] expresses $\mathcal{S}$-matrix elements as correlators in a CFT living on the night sky. Poincaré invariance imposes additional selection rules on the allowed positions of operators. As a consequence, $n$-point correlators are only supported on certain patches of the celestial sphere, depending on the labeling of each operator as incoming/outgoing. Here we initiate a study of the celestial geometry, examining the kinematic support of celestial amplitudes for different crossing channels. We give simple geometric rules for determining this support. For $n\ge 5$, we can view these channels as tiling together to form a covering of the [[0022 Celestial sphere|celestial sphere]]. Our analysis serves as a stepping off point to better understand the analyticity of celestial correlators and illuminate the connection between the 4D kinematic and 2D CFT notions of crossing symmetry.\] # Monteiro ## From Moyal deformations to chiral higher-spin theories and to celestial algebras \[Links: [arXiv](https://arxiv.org/abs/2212.11266), [PDF](https://arxiv.org/pdf/2212.11266.pdf)\] \[Abstract: We study the connection of [[0513 Moyal deformation|Moyal deformations]] of [[0234 Self-dual gravity|self-dual gravity]] and [[0136 Self-dual Yang-Mills|self-dual Yang-Mils theory]] to chiral [[0421 Higher-spin gravity|higher-spin theories]], and also to deformations of operator algebras in [[0010 Celestial holography|celestial holography]]. The relation to Moyal deformations illuminates various aspects of the structure of chiral higher-spin theories. For instance, the appearance of the self-dual kinematic algebra in all the theories considered here leads via the double copy to vanishing tree-level scattering amplitudes. Regarding celestial holography, the Moyal deformation of self-dual gravity was recently shown to lead to the loop algebra of $W_{\wedge}$, and we obtain here the analogous deformation of a [[0069 Kac-Moody algebra|Kac-Moody algebra]] corresponding to Moyal-deformed self-dual Yang-Mills theory. We also introduce the celestial algebras for various chiral higher-spin theories.\] # Nahum, Roy, Vijay, Zhou ## Real-time correlators in chaotic quantum many-body systems \[Links: [arXiv](https://arxiv.org/abs/2205.11544), [PDF](https://arxiv.org/pdf/2205.11544.pdf)\] \[Abstract: We study real-time local correlators $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle$ in [[0008 Quantum chaos|chaotic]] quantum many-body systems. These correlators show universal structure at late times, determined by the dominant operator-space Feynman trajectories for the evolving operator $\mathcal{O}(\mathbf{x},t)$. The relevant trajectories involve the operator contracting to a point at both the initial and final time and so are structurally different from those dominating the [[0482 Out-of-time-order correlator|out-of-time-order correlator]]. In the absence of conservation laws, correlations decay exponentially: $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle\sim\exp(-s_\mathrm{eq} r(\mathbf{v}) t)$, where $\mathbf{v}= \mathbf{x}/ t$ defines a spacetime ray, and $r(\mathbf{v})$ is an associated decay rate. We express $r(\mathbf{v})$ in terms of cost functions for various spacetime structures. In 1+1D, operator histories can show a phase transition at a critical ray velocity $v_c$, where $r(\mathbf{v})$ is nonanalytic. At low $v$, the dominant Feynman histories are "fat": the operator grows to a size of order $t^\alpha\gg 1$ before contracting to a point again. At high $v$ the trajectories are "thin": the operator always remains of order-one size. In a Haar-random unitary circuit, this transition maps to a simple binding transition for a pair of random walks (the two spatial boundaries of the operator). In higher dimensions, thin trajectories always dominate. We discuss ways to extract the [[0167 Butterfly velocity|butterfly velocity]] $v_B$ from the time-ordered correlator, rather than the [[0482 Out-of-time-order correlator|OTOC]]. Correlators in the random circuit may alternatively be computed with an effective Ising-like model: a special feature of the Ising weights for the Haar brickwork circuit gives $v_c=v_B$. This work addresses lattice models, but also suggests the possibility of morphological phase transitions for real-time Feynman diagrams in quantum field theories.\] ## Summary - discuss ways of obtaining the [[0167 Butterfly velocity|butterfly velocity]] from a two-point function - uses a path integral approach for computing the real-time correlator # Numasawa, Tsiares ## Universal Dynamics of Heavy Operators in Boundary CFT$_2$ \[Links: [arXiv](https://arxiv.org/abs/2202.01633), [PDF](https://arxiv.org/pdf/2202.01633.pdf)\] \[Abstract: We derive a universal asymptotic formula for generic boundary conditions for the average value of the bulk-to-boundary and boundary [[0030 Operator product expansion|Operator Product Expansion]] coefficients of any unitary, compact two-dimensional [[0548 Boundary CFT|Boundary CFT]] (BCFT) with $c>1$. The asymptotic limit consists of taking one or more boundary primary operators -- which transform under a single copy of the [[0032 Virasoro algebra|Virasoro algebra]] -- to have parametrically large conformal dimension for fixed [[0033 Central charge|central charge]]. In particular, we find a *single* universal expression that interpolates between distinct heavy regimes, exactly as in the case of bulk OPE asymptotics ([[2019#Collier, Maloney, Maxfield, Tsiares]]). The expression depends universally on the boundary entropy and the central charge, and not on any other details of the theory. We derive these asymptotics by studying crossing symmetry of various correlation functions on higher genus Riemann surfaces with open boundaries. Essential in the derivation is the use of the irrational versions of the crossing kernels that relate holomorphic Virasoro blocks in different channels. Our results strongly suggest an extended version of the [[0040 Eigenstate thermalisation hypothesis|Eigenstate Thermalization Hypothesis]] for boundary OPE coefficients, where the hierarchy between the diagonal and non-diagonal term in the ansatz is further controlled by the boundary entropy. We finally comment on the applications of our results in the context of $\text{AdS}_3/\text{BCFT}_2$, as well as on the recent relation of BCFTs with lower dimensional models of evaporating black holes.\] # Omiya, Wei ## Causal Structures and Nonlocality in Double Holography \[Links: [arXiv](https://arxiv.org/abs/2107.01219), [PDF](https://arxiv.org/pdf/2107.01219.pdf)\] \[Abstract: [[0544 Double holography|Double holography]] plays a crucial role in recent studies of [[0304 Hawking radiation|Hawking radiation]] and [[0131 Information paradox|information paradox]] by relating an intermediate picture, in which a dynamical gravity living on an end-of-the-world brane is coupled to a non-gravitational heat bath, to a much better-understood [[0548 Boundary CFT|BCFT]] picture as well as a bulk picture. In this paper, causal structures in generic double holographic setups are studied. We find that the causal structure in the bulk picture is compatible with causality in the BCFT picture, thanks to a generalization of the [[0477 Gao-Wald theorem|Gao-Wald theorem]]. On the other hand, consistency with the bulk causal structure requires the effective theory in the intermediate picture to contain a special type of superluminal and nonlocal effect which is significant at long range or IR. These are confirmed by both geometrical analysis and commutators of microscopic fields. Subregion correspondences in double holography are discussed with the knowledge of this nonlocality. Possible fundamental origins of this nonlocality and its difference with other types of nonlocality will also be discussed.\] # Pappalardi, Kurchan ## Quantum bounds on the generalized Lyapunov exponents \[Links: [arXiv](https://arxiv.org/abs/2212.10123), [PDF](https://arxiv.org/pdf/2212.10123.pdf)\] \[Abstract: We discuss the generalized quantum [[0466 Lyapunov exponent|Lyapunov exponents]] $L_q$, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which plays the role of a large deviation function, obtained from the exponents $L_q$ via a Legendre transform. We show that such exponents obey a generalized [[0474 Chaos bound|bound to chaos]] due to the fluctuation-dissipation theorem, as already discussed in the literature. The bounds for larger $q$ are actually stronger, placing a limit on the large deviations of chaotic properties. Our findings at infinite temperature are exemplified by a numerical study of the kicked top, a paradigmatic model of [[0008 Quantum chaos|quantum chaos]].\] # Pasterski, Verlinde (Jan, a) ## Chaos in Celestial CFT \[Links: [arXiv](https://arxiv.org/abs/2201.01630), [PDF](https://arxiv.org/pdf/2201.01630.pdf)\] \[Abstract: [[0010 Celestial holography|Celestial holography]] proposes a duality between gravitational scattering in asymptotically flat spacetime and a conformal field theory living on the [[0022 Celestial sphere|celestial sphere]]. Its dictionary relates the infinite dimensional space-time symmetry group to [[0106 Ward identity|Ward identities]] of the CFT. The spontaneous breaking of these asymptotic symmetries governs the dynamics of the soft sector in the CFT. Here we show that this sector encodes non-trivial backreaction effects that exhibit characteristics of maximal quantum chaos. A key element in the derivation is the identification of the Hilbert space of celestial CFT, defined through radial quantization, with that of a constantly accelerating Rindler observer. From the point of view of the bulk, Rindler particles exhibit Lyapunov behavior due to [[0117 Shockwave|shockwave]] interactions that shift the observer horizon. From the point of view of the boundary, the superrotation Goldstone modes affect the relevant representations of the celestial Virasoro symmetry in a manner that induces Lyapunov behavior of [[0482 Out-of-time-order correlator|out-of-time-ordered]] celestial correlators.\] ## Refs - [[0008 Quantum chaos]] - [[0010 Celestial holography]] # Pasterski, Verlinde (Jan, b) ## Mapping SYK to the Sky \[Links: [arXiv](https://arxiv.org/abs/2201.05054), [PDF](https://arxiv.org/pdf/2201.05054.pdf)\] \[Abstract: The infrared behavior of gravity in 4D asymptotically flat spacetime exhibits a rich set of symmetries. This has led to a proposed [[0010 Celestial holography|holographic duality]] between the gravitational $\mathcal{S}$-matrix and a dual field theory living on the celestial sphere. Most of our current understanding of the dictionary relies on knowledge of the 4D bulk. As such, identifying intrinsic 2D models that capture the correct symmetries and [[0009 Soft theorems|soft]] dynamics of 4D gravity is an active area of interest. Here we propose that a 2D generalization of [[0201 Sachdev-Ye-Kitaev model|SYK]] provides an instructive toy model for the soft limit of the gravitational sector in 4D asymptotically flat spacetime. We find that the symmetries and soft dynamics of the 2D SYK model capture the salient features of the celestial theory: exhibiting [[0008 Quantum chaos|chaotic]] dynamics, [[0028 Conformal symmetry|conformal invariance]], and a [[0328 w(1+infinity)|w]]$_{1+\infty}$ symmetry. The holographic map from 2D SYK operators to the 4D bulk employs the Penrose [[0330 Twistor theory|twistor]] transform.\] # Post, van der Heijden, Verlinde ## A universe field theory for JT gravity \[Links: [arXiv](https://arxiv.org/abs/2201.08859), [PDF](https://arxiv.org/pdf/2201.08859.pdf)\] \[Abstract: We present a field theory description for the non-perturbative splitting and joining of baby universes in Euclidean [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]]. We show how the gravitational path integral, defined as a sum over topologies, can be reproduced from the perturbative expansion of a Kodaira-Spencer (KS) field theory for the complex structure deformations of the spectral curve. We use that the Schwinger-Dyson equations for the KS theory can be mapped to the topological recursion relations. We refer to this dual description of JT gravity as a 'universe field theory'. By introducing non-compact D-branes in the target space geometry, we can probe non-perturbative aspects of JT gravity. The relevant operators are obtained through a modification of the JT path integral with Neumann boundary conditions. The KS/JT identification suggests that the ensemble average for JT gravity can be understood in terms of a more standard open/closed duality in topological string theory.\] ## Summary - *presents* a field theory description for [[0051 Baby universes|baby universes]] in [[0050 JT gravity|JT]] - *maps* some non-perturbative expansion to properties of [[0389 Kodaira-Spencer field theory|KS field theory]] - *suggests* that [[0154 Ensemble averaging|ensemble averaging]] can be understood in terms of a more standard open/closed duality in topological string theory # Prabhu, Satishchandran, Wald ## Infrared Finite Scattering Theory in Quantum Field Theory and Quantum Gravity \[Links: [arXiv](https://arxiv.org/abs/2203.14334), [PDF](https://arxiv.org/pdf/2203.14334.pdf)\] \[Abstract: [[0295 Infrared divergences in scattering amplitude|Infrared (IR) divergences]] arise in scattering theory with massless fields and are manifestations of the [[0287 Memory effect|memory effect]]. There is nothing singular about states with memory, but they do not lie in the standard Fock space. IR divergences are artifacts of trying to represent states with memory in the standard Fock space. For collider physics, one can impose an IR cutoff and calculate inclusive quantities. But, this approach cannot treat memory as a quantum observable and is highly unsatisfactory if one views the S-matrix as fundamental in QFT and quantum gravity, since the S-matrix is undefined. For a well-defined S-matrix, it is necessary to define in/out Hilbert spaces with memory. Such a construction was given by [[0272 Faddeev-Kulish|Faddeev and Kulish]] (FK) for QED. Their construction "dresses" momentum states of the charged particles by pairing them with memory states of the electromagnetic field to produce states of vanishing large gauge charges at spatial infinity. However, in massless QED, due to [[0078 Collinear limit|collinear]] divergences, the "dressing" has an infinite energy flux so these states are unphysical. In Yang-Mills theory the "soft particles" used for dressing also contribute to the current flux, invalidating the FK procedure. In quantum gravity, the analogous FK construction would attempt to produce a Hilbert space of eigenstates of supertranslation charges at spatial infinity. However, we prove that there are no eigenstates of supertranslation charges except the vacuum. Thus, the FK construction fails in quantum gravity. We investigate some alternatives to FK constructions but find that these also do not work. We believe that to treat scattering at a fundamental level in quantum gravity - as well as in massless QED and YM theory - it is necessary to take an algebraic viewpoint rather than shoehorn the in/out states into some fixed Hilbert space. We outline the framework of such an IR finite scattering theory.\] ## Summary - [[0272 Faddeev-Kulish]] which works for massive QED fails for massless QED, YM and gravity -> massive QED is actually a 'fluke' - perfectly okay to talk about correlations function; but there is no reasonable Hilbert space for scattering ## Key idea - use charge conservation at spatial infinity # Ren, Spradlin, Srikant, Volovich ## On Effective Field Theories with Celestial Duals \[Links: [arXiv](https://arxiv.org/abs/2206.08322), [PDF](https://arxiv.org/pdf/2206.08322.pdf)\] \[Abstract: We show that associativity of the tree-level OPE in a [[0010 Celestial holography|celestial CFT]] imposes constraints on the coupling constants of the corresponding bulk theory. These constraints are the same as those derived in [[2021#Mago, Ren, Srikant, Volovich|arXiv:2111.11356]] from the [[0453 Jacobi identity or associativity of celestial OPE|Jacobi identity]] of the algebra of soft modes. The constrained theories are interesting as apparently well-defined celestial CFTs with a deformed [[0328 w(1+infinity)|w(1+infinity)]] symmetry algebra. We explicitly work out the ramifications of these constraints on scattering amplitudes involving gluons, gravitons and scalars in these theories. We find that all four-point amplitudes constructible solely from holomorphic or anti-holomorphic three-point amplitudes vanish on the support of these constraints, which implies that all purely holomorphic or purely anti-holomorphic higher-point amplitudes vanish.\] ## Summary - studies the ramifications of [[0453 Jacobi identity or associativity of celestial OPE|Jacobi identity or associativity of celestial OPE]] - most theories fail to satisfy the constraints including Heterotic string theory and closed bosonic string theory ## A theory that is okay - chiral higher-spin theory has: $\kappa_{s_{1}, s_{2}, s_{3}} \sim \frac{\left(l_{P}\right)^{s_{1}+s_{2}+s_{3}-1}}{\Gamma\left(s_{1}+s_{2}+s_{3}-1\right)} \quad s_{1}+s_{2}+s_{3}>0$ - this satisfies all the constraints ## A claim about all-line shift constructable amplitudes > If an amplitude is all-line shift constructible and each term breaks down into only purely holomorphic or purely anti-holomorphic three-point building blocks, then the entire amplitude must vanish. # Rosso ## A Solvable Model of Flat Space Holography \[Links: [arXiv](https://arxiv.org/abs/2209.14372), [PDF](https://arxiv.org/pdf/2209.14372.pdf)\] \[Abstract: We propose an explicit realization of [[0491 Flat holography|flat space holography]] in two dimensions where both sides of the duality are independently defined and the boundary theory is completely solvable. In the bulk, we define a novel $\mathcal{N}$ = 1 flat space supergravity theory and exactly compute the full topological expansion of its Euclidean partition function with an arbitrary number of boundaries. On the boundary, we consider a double scaled Hermitian random matrix model with Gaussian potential and use the loop equations to show it independently reproduces the bulk partition function to all orders in the topological expansion. The non-perturbative completion of the supergravity theory provided by the solvable Gaussian matrix model allows for the exact, and in many cases analytic, computation of observables in flat space quantum gravity.\] # Sasieta ## Wormholes from heavy operator statistics in AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/2211.11794), [PDF](https://arxiv.org/pdf/2211.11794.pdf)\] \[Abstract: We construct higher dimensional Euclidean AdS wormhole solutions that reproduce the statistical description of the correlation functions of an ensemble of heavy CFT operators. We consider an operator which effectively backreacts on the geometry in the form of a thin shell of dust particles. Assuming dynamical chaos in the form of the ETH ansatz, we demonstrate that the semiclassical path integral provides an effective statistical description of the microscopic features of the thin shell operator in the CFT. The Euclidean wormhole solutions provide microcanonical saddlepoint contributions to the cumulants of the correlation functions over the ensemble of operators. We finally elaborate on the role of these wormholes in the context of non-perturbative violations of bulk [[0187 Global symmetries in QG|global symmetries]] in AdS/CFT.\] # Schlenker, Witten ## No Ensemble Averaging Below the Black Hole Threshold \[Links: [arXiv](https://arxiv.org/abs/2202.01372), [PDF](https://arxiv.org/pdf/2202.01372.pdf)\] \[Abstract: In the [[0001 AdS-CFT|AdS/CFT]] correspondence, amplitudes associated to connected bulk manifolds with disconnected boundaries have presented a longstanding mystery. A possible interpretation is that they reflect the effects of [[0154 Ensemble averaging|averaging over an ensemble]] of boundary theories. But in examples in dimension $D\geq 3$, an appropriate ensemble of boundary theories does not exist. Here we sharpen the puzzle by identifying a class of "sub-threshold" observables that we claim do not show effects of ensemble averaging. These are amplitudes that do not involve black hole states. To support our claim, we explore the example of $D=3$, and show that connected solutions of Einstein's equations with disconnected boundary never contribute to sub-threshold observables. To demonstrate this requires some novel results about the renormalized volume of a hyperbolic three-manifold, which we prove using modern methods in hyperbolic geometry. Why then do any observables show apparent ensemble averaging? We propose that this reflects the chaotic nature of black hole physics and the fact that the Hilbert space describing a black hole does not have a large $N$ limit.\] ## Summary - there is a class of sub-threshold observables that do not show effects of [[0154 Ensemble averaging|ensemble averaging]] - i.e. ensemble averaging only affects BHs - i.e. quantities accessible via integrability are not affected by ensemble averaging ## Renormalised volume At large $N$, the contribution of a bulk geometry is asymptotically proportional to $\exp(-V_R(X)/4\pi Gl^2)$. ## Sub-threshold amplitudes - a Riemann surface $M$ is a sub-threshold amplitude only if the partition function diverges at large $c$ when each of the independent circles in $M$ are pinched - it is shown that the partition function diverges in the pinching limit only when the circle is the boundary of a disk in the 3d manifold $X$ - a hyperbolic three-manifold $X$ contributes to sub-threshold amplitudes on a Riemann surface $M$ only if the boundary of $X$ is connected and consists only of $M$ - even if $X$ has connected boundary $M$, it needs to be a handlebody (or Schottky manifold) to contribute, meaning for some embedding of $M$ in $\mathbb{R}^3$, $X$ is topologically the interior of $M$ # Serantes, Withers ## Convergence of the FG expansion and complex BH anatomy \[Links: [arXiv](https://arxiv.org/abs/2207.07132), [PDF](https://arxiv.org/pdf/2207.07132.pdf)\] \[Abstract: \] ## Assumptions - the stress tensor is already the 'correct' one: either after requiring regularity in the bulk or computed from CFT - analytically continue the radial direction to the complex domain ## Summary - studies convergence of [[0011 Fefferman-Graham expansion|FG expansion]] given real analytic source (boundary metric) and vev (holographic stress tensor) by analysing the singularities of the metric analytically continued to complex radial coordinate $z$ # Shahbazi-Moghaddam ## Restricted Quantum Focusing \[Links: [arXiv](https://arxiv.org/abs/2212.03881), [PDF](https://arxiv.org/pdf/2212.03881.pdf)\] \[Abstract: [[0243 Quantum focusing conjecture|Quantum Focusing]] is a powerful conjecture, which plays a key role in the current proofs of many well-known quantum gravity theorems, including various consistency conditions, and causality constraints in [[0001 AdS-CFT|AdS/CFT]]. I conjecture a (weaker) *restricted* quantum focusing, which I argue is sufficient to derive all known essential implications of quantum focusing. Subject to a technical assumption, I prove this conjecture on brane-world semiclassical gravity theories which are holographically dual to Einstein gravity in a higher dimensional anti-de Sitter spacetime.\] # Speranza ## Ambiguity resolution for integrable gravitational charges \[Links: [arXiv](https://arxiv.org/abs/2202.00133), [PDF](https://arxiv.org/pdf/2202.00133.pdf)\] \[Abstract: Recently, [[0393 CLP extended phase space|CLP]] have shown that nonzero charges integrating Hamilton's equation can be defined for all diffeomorphisms acting near the boundary of a subregion in a gravitational theory. This is done by extending the phase space to include a set of embedding fields that parameterize the location of the boundary. Because their construction differs from previous works on extended phase spaces by a covariant phase space ambiguity, the question arises as to whether the resulting charges are unambiguously defined. Here, we demonstrate that ambiguity-free charges can be obtained by appealing to the variational principle for the subregion, following recent developments on dealing with boundaries in the covariant phase space. Resolving the ambiguity produces corrections to the diffeomorphism charges, and also generates additional obstructions to integrability of Hamilton's equation. We emphasize the fact that the CLP extended phase space produces nonzero diffeomorphism charges distinguishes it from previous constructions in which diffeomorphisms are pure gauge, since the embedding fields can always be eliminated from the latter by a choice of unitary gauge. Finally, we show that Wald-Zoupas charges, with their characteristic obstruction to integrability, are associated with a modified transformation in the extended phase space, clarifying the reason behind integrability of Hamilton's equation for standard diffeomorphisms.\] ## Summary - *uses* variational principle for [[0053 Subregion in gravity|subregions]] to fix an ambiguity in the gravitational charges # Stanford, Yang ## Firewalls from wormholes \[Links: [arXiv](https://arxiv.org/abs/2208.01625), [PDF](https://arxiv.org/pdf/2208.01625.pdf)\] \[Abstract: Spacetime wormholes can lead to surprises in black hole physics. We show that a very old black hole can tunnel to a white hole/[[0195 Firewall|firewall]] by emitting a large [[0051 Baby universes|baby universe]]. We study the process for a perturbed thermofield double black hole in [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]], using the lowest order (genus one) spacetime wormhole that corresponds to single [[0051 Baby universes|baby-universe]] emission. The probability for tunneling to a white hole is proportional to $t^2 e^{−2S}$ where $t$ is the age of the black hole and $S$ is the entropy of one black hole.\] # Sugiura, Takeda ## Bulk reconstruction of AdS$_{d+1}$ metrics and developing kinematic space \[Links: [arXiv](https://arxiv.org/abs/2212.10065), [PDF](https://arxiv.org/pdf/2212.10065.pdf)\] \[Abstract: The metrics of the global, Poincaré, and Rindler AdS$_{d+1}$ are explicitly [[0026 Bulk reconstruction|reconstructed]] with given [[0027 Bulk reconstruction using lightcone cuts|lightcone cuts]]. We first compute the metric up to a conformal factor with the lightcone cuts method introduced by Engelhardt and Horowitz. While a general prescription to determine the conformal factor is not known, we recover the factor by identifying the causal information surfaces from the lightcone cuts and finding that they are minimal. In addition, we propose a new type of kinematic space as the space of minimal surfaces in AdS$_{d+1}$, where a metric is introduced as a generalization of the case of $d=2$. This metric defines the set of bulk points, which is equivalent to that of lightcone cuts. Some other properties are also studied towards establishing a reconstruction procedure for general bulk metrics.\] ## Refs - [[0027 Bulk reconstruction using lightcone cuts]] - earlier work [[2021#Takeda]] # Swingle, van Raamsdonk ## Enhanced Negative Energy with a Massless Dirac Field \[Links: [arXiv](https://arxiv.org/abs/2212.02609), [PDF](https://arxiv.org/pdf/2212.02609.pdf)\] \[Abstract: Motivated by [[0083 Traversable wormhole|traversable wormhole]] constructions that require large amounts of negative energy, we explore constraints on the amount of negative energy that can be carried by a free Dirac field in a slab-shaped region between two parallel spatial planes. Specifically, we ask what is the minimum possible uniform energy density that can exist at some time, considering all possible states and all possibilities for the physics outside the slab. The vacuum state where we identify the two sides of the slab with antiperiodic boundary conditions gives one possible state with uniform negative energy, but we argue that states with more negative energy exist above $1+1$ dimensions. Technically, we reduce the problem to studying a massive Dirac field on an interval in 1+1 dimensions and numerically search for states with uniform energy density in a lattice regulated model. We succeed in finding states with enhanced negative energy (relative to the antiperiodic vacuum) which also appear to have a sensible continuum limit. Our results for the mass-dependence of the minimum uniform energy density in $1+1$ dimensions suggest that for a $3+1$ dimensional massless Dirac fermion, it is possible to have states with arbitrarily large uniform negative energy density in an arbitrarily wide slab\] # Tran (Dec) ## Constraining higher-spin $S$-matrices \[Links: [arXiv](https://arxiv.org/abs/2212.02540), [PDF](https://arxiv.org/pdf/2212.02540.pdf)\] \[Abstract: There are various no-go theorems that tightly constrain the existence of local higher-spin theories with non-trivial $S$-matrix in flat space. Due to the existence of higher-spin Yang-Mills theory with non-trivial scattering amplitudes, it makes sense to revisit Weinberg’s soft theorem – a direct consequence of the Lorentz invariance of the $S$-matrix that does not take advantage of unitarity and parity invariance. By working with the chiral representation – a representation originated from [[0330 Twistor theory|twistor theory]], we show that Weinberg’s [[0009 Soft theorems|soft theorem]] can be evaded and non-trivial higher-spin $S$-matrix is possible. In particular, we show that Weinberg’s soft theorem is more closely related to the number of derivatives in the interactions rather than spins. We also observe that all constraints imposed by gauge invariance of the $S$-matrix are accompanied by polynomials in the soft momentum of the emitted particle where the zeroth order in the soft momentum is charge conservation law.\] # Verlinde, Zurek ## Modular Fluctuations from Shockwave Geometries \[Links: [arXiv](https://arxiv.org/abs/2208.01059), [PDF](https://arxiv.org/pdf/2208.01059.pdf)\] \[Abstract: Modular fluctuations have previously been shown to obey an area law $\left\langle\Delta K^2\right\rangle=\langle K\rangle=A / 4 G_N$. Furthermore, modular fluctuations generate fluctuations in the spacetime geometry of empty causal diamonds. Here we demonstrate the physical origin of these fluctuations, showing that the modular area law, in $d$−dimensionsal Minkowski space, can be reproduced from [[0117 Shockwave|shockwaves]] arising from vacuum fluctuations. The size of the vacuum fluctuations is fixed by commutation relations in [[0450 Light-ray operators|light-ray operators]], of the same form postulated by 't Hooft in the context of black hole horizons.\] ## Summary - shows that fluctuations in the [[0416 Modular Hamiltonian|modular Hamiltonian]] are due to the fluctuations in the spacetime geometry near light fronts that take the form of gravitational [[0117 Shockwave|shockwaves]] ## Related - [[0416 Modular Hamiltonian]] - [[0117 Shockwave]] # Wang, Pan ## Pole-skipping of Holographic Correlators: Aspects of Gauge Symmetry and Generalizations \[Links: [arXiv](https://arxiv.org/abs/2209.04296), [PDF](https://arxiv.org/pdf/2209.04296.pdf)\] \[Abstract: In the framework of [[0001 AdS-CFT|anti-de Sitter space/conformal field theory (AdS/CFT)]], we study the [[0179 Pole skipping|pole-skipping]] phenomenon of the holographic correlators of boundary operators. We explore the locations of the pole-skipping points case by case with the models of $U(1)$-gauged form fields propagating in the asymptotic AdS bulk of finite temperature. In general, in different cases all the first-order points are located at the Matsubara frequency with corresponding wave vectors regularly dispersed in the momentum space. Specifically, in the massless cases with $U(1)$ symmetry, the wave vectors of the pole-skipping points have a form-number dependence, and a trans-mode equivalence in the dual fields is found in correspondence with electromagnetic duality. In the massive cases with explicit symmetry breaking, the points degenerate to be independent of the form number. We expect in such kind of pole-skipping properties implications of distinctive physics in the [[0008 Quantum chaos|chaotic]] systems. Our near-horizon computation is verified with the double-trace method especially in the example of 2-form where there is dimension-dependent boundary divergence. We illustrate in these cases that the pole-skipping properties of the holographic correlators are determined by the IR physics, consistent with the ordinary cases in previous studies.\] # Wang, Wang ## Pole skipping in holographic theories with bosonic fields \[Links: [arXiv](https://arxiv.org/abs/2208.01047), [pdf](https://arxiv.org/pdf/2208.01047.pdf), [PRL](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.231603)\] \[Abstract: We study [[0179 Pole skipping|pole skipping]] in holographic CFTs dual to diffeomorphism invariant theories containing an arbitrary number of bosonic fields in the large $N$ limit. Defining a weight to organize the bulk equations of motion, a set of general pole-skipping conditions are derived. In particular, the frequencies simply follow from general covariance and weight matching. In the presence of higher spin fields, we find that the imaginary frequency for the highest-weight pole-skipping point equals the higher-spin [[0466 Lyapunov exponent|Lyapunov exponent]] which lies outside of the [[0474 Chaos bound|chaos bound]]. Without higher spin fields, we show that the energy density [[0103 Two-point functions|Green's function]] has its highest-weight pole skipping happening at a location related to the [[0482 Out-of-time-order correlator|OTOC]] for arbitrary [[0006 Higher-derivative gravity|higher-derivative gravity]], with a Lyapunov exponent saturating the chaos bound and a [[0167 Butterfly velocity|butterfly velocity]] matching that extracted from a [[0117 Shockwave|shockwave]] calculation. We also suggest an explanation for this matching at the metric level by obtaining the on-shell shockwave solution from a regularized limit of the metric perturbation at the skipped pole.\] ## Summary - generalises the discussion of [[0179 Pole skipping|pole-skipping]] to arbitrary integer spins - reproduces the [[0466 Lyapunov exponent|Lyapunov exponent]] characterising [[0008 Quantum chaos|chaos]] for higher spins - in particular, they violate the [[0474 Chaos bound|chaos bound]] for spins higher than 2 - shows that the [[0167 Butterfly velocity|butterfly velocity]] computed between [[0179 Pole skipping|pole-skipping]] and [[0117 Shockwave|shockwave]] methods are the same for all [[0006 Higher-derivative gravity|higher derivative gravitational theories]] - shows that the [[0117 Shockwave|shockwave]] can be understood as a regularised [[0325 Quasi-normal modes|QNM]] at a special frequency and wavenumber ## Refs - fermionic analogue: [[2023#Ning, Wang, Wang]] <!-- talk about finite number of contractions in Lagrangian quasi-quasi-normal --> # Weber, Haneder, Richter, Urbina ## Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity \[Links: [arXiv](https://arxiv.org/abs/2208.13802), [PDF](https://arxiv.org/pdf/2208.13802.pdf)\] \[Abstract: Based on the discovery of the duality between [[0050 JT gravity|Jackiw-Teitelboim]] quantum gravity and a double-scaled [[0197 Matrix model|matrix ensemble]] by [[2019#Saad, Shenker, Stanford|Saad, Shenker and Stanford]] in 2019, we show how consistency between the two theories in the universal [[0579 Random matrix theory|Random Matrix Theory]] (RMT) limit imposes a set of constraints on the volumes of moduli spaces of Riemannian manifolds. These volumes are given in terms of polynomial functions, the Weil-Petersson volumes, solving a celebrated nonlinear recursion formula that is notoriously difficult to analyze. Since our results imply linear relations between the coefficients of the Weil-Petersson volumes, they therefore provide both a stringent test for their symbolic calculation and a possible way of simplifying their construction. In this way, we propose a long-term program to improve the understanding of mathematically hard aspects concerning moduli spaces of hyperbolic manifolds by using universal RMT results as input.\] # Wei, Yoneta ## Counting atypical black hole microstates from entanglement wedges \[Links: [arXiv](https://arxiv.org/abs/2211.11787), [PDF](https://arxiv.org/pdf/2211.11787.pdf)\] \[Abstract: Disentangled black hole microstates are atypical states in holographic CFTs whose gravity duals do not have smooth horizons. If there exist sufficiently many disentangled microstates to account for the entire Bekenstein-Hawking entropy, then any black hole microstate can be written as a superposition of states without smooth horizons. We show that there exist sufficiently many disentangled microstates to account for almost the entire Bekenstein-Hawking entropy of a large AdS black hole at the semiclassical limit $G_N\rightarrow 0$. In addition, we also argue that in generic quantum many-body systems with short-ranged interactions, there exist sufficiently many area law states in the microcanonical subspace to account for almost the entire thermodynamic entropy in the standard thermodynamic limit. Area law states are atypical since a typical state should contain volume law entanglement. Furthermore, we also present an explicit way to construct such a set of area law states, and argue that the same construction may also be used to construct disentangled states.\] ## Summary - shows that (a weak form of) the second possibility in [[2020#Hayden, Penington]] is true ## Disentangled states - *not* dual to smooth geometries \[*Many thanks to Zixia for explaining this paper to me.*\] # Wong ## A note on the bulk interpretation of the quantum extremal surface formula \[Links: [arXiv](https://arxiv.org/abs/2212.03193), [PDF](https://arxiv.org/pdf/2212.03193.pdf)\] \[Abstract: Defining quantum information quantities directly in bulk quantum gravity is a difficult problem due to the fluctuations of spacetime. Some progress was made recently in [[2022#Mertens, Simon, Wong]], which provided a bulk interpretation of the Bekenstein Hawking formula for two sided [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black holes in terms of the [[0301 Entanglement entropy|entanglement entropy]] of gravitational [[0556 Edge mode|edge modes]]. We generalize those results to give a bulk entanglement entropy interpretation of the [[0212 Quantum extremal surface|quantum extremal surface]] formula in [[0002 3D gravity|AdS3 gravity]], as applied to a single interval in the boundary theory. Our computation further supports the proposal that AdS3 gravity can be viewed as a topological phase in which the bulk gravity edge modes are anyons transforming under the [[0508 Quantum group|quantum group]] $\mathrm{SL}^+_q (2, \mathbb{R})$. These edge modes appear when we cut open the Euclidean path integral along bulk co-dimension 2 slices, and satisfies a shrinkable boundary condition which ensures that the Gibbons-Hawking calculation gives the correct [[0248 Black hole microstates|state counting]].\] ## Refs - earlier work [[2022#Mertens, Simon, Wong]] ## Related - [[0212 Quantum extremal surface]] # Xiao, Yang ## On Penrose inequality in holography \[Links: [arXiv](https://arxiv.org/abs/2204.12239), [PDF](https://arxiv.org/pdf/2204.12239.pdf)\] \[Abstract: The recent holographic deduction of [[0476 Penrose inequality|Penrose inequality]] only assumes null energy condition while the weak or dominant energy condition is required in usual geometric proof. This paper makes a step toward filling up gap between these two approaches. For planar/spherically symmetrically asymptotically Schwarzschild anti-de Sitter (AdS) black holes, we give a purely geometric proof for Penrose inequality by assuming the [[0480 Null energy condition|null energy condition]]. We also point out that two naive generalizations of charged Penrose inequality are not generally true and propose two new candidates. When the spacetime is asymptotically AdS but not Schwarzschild-AdS, the total mass is defined according to holographic renormalization and depends on scheme of quantization. In this case, the holographic argument implies that the Penrose inequality should still be valid but this paper use concrete example to show that whether the Penrose inequality holds or not will depend on what kind of quantization scheme we employ.\] ## Summary - proves that any potential spherically symmetric hairy BH cannot dominate the canonical ensemble - assumption needed: the CFT microcanonical ensemble does not break translational symmetry spontaneously; an argument for this: generalising [[2019#Engelhardt, Horowitz]] to fix energy density everywhere rather than the total energy # Xu, Swingle (Review) ## Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial \[Links: [arXiv](https://arxiv.org/abs/2202.07060), [PDF](https://arxiv.org/pdf/2202.07060)\] \[Abstract: This tutorial article introduces the physics of quantum information scrambling in quantum many-body systems. The goals are to understand how to precisely quantify the spreading of quantum information and how causality emerges in complex quantum systems. We introduce a general framework to study the dynamics of quantum information, including detection and decoding. We show that the dynamics of quantum information is closely related to operator dynamics in the Heisenberg picture, and, under certain circumstances, can be precisely quantified by the so-called [[0482 Out-of-time-order correlator|out-of-time ordered correlator]]~(OTOC). The general behavior of OTOC is discussed based on several toy models, including the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev]] model, random circuit models, and Brownian models, in which OTOC is analytically tractable. We introduce numerical methods, including exact diagonalization and [[0054 Tensor network|tensor network]] methods, to calculate OTOC for generic quantum many-body systems. We also survey current experimental schemes for measuring OTOC in various quantum simulators.\]