2019 - otherworldlines

# Adamo, Mason, Sharma ## Celestial amplitudes and conformal soft theorems \[Links: [arXiv](https://arxiv.org/abs/1905.09224), [PDF](https://arxiv.org/pdf/1905.09224.pdf)\] \[Abstract: Scattering amplitudes in $d+2$ dimensions can be expressed in terms of a [[0148 Conformal basis|conformal basis]], for which the $S$-matrix behaves as a CFT correlation function on the celestial $d$-sphere. We explain how compact expressions for the full tree-level $S$-matrix of gauge theory, gravity and other QFTs extend to this conformal basis, and are easily derived from [[0348 Ambitwistor strings|ambitwistor strings]]. Using these formulae and their worldsheet origins, we prove various tree-level '[[0390 Conformally soft theorems|conformal soft theorems]]' in gauge theory and gravity in any dimension; these arise from limits where the scaling dimension of an external state in the scattering process takes special values. These conformally soft limits are obscure from standard methods, but they are easily derived with ambitwistor strings. Additionally, we make an identification between the residues of conformally soft vertex operator insertions in ambitwistor strings and charges generating [[0060 Asymptotic symmetry|asymptotic symmetries]].\] ## Summary - derive tree-level expressions in conformal basis using ambitwister strings for gauge theory, gravity and other QFTs - prove various tree-level conformal [[0009 Soft theorems|soft theorems]] - these arise at special values of the scaling dimension - these are obscure from standard methods but obvious from ambitwister strings - identify residues of conformally soft vertex operator insertions in ambitwister strings with charges generating [[0060 Asymptotic symmetry|asymptotic symmetries]] ## Ambitwister strings - they underpin scattering equations and CHY formula for massless scattering in *momentum basis*, but also encode non-linear stuff -> must also encode results in conformal basis ## Special values of $\Delta$ - gluons or gravitons become pure gauge at special values of $\Delta$, but the amplitudes still have non-trivial limits - gauge theory - $\Delta=1$: pure gauge, leading soft theorem - $\Delta=0$: not pure gauge, but still correspond to a subleading soft energetic soft theorem - gravity theory - $\Delta=1$: pure gauge, leading soft theorem - $\Delta=0$: pure gauge, subleading soft theorem - $\Delta=-1$: not mentioned in this paper (I think), but correspond to subsubleading soft theorem - see [[0009 Soft theorems]] # Agon, Mezei ## Bit Threads and the Membrane Theory of Entanglement Dynamics \[Links: [arXiv](https://arxiv.org/abs/1910.12909), [PDF](https://arxiv.org/pdf/1910.12909.pdf)\] \[Abstract: Recently, an effective *[[0433 Membrane theory of entanglement dynamics|membrane theory]]* was proposed that describes the ''[[0429 Hydrodynamics|hydrodynamic]]'' regime of the entanglement dynamics for general [[0008 Quantum chaos|chaotic systems]]. Motivated by the new *[[0211 Bit thread|bit threads]]* formulation of [[0007 RT surface|holographic entanglement entropy]], given in terms of a convex optimization problem based on flow maximization, or equivalently tight packing of bit threads, we reformulate the membrane theory as a max flow problem by proving a max flow-min cut theorem. In the context of holography, we explain the relation between the max flow program dual to the membrane theory and the max flow program dual to the holographic surface extremization prescription by providing an explicit map from the membrane to the bulk, and derive the former from the latter in the "hydrodynamic" regime without reference to minimal surfaces or membranes.\] # Aharony, Urbach, Weiss ## Generalized Hawking-Page transitions \[Links: [arXiv](https://arxiv.org/abs/1904.07502), [PDF](https://arxiv.org/pdf/1904.07502.pdf)\] \[Abstract: We construct holographic backgrounds that are [[0231 Bulk solutions for CFTs on non-trivial geometries|dual]] by the [[0001 AdS-CFT|AdS/CFT correspondence]] to Euclidean conformal field theories on products of spheres $S^{d_1}\times S^{d_2}$, for conformal field theories whose dual may be approximated by classical Einstein gravity (typically these are large N strongly coupled theories). For $d_2=1$ these backgrounds correspond to thermal field theories on $S^{d_1}$, and Hawking and Page found that there are several possible bulk solutions, with two different topologies, that compete with each other, leading to a [[0012 Hawking-Page transition|phase transition]] as the relative size of the spheres is modified. By numerically solving the Einstein equations we find similar results also for $d_2>1$, with bulk solutions in which either one or the other sphere shrinks to zero smoothly at a minimal value of the radial coordinate, and with a first order phase transition (for $d_1+d_2 < 9$) between solutions of two different topologies as the relative radius changes. For a critical ratio of the radii there is a (sub-dominant) singular solution where both spheres shrink, and we analytically analyze the behavior near this radius. For $d_1+d_2 < 9$ the number of solutions grows to infinity as the critical ratio is approached.\] ## Refs - [[0231 Bulk solutions for CFTs on non-trivial geometries]] ## Summary - total $d\ge9$: expect ==second-order== phase transition between two topologies (see p.10 bottom of sec.3) - for total $d<9$: expand around singular solution at critical ratio and find infinitely many solutions with the same asymptotic radii ## Singular solution - there is an interesting oscillation in the plane of the boundary sphere ratio and $r_0$ - to obtain the singular solution analytically, use an ansatz $h(z)=\alpha f(z)$ for the metric $d z^{2}+f^{2}(z) d \Omega_{d_{1}}^{2}+h^{2}(z) d \Omega_{d_{2}}^{2}$ - problem: not necessarily the dominant solution - I also think that there might be a continuous family of singular solutions (I don't see if there are enough BC) - to find the dependence on the boundary sphere ratio, do a linearised calculation for large $r$ - to find the dependence on $r_0$, use the fact that $r_0$ is much smaller than AdS scale so it is almost flat near the surface of the bubble; the only scale would then be $z/r_0$, so the solution must be a function of it ## Calculating action - conformal frame - used conformal freedom to set $\rho=1$ (FG radius) at bubble surface - therefore needs to use $I\left[\exp (2 \sigma) g_{(0)}\right]=I\left[g_{(0)}\right]+\int d^{d} x \mathcal{A}(x) \sigma(x)$ to find the action for the correct conformal boundary - i.e. there is conformal anomaly ## Numerical renormalisation 1. first write the CT as an integration over radius: $I_{r e g}+I_{c t}=\int_{\varepsilon}^{1} d \rho\left(L_{r e g}(\rho)-\partial_{\rho} I_{c t}(\rho)\right)+I_{c t}(\varepsilon=1)$ 2. then add a cutoff at IR boundary to avoid the divergence due to the new expression: $I_{\text {numerical }}^{[\varepsilon, 1]}=\int_{\varepsilon}^{\delta} d \rho\left(L_{r e g}(\rho)-\partial_{\rho} I_{c t}(\rho)\right)+\int_{\delta}^{1} d \rho L_{r e g}(\rho)+\left.I_{c t}\right|_{\rho=\delta}$ 3. finally if we want better accuracy, we match a series expansion. - $I_{\text {analytical }}^{[0, \varepsilon]}=I^{[0, \varepsilon]}+O\left(\varepsilon^{n}\right)$ - $I_{\text {ren }}^{[0,1]}=I_{\text {analytical }}^{[0, \varepsilon]}\left[g_{(0)}^{n u m}, g_{(d)}^{n u m}\right]+I_{\text {numerical }}^{[\varepsilon, 1]}$ - need to find $g_{(0)}^{n u m}$ and $g_{(d)}^{n u m}$ by matching the fitting the solution between 0 and some small $\rho=\varepsilon_{\text{sampling}}$ to an analytical asymptotic expansion up to order $\rho^{d+1}$ - n.b. there is trade-off in choosing $\varepsilon$ # Akers, Levine, Leichenauer ## Large Breakdowns of Entanglement Wedge Reconstruction \[Links: [arXiv](https://arxiv.org/abs/1908.03975), [PDF](https://arxiv.org/pdf/1908.03975.pdf)\] \[Abstract: We show that the bulk region reconstructable from a given boundary subregion --- which we term the reconstruction wedge --- can be much smaller than the [[0219 Entanglement wedge reconstruction|entanglement wedge]] even when backreaction is small. We find arbitrarily large separations between the reconstruction and entanglement wedges in near-vacuum states for regions close to an entanglement phase transition, and for more general regions in states with large energy (but very low energy density). Our examples also illustrate situations for which the quantum extremal surface is macroscopically different from the [[0007 RT surface|Ryu-Takayanagi surface]].\] ## Summary - *finds* that reconstruction wedge can be much smaller than the entanglement wedge - even when the backreaction is small - example - near-vacuum states near phase transition - or large energy states (but low energy density) # Almheiri, Engelhardt, Marolf, Maxfield ## The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole \[Links: [arXiv](https://arxiv.org/abs/1905.08762), [PDF](https://arxiv.org/pdf/1905.08762)\] \[Abstract: Bulk quantum fields are often said to contribute to the [[0007 RT surface|generalized entropy]] $\frac{A}{4G_N} +S_{\mathrm{bulk}}$ only at $O(1)$. Nonetheless, in the context of evaporating black holes, $O(1/G_N)$ gradients in $S_{\mathrm{bulk}}$ can arise due to large boosts, introducing a [[0212 Quantum extremal surface|quantum extremal surface]] far from any classical extremal surface. We examine the effect of such bulk quantum effects on quantum extremal surfaces (QESs) and the resulting entanglement wedge in a simple two-boundary 2d bulk system defined by [[0050 JT gravity|Jackiw-Teitelboim gravity]] coupled to a $1+1$ CFT. Turning on a coupling between one boundary and a further external auxiliary system which functions as a heat sink allows a two-sided otherwise-eternal black hole to evaporate on one side. We find the generalized entropy of the QES to behave as expected from general considerations of unitarity, and in particular that ingoing information disappears from the entanglement wedge after a scambling time $\frac{\beta}{2\pi} \ln \Delta S + O(1)$ in accord with expectations for holographic implementations of the [[0217 Hayden-Preskill decoding criterion|Hayden-Preskill protocol]]. We also find an interesting QES phase transition at what one might call the Page time for our process.\] ## Related topics - [[0131 Information paradox]] # Almheiri, Hartman, Maldacena, Shaghoulian, Tajdini ## Replica Wormholes and the Entropy of Hawking Radiation \[Links: [arXiv](https://arxiv.org/abs/1911.12333), [PDF](https://arxiv.org/pdf/1911.12333.pdf)\] \[Abstract: \] ## Comments on [[0206 Replica wormholes|replica wormholes]] - can consider one or two intervals - replica wormhole gives island rule # Almheiri, Mahajan, Maldacena ## Islands outside the horizon \[Links: [arXiv](https://arxiv.org/abs/1910.11077), [PDF](https://arxiv.org/pdf/1910.11077.pdf)\] \[Abstract: \] ## Refs - root [[0131 Information paradox]] - [[0243 Quantum focusing conjecture]] about [[0213 Islands|Islands]] ## Summary - [[0243 Quantum focusing conjecture]] avoids causality issue - (Zhencheng) although island is outside the horizon, but if you decouple gravity and matter (which we should), island is inside the horizon - a version of [[0131 Information paradox]] in ==HH state== - islands resolves it ## Comments from other papers - [[2021#Engelhardt, Penington, Shahbazi-Moghaddam (Feb)]]: "quantum effects can allow the causal wedge to be outside the outermost extremal wedge when defined using time evolution couples the asymptotic boundary to an auxiliary system. However, this is only true if we do not include the auxiliary coupled system when defining the outermost extremal wedge. When comparing apples to apples by doing so, one indeed finds that the causal wedge is still contained in the outermost extremal wedge" - [[2020#Engelhardt, Folkestad]]: That is, do quantum trapped surfaces \[52\] lie behind event horizons? In \[50\], quantum extremal surfaces \[47\] “outside” of the horizon were found; in this case the existence of nonstandard boundary conditions at the AdS boundary were crucial. Interestingly, the quantum focusing conjecture \[69\] in this case nevertheless enforces the absence of causal communication between the quantum extremal surface and I . These complications illustrate the subtleties that must be accounted for in formulating a quantum version of our proof, in which evaporating singularities can no longer be ignored: the absence of causal communication from quantum trapped surfaces to I is not equivalent to the absence of quantum trapped surfaces in the causal wedge. This suggests that the correct generalization may actually involve an understanding of whether communication can occur in practice rather than whether or not it is forbidden by causal structure. # Almheiri, Mahajan, Maldacena, Zhao ## The Page curve of Hawking radiation from semiclassical geometry \[Links: [arXiv](https://arxiv.org/abs/1908.10996), [PDF](https://arxiv.org/pdf/1908.10996)\] \[Abstract: We consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the [[0007 RT surface|RT/HRT surfaces]] in the higher-dimensional theory. Using this we compute the entropy of [[0304 Hawking radiation|Hawking radiation]] and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of [[0220 ER=EPR|ER=EPR]]. The black hole interior then becomes part of the entanglement wedge of the radiation. Inspired by this, we propose a new rule for computing the entropy of quantum systems entangled with gravitational systems which involves searching for "[[0213 Islands|islands]]" in determining the entanglement wedge.\] # Bao, Cao, Fischetti, Keeler ## Towards bulk metric reconstruction from extremal area variations \[Links: [arXiv](https://arxiv.org/abs/1904.04834), [PDF](https://arxiv.org/pdf/1904.04834.pdf)\] \[Abstract: The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the [[0301 Entanglement entropy|entanglement entropies]] of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension $d \geq 4$, knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicit spacetime metric [[0026 Bulk reconstruction|reconstruction]].\] # Bao, Chatwin-Davies, Niehoff, Usatyuk ## Bulk reconstruction beyond the entanglement wedge \[Links: [arXiv](https://arxiv.org/abs/1911.00519), [PDF](https://arxiv.org/pdf/1911.00519.pdf)\] \[Abstract: We study the portion of an asymptotically Anti de Sitter geometry's bulk where the metric can be reconstructed, given the areas of minimal 2-surfaces anchored to a fixed boundary subregion. We exhibit situations in which this region can reach parametrically far outside of the [[0219 Entanglement wedge reconstruction|entanglement wedge]]. If the setting is furthermore holographic, so that the bulk geometry is dual to a state in a conformal field theory (CFT), these minimal 2-surface areas can be deduced from the expectation values of operators localized within the boundary subregion. This presents us with an alternative: Either the reduced CFT state encodes significant information about the bulk beyond the entanglement wedge, challenging conventional intuition about holographic subregion duality; or the reduced CFT state fails to contain information about operators whose expectation values give the areas of minimal 2-surfaces anchored within that subregion, challenging conventional intuition about the holographic dictionary.\]  # Bautista, Dabholkar, Erbin ## Quantum Gravity from Timelike Liouville theory \[Links: [arXiv](https://arxiv.org/abs/1905.12689), [PDF](https://arxiv.org/pdf/1905.12689)\] \[Abstract: A proper definition of the path integral of quantum gravity has been a long-standing puzzle because the Weyl factor of the Euclidean metric has a wrong-sign kinetic term. We propose a definition of two-dimensional [[0562 Liouville theory|Liouville]] quantum gravity with cosmological constant using conformal bootstrap for the [[0622 Timelike Liouville|timelike Liouville theory]] coupled to supercritical matter. We prove a no-ghost theorem for the states in the BRST cohomology. We show that the four-point function constructed by gluing the timelike Liouville three-point functions is well defined and crossing symmetric (numerically) for external Liouville energies corresponding to *all* physical states in the BRST cohomology with the choice of the Ribault-Santachiara contour for the internal energy.\] # Belin, Iqbal, Kruthoff ## Bulk entanglement entropy for photons and gravitons in AdS \[Links: [arXiv](https://arxiv.org/abs/1912.00024), [PDF](https://arxiv.org/pdf/1912.00024.pdf)\] \[Abstract: We study quantum corrections to [[0007 RT surface|holographic entanglement entropy]] in AdS$_3$/CFT$_2$; these are given by the bulk entanglement entropy across the [[0007 RT surface|Ryu-Takayanagi surface]] for all fields in the effective gravitational theory. We consider bulk $U(1)$ gauge fields and gravitons, whose dynamics in AdS$_3$ are governed by Chern-Simons terms and are therefore topological. In this case the relevant Hilbert space is that of the [[0556 Edge mode|edge excitations]]. A novelty of the holographic construction is that such modes live not only on the bulk entanglement cut but also on the AdS boundary. We describe the interplay of these excitations and provide an explicit map to the appropriate extended Hilbert space. We compute the bulk entanglement entropy for the CFT vacuum state and find that the effect of the bulk entanglement entropy is to renormalize the relation between the effective holographic central charge and Newton's constant. We also consider excited states obtained by acting with the $U(1)$ current on the vacuum, and compute the difference in bulk entanglement entropy between these states and the vacuum. We compute this UV-finite difference both in the bulk and in the CFT finding a perfect agreement.\] # Benjamin, Ooguri, Shao, Wang ## Lightcone Modular Bootstrap and Pure Gravity \[Links: [arXiv](https://arxiv.org/abs/1906.04184), [PDF](https://arxiv.org/pdf/1906.04184.pdf)\] \[Abstract: We explore the large spin spectrum in two-dimensional conformal field theories with a finite twist gap, using the modular bootstrap in the lightcone limit. By recursively solving the modular crossing equations associated to different $PSL(2,\mathbb{Z})$ elements, we identify the universal contribution to the density of large spin states from the vacuum in the dual channel. Our result takes the form of a sum over $PSL(2,\mathbb{Z})$ elements, whose leading term generalizes the usual [[0406 Cardy formula|Cardy formula]] to a wider regime. Rather curiously, the contribution to the density of states from the vacuum becomes negative in a specific limit, which can be canceled by that from a non-vacuum Virasoro primary whose twist is no bigger than $c-1\over16$. This suggests a new upper bound of $c-1\over 16$ on the twist gap in any $c>1$ compact, unitary conformal field theory with a vacuum, which would in particular imply that pure AdS$_3$ [[0002 3D gravity|gravity]] does not exist. We confirm this negative density of states in the pure gravity partition function by Maloney, Witten, and Keller. We generalize our discussion to theories with $\mathcal{N}=(1,1)$ supersymmetry, and find similar results.\] # Bern, Carrasco, Chiodaroli, Johansson, Roiban (Review) ## The Duality Between Color and Kinematics and its Applications \[Links: [arXiv](https://arxiv.org/abs/1909.01358), [PDF](https://arxiv.org/pdf/1909.01358.pdf)\] \[Abstract: This review describes the [[0152 Colour-kinematics duality|duality between color and kinematics]] and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated [[0067 Double copy|double-copy]] structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.\] ## Important equations - (2.31) Writing $(m-2)!$ basis amplitudes in terms of $(m-3)!$ amplitudes ## Double copy - (2.54) $\mathcal{M}_{m}^{\text {tree }}=\left.\mathcal{A}_{m}^{\text {tree }}\right|_{c_{i} \rightarrow n_{i}}$=\sum_{\tau \in S_{m-2}} A_{m}^{\text {tree }}(1, \tau(2, \ldots, m-1), m) n(1, \tau(2, \ldots, m-1), m)$=-i \sum_{\sigma, \rho \in S_{m-3}} A_{m}^{\text {tree }}(1, \sigma, m-1, m) S[\sigma \mid \rho] \tilde{A}_{m}^{\text {tree }}(1, \rho, m, m-1)$ # Bhattacharya, Bhattacharyya, Dinda, Kundu ## An entropy current for dynamical black holes in four-derivative theories of gravity \[Links: [arXiv](https://arxiv.org/abs/1912.11030), [PDF](https://arxiv.org/pdf/1912.11030.pdf)\] \[Abstract: We propose an entropy current for dynamical black holes in a theory with arbitrary four derivative corrections to [[0554 Einstein gravity|Einstein's gravity]], linearized around a stationary black hole. The [[0425 Gauss-Bonnet gravity|Einstein-Gauss-Bonnet theory]] is a special case of the class of theories that we consider. Within our approximation, our construction allows us to write down a completely local version of the [[0005 Black hole second law|second law of black hole thermodynamics]], in the presence of the higher derivative corrections considered here. This ultra-local, stronger form of the second law is a generalization of a weaker form, applicable to the total entropy, integrated over a compact 'time-slice' of the horizon, a proof of which has been recently presented in [[2015#Wall (Essay)]]. We also provide a general algorithm to construct the entropy current for the four derivative theories, which may be straightforwardly generalized to arbitrary [[0006 Higher-derivative gravity|higher derivative corrections]] to Einstein's gravity. This algorithm highlights the possible ambiguities in defining the entropy current.\] ## Comments - contains a review of [[2015#Wall (Essay)]] (see that page for notes) ## Refs - [[2021#Bhattacharyya, Dhivakar, Dinda, Kundu, Patra, Roy]]: generalisation to arbitrary higher derivative gravity # Blake, Davison, Vegh ## Horizon constraints on holographic Green’s functions \[Links: [arXiv](https://arxiv.org/abs/1904.12883), [PDF](https://arxiv.org/pdf/1904.12883.pdf)\] \[Abstract: We explore a new class of general properties of thermal holographic Green's functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically anti-de Sitter spacetimes. We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green's functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations. From a boundary perspective these '[[0179 Pole skipping|pole-skipping]]' points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green's function intersects with a line of zeroes. As a consequence the dispersion relations of collective modes in the boundary theory at energy scales $\omega\sim T$ are directly constrained by the bulk dynamics near the black-brane horizon. For the case of conserved $U(1)$ current and energy-momentum tensor operators we give examples where the dispersion relations of hydrodynamic modes pass through a succession of pole-skipping points as real wavenumber is increased. We discuss implications of our results for transport, [[0429 Hydrodynamics|hydrodynamics]] and [[0008 Quantum chaos|quantum chaos]] in holographic systems.\] ## Comments - anomalous points are called Type-II in [[2020#Ahn, Jahnke, Jeong, Kim, Lee, Nishida]] ## Refs - simultaneous paper [[2019#Grozdanov, Kovtun, Starinets, Tadic (Apr, Long)]] - [[0179 Pole skipping]] ## Summary - studies [[0179 Pole skipping|pole skipping]] in the lower-half complex plane (decaying rather than growing modes) - find that these depend heavily on the action and matter profiles - examples include ==minimally coupled scalar field== and $U(1)$ currents # Blommaert, Mertens, Verschelde ## Eigenbranes in Jackiw-Teitelboim gravity \[Links: [arXiv](https://arxiv.org/abs/1911.11603), [PDF](https://arxiv.org/pdf/1911.11603)\] \[Abstract: It was proven recently that [[0050 JT gravity|JT gravity]] can be defined as an ensemble of $L \times L$ Hermitian matrices. We point out that the eigenvalues of the matrix correspond in JT gravity to [[0658 FZZT brane|FZZT]]-type boundaries on which spacetimes can end. We then investigate an ensemble of matrices with $1\ll N \ll L$ eigenvalues held fixed. This corresponds to a version of JT gravity which includes $N$ FZZT-type boundaries in the path integral contour and which is found to emulate a discrete quantum chaotic system. In particular this version of JT gravity can capture the behavior of finite-volume holographic correlators at late times, including erratic oscillations.\] # Bousso, Shahbazi-Moghaddam, Tomasevic (Aug, Letter) ## Quantum Penrose Inequality \[Links: [arXiv](https://arxiv.org/abs/1908.02755), [PDF](https://arxiv.org/pdf/1908.02755.pdf)\] \[Abstract: \] ## Refs - long version: [[BoussoShahbazi-MoghaddamTomasevic201909]] ## Summary - shows that classical [[0476 Penrose inequality]] can be violated by quantum matter at $O(1)$ not just $O(\hbar)$ # Brown, Gharibyan, Penington, Susskind ## The Python's Lunch: geometric obstructions to decoding Hawking radiation \[Links: [arXiv](https://arxiv.org/abs/1912.00228), [PDF](https://arxiv.org/pdf/1912.00228.pdf)\] \[Abstract: According to [[2013#Harlow, Hayden]] the task of distilling information out of [[0304 Hawking radiation|Hawking radiation]] appears to be computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. We trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by [[0054 Tensor network|tensor network]] models, we conjecture a precise formula relating the computational hardness of distilling information to geometric properties of the wormhole - specifically to the exponential of the difference in generalized entropies between the two non-minimal quantum extremal surfaces that constitute the obstruction. Due to its shape, we call this obstruction the "[[0196 Python's lunch|Python's Lunch]]", in analogy to the reptile's postprandial bulge.\] ## Refs - proposes [[0196 Python's lunch]] - [[0204 Quantum complexity]] # Campiglia, Laddha ## Loop Corrected Soft Photon Theorem as a Ward Identity \[Links: [arXiv](https://arxiv.org/abs/1903.09133), [PDF](https://arxiv.org/pdf/1903.09133.pdf)\] \[Abstract: \] ## Refs - [[0009 Soft theorems]] # Cardona ## Correlation functions at the bulk point singularity from the gravitational eikonal S-matrix \[Links: [arXiv](https://arxiv.org/abs/1906.08734), [PDF](https://arxiv.org/pdf/1906.08734.pdf)\] \[Abstract: \] ## Summary - propose a map from ==flat space== S-matrix to conformal correlation functions - try the map on perturbative scattering - eikonal limit of gravity scattering maps to a correlation function of the expected form at [[0128 Bulk point singularity]] # Cardoso, Gualtieri, Moore ## Gravitational waves and higher dimensions: Love numbers and Kaluza-Klein excitations \[Links: [arXiv](https://arxiv.org/abs/1910.09557), [PDF](https://arxiv.org/pdf/1910.09557.pdf)\] \[Abstract: Gravitational-wave (GW) observations provide a wealth of information on the nature and properties of black holes. Among these, [[0581 Tidal Love numbers|tidal Love numbers]] or the multipole moments of the inspiralling and final objects are key to a number of constraints. Here, we consider these observations in the context of higher-dimensional scenarios, with flat large extra dimensions. We show that -- as might be anticipated, but not always appreciated in the literature -- physically motivated set-ups are unconstrained by gravitational-wave data. Dynamical processes that do not excite the Kaluza-Klein (KK) modes lead to a signal identical to that in four-dimensional general relativity in vacuum . In addition, any possible excitation of the KK modes is highly suppressed relative to the dominant quadrupolar term; given existing constraints on the extra dimensions and the masses of the objects seen in gravitational-wave observations, KK modes appear at post-Newtonian order $\sim 10^{11}$. Finally, we re-compute the tidal Love numbers of spherical black holes in higher dimensions. We confirm that these are different from zero, but comparing with previous computations we find a different magnitude and sign.\] # Ceplak, Ramdial, Vegh ## Fermionic pole-skipping in holography \[Links: [arXiv](https://arxiv.org/abs/1910.02975), [PDF](https://arxiv.org/pdf/1910.02975.pdf)\] \[Abstract: We examine [[0103 Two-point functions|thermal Green's functions]] of fermionic operators in quantum field theories with gravity duals. The calculations are performed on the gravity side using ingoing Eddington-Finkelstein coordinates. We find that at negative imaginary Matsubara frequencies and special values of the wavenumber, there are multiple solutions to the bulk equations of motion that are ingoing at the horizon and thus the boundary Green's function is not uniquely defined. At these points in Fourier space a line of poles and a line of zeros of the correlator intersect. We analyze these '[[0179 Pole skipping|pole-skipping]]' points in three-dimensional asymptotically anti-de Sitter spacetimes where exact Green's functions are known. We then generalize the procedure to higher-dimensional spacetimes. We also discuss the special case of a fermion with half-integer mass in the [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] background. We discuss the implications and possible generalizations of the results.\] ## Summary - [[0179 Pole skipping|pole skipping]] for fermions happens at half-integer values of $2\pi T$ ## Decomposition - $\psi=\psi_{+}+\psi_{-}, \quad \Gamma^{\underline{\underline{r}}} \psi_{\pm}=\pm \psi_{\pm}, \quad P_{\pm} \equiv \frac{1}{2}\left(1 \pm \Gamma^{\underline{r}}\right)$ - $\psi_a=\psi_a^{(+)}+\psi_a^{(-)}, \quad \hat{k}_i \Gamma^{\underline{v i}} \psi_a^{(\pm)}=\pm \psi_a^{(\pm)}, \quad P^{(\pm)} \equiv \frac{1}{2}\left(1 \pm \hat{k}_i \Gamma^{\underline{v i}}\right)$ - $a=\pm$ - consequences: - only need to deal with $\left(\psi_{+}^{(+)}, \psi_{-}^{(-)}\right)$ - because the equations for $\left(\psi_{+}^{(-)}, \psi_{-}^{(+)}\right)$ are equivalent ## Leading pole-skipping - (5.13) $\begin{aligned} \left(\mathcal{S}_{+}^{(+)}\right)^{(0)}&=\Gamma^{\underline{v}}\left[-i \omega+\frac{r_0^2 f^{\prime}\left(r_0\right)}{4}\right. \left.+\frac{m r_0}{2}+\frac{i k r_0}{2 \sqrt{h\left(r_0\right)}}\right]\left(\psi_{-}^{(-)}\right)^{(0)} \\ &+ {\left[-i \omega+\frac{r_0^2 f^{\prime}\left(r_0\right)}{4}-\frac{m r_0}{2}-\frac{i k r_0}{2 \sqrt{h\left(r_0\right)}}\right]\left(\psi_{+}^{(+)}\right)^{(0)}=0 } \end{aligned}$ - can bring to a form that is more appropriate for applying the argument of [[2022#Wang, Wang]] by taking a linear combination - or perhaps even better: some more general linear combinations of the four d.o.f. $\psi_{\pm}^{(\pm)}$ ## Anomalous points - for BTZ, near horizon predictions of the locations of pole skipping exactly agree with intersections of zeros and poles of the Green's function - in higher dimensions, at special values of $m$, two pole-skipping points can coincide, and they seem to coincide with double poles of the Green's function, rather than zero-pole intersections - I suspect: since this only happens for special values of $m$, we can take $m$ to be slightly away from these values, where the near horizon analysis should give $0/0$; then let us go to these special values of $m$, where two pole-skipping points coincide, then we should get $0^2/0^2$, which should still be pole skipping # Cheamsawat, Gibbons, Wiseman ## A new energy upper bound for AdS black holes inspired by free field theory \[Links: [arXiv](https://arxiv.org/abs/1906.07192), [PDF](https://arxiv.org/pdf/1906.07192.pdf)\] \[Abstract: \] ## Summary - studies [[0314 Holographic constraints on CFT energies]] by studying BHs in the bulk directly ## How about solitons - see Discussion - they are ignored for simplicity but the same arguments work for them as well # Chen ## Pulling Out the Island with Modular Flow \[Links: [arXiv](https://arxiv.org/abs/1912.02210), [PDF](https://arxiv.org/pdf/1912.02210.pdf)\] \[Abstract: Recent works have suggested that the entanglement wedge of [[0304 Hawking radiation|Hawking radiation]] coming from an AdS black hole, will include an island inside the black hole interior after the Page time. In this paper, we propose a concrete way to extract the information from the island by acting only on the radiation degrees of freedom, building on [[0048 JLMS|the equivalence between the boundary and bulk modular flow]]. We consider examples with black holes in [[0050 JT gravity|JT gravity]] coupled to baths. In the case that the bulk conformal fields contain free massless fermion field, we provide explicit bulk picture of the information extraction process, where we find that one can almost pull out an operator from the island to the bath with [[0416 Modular Hamiltonian|modular flow]].\] # Choi, Bao, Qi, Altman ## Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition \[Links: [arXiv](https://arxiv.org/abs/1903.05124), [PDF](https://arxiv.org/pdf/1903.05124.pdf)\] \[Abstract: We analyze the [[0522 Entanglement dynamics|dynamics of entanglement entropy]] in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by the volume-law and area-law scaling [[0301 Entanglement entropy|entanglement entropy]] in steady states. The transition between the two phases is understood from the point of view of [[0146 Quantum error correction|quantum error correction]]: the [[0008 Quantum chaos|chaotic]] unitary evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling. We confirm these results using numerical simulations and obtain the phase diagram of our model. Our work shows that information scrambling plays a crucial role in understanding the dynamics of entanglement in an open quantum system and relates the entanglement phase transition to changes in quantum channel capacity.\] # Collier, Maloney, Maxfield, Tsiares ## Universal Dynamics of Heavy Operators in CFT$_2$ \[Links: [arXiv](https://arxiv.org/abs/1912.00222), [PDF](https://arxiv.org/pdf/1912.00222.pdf)\] \[Abstract: We obtain an asymptotic formula for the average value of the [[0030 Operator product expansion|operator product expansion]] coefficients of any unitary, compact two dimensional CFT with $c>1$. This formula is valid when one or more of the operators has large dimension or -- in the presence of a twist gap -- has large spin. Our formula is universal in the sense that it depends only on the [[0033 Central charge|central charge]] and not on any other details of the theory. This result unifies all previous asymptotic formulas for CFT$_2$ structure constants, including those derived from [[0021 Crossing symmetry|crossing symmetry]] of four point functions, [[0612 Modular invariance|modular covariance]] of torus correlation functions, and higher genus modular invariance. We determine this formula at finite central charge by deriving [[0573 Crossing kernel|fusion kernel]] for higher genus crossing equations, which give analytic control over the structure constants even in the absence of exact knowledge of the [[0031 Conformal block|conformal blocks]]. The higher genus modular kernels are obtained by sewing together the elementary kernels for four-point crossing and modular transforms of torus one-point functions. Our asymptotic formula is related to the DOZZ formula for the structure constants of Liouville theory, and makes precise the sense in which Liouville theory governs the universal dynamics of heavy operators in any CFT. The large central charge limit provides a link with [[0002 3D gravity|3D gravity]], where the averaging over heavy states corresponds to a coarse-graining over black hole microstates in holographic theories. Our formula also provides an improved understanding of the [[0040 Eigenstate thermalisation hypothesis|Eigenstate Thermalization Hypothesis]] (ETH) in CFT$_2$, and suggests that ETH can be generalized to other kinematic regimes in two dimensional CFTs.\] ## Universal formula for OPE coefficients Just like the Cardy formula is the dual of the statement that the identity has conformal weights $h=\bar{h}=0$, the dual of the statement that (for unitary, compact CFTs) $C_{i i \mathbb{1}}=1$ for any $i$ is a universal formula for the OPE coefficients:$\overline{C_{i j k}{ }^2} \sim C_0\left(h_i, h_j, h_k\right) C_0(\bar{h}_i, \bar{h}_j, \bar{h}_k),$where$C_0\left(h_i, h_j, h_k\right) \equiv \frac{1}{\sqrt{2}} \frac{\Gamma_b(2 Q)}{\Gamma_b(Q)^3} \frac{\prod_{ \pm \pm \pm} \Gamma_b\left(\frac{Q}{2} \pm i P_i \pm i P_j \pm i P_k\right)}{\prod_{a \in\{i, j, k\}} \Gamma_b\left(Q+2 i P_a\right) \Gamma_b\left(Q-2 i P_a\right)}.$The formula is secretly three formulas: holding two, one or zero operators fixed respectively and taking the remaining ones heavy. The averaging is only over heavy operators. The three formulas are derived using different types of crossing symmetry: (1) with two operators fixed: crossing symmetry of 4-point functions with pairwise identical external operators; (2) with one fixed: modular invariance of torus 2-point functions of identical operators; (3) none fixed: modular invariance of genus two partition function. They can be obtained by sewing one, two, and three points, respectively, of two two-spheres, each with three insertions. # Cotler, Jensen, Maloney ## Low-dimensional de Sitter quantum gravity \[Links: [arXiv](https://arxiv.org/abs/1905.03780), [PDF](https://arxiv.org/pdf/1905.03780)\] \[Abstract: We study aspects of [[0050 JT gravity|Jackiw-Teitelboim]] (JT) quantum gravity in two-dimensional nearly de Sitter (dS) spacetime, as well as pure de Sitter quantum gravity in three dimensions. These are each theories of boundary modes, which include a reparameterization field on each connected component of the boundary as well as topological degrees of freedom. In two dimensions, the boundary theory is closely related to the Schwarzian path integral, and in three dimensions to the quantization of coadjoint orbits of the Virasoro group. Using these boundary theories we compute loop corrections to the wavefunction of the universe, and investigate gravitational contributions to scattering. Along the way, we show that JT gravity in dS$_2$ is an analytic continuation of JT gravity in Euclidean AdS$_2$, and that pure gravity in dS$_3$ is a continuation of pure gravity in Euclidean AdS$_3$. We define a genus expansion for de Sitter JT gravity by summing over higher genus generalizations of surfaces used in the Hartle-Hawking construction. Assuming a conjecture regarding the volumes of moduli spaces of such surfaces, we find that the de Sitter genus expansion is the continuation of the recently discovered AdS genus expansion. Then both may be understood as coming from the genus expansion of the same double-scaled matrix model, which would provide a non-perturbative completion of de Sitter JT gravity.\] # Czech, de Boer, Ge, Lamprou ## A Modular Sewing Kit for Entanglement Wedges \[Links: [arXiv](https://arxiv.org/abs/1903.04493), [PDF](https://arxiv.org/pdf/1903.04493.pdf)\] \[Abstract: \] - [[0423 Berry phase]] # Czech, Dong ## Holographic Entropy Cone with Time Dependence in Two Dimensions \[Links: [arXiv](https://arxiv.org/abs/1905.03787), [PDF](https://arxiv.org/pdf/1905.03787)\] \[Abstract: In holographic duality, if a boundary state has a geometric description that realizes the [[0007 RT surface|Ryu-Takayanagi]] proposal then its entanglement entropies must obey certain inequalities that together define the so-called [[0259 Holographic entropy cone|holographic entropy cone]]. A large family of such inequalities have been proven under the assumption that the bulk geometry is static, using a method involving contraction maps. By using kinematic space techniques, we show that in two boundary (three bulk) dimensions, all entropy inequalities that can be proven in the static case by contraction maps must also hold in holographic states with time dependence.\] # Das, Ezhuthachan, Kundu ## Real Time Dynamics in Low Point Correlators in 2d BCFT \[Links: [arXiv](https://arxiv.org/abs/1907.08763), [PDF](https://arxiv.org/pdf/1907.08763.pdf)\] \[Abstract: \] ## Summary - [[0008 Quantum chaos]] in [[0181 AdS-BCFT]] - 3-point function in BCFT?  # de Rham, Tolley ## Speed of gravity \[Links: [arXiv](https://arxiv.org/abs/1909.00881), [PDF](https://arxiv.org/pdf/1909.00881.pdf)\] \[Abstract: \] ## Refs - later paper by them [[2020#de Rham, Tolley]] ## Summary - speed of gravitational waves differs from light on **cosmological and other spontaneously Lorentz breaking** backgrounds - results from loop contributions from **massive** fields of any spin, or from tree level effects from **massive** higher spins, $s>2$ - n.b. both massive # Dias, Reall, Santos ## The BTZ black hole violates strong cosmic censorship \[Links: [arXiv](https://arxiv.org/abs/1906.08265), [PDF](https://arxiv.org/pdf/1906.08265.pdf)\] \[Abstract: We investigate the stability of the inner horizon of a rotating [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black hole. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. This is demonstrated for scalar fields, for massive Chern-Simons fields, for Proca fields, and for massive spin-2 fields. Thus the [[0208 Strong cosmic censorship|strong cosmic censorship]] conjecture is violated by a near-extremal BTZ black hole in a large class of theories. However, we show that a weaker "rough" version of the conjecture is respected. We calculate the renormalized energy-momentum tensor of a scalar field in the Hartle-Hawking state in the BTZ geometry. We show that the result is finite at the inner horizon of a near-extremal black hole. Hence the backreaction of vacuum polarization does not enforce strong cosmic censorship.\] # Dong, Marolf ## One-loop universality of holographic codes \[Links: [arXiv](https://arxiv.org/abs/1910.06329), [PDF](https://arxiv.org/pdf/1910.06329.pdf)\] \[Abstract: Recent work showed holographic [[0146 Quantum error correction|error correcting codes]] to have simple universal features at $O(1/G)$. In particular, states of fixed [[0007 RT surface|Ryu-Takayanagi (RT)]] area in such codes are associated with flat entanglement spectra indicating maximal entanglement between appropriate subspaces. We extend such results to one-loop order ($O(1)$ corrections) by controlling both [[0006 Higher-derivative gravity|higher-derivative corrections]] to the bulk effective action and dynamical quantum fluctuations below the cutoff. This result clarifies the relation between the bulk path integral and the quantum code, and implies that i) simple [[0054 Tensor network|tensor network]] models of holography continue to match the behavior of holographic CFTs beyond leading order in $G$, ii) the relation between bulk and boundary modular Hamiltonians derived by [[2016#Jafferis, Lewkowycz, Maldacena, Suh|Jafferis, Lewkowycz, Maldacena, and Suh]] holds as an operator equation on the code subspace and not just in code-subspace expectation values, and iii) the code subspace is invariant under an appropriate notion of modular flow. A final corollary requires interesting cancelations to occur in the bulk renormalization-group flow of holographic quantum codes. Intermediate technical results include showing the [[2013#Lewkowycz, Maldacena|Lewkowycz-Maldacena]] computation of RT entropy to take the form of a Hamilton-Jacobi variation of the action with respect to boundary conditions, corresponding results for higher-derivative actions, and generalizations to allow RT surfaces with finite conical angles.\] ## Summary - calculation of [[0145 Generalised area|HEE]] - improves on [[2013#Dong]] in that it now has no ambiguity and allows for finite Renyi number $n$ - gives series expansions for metric components in terms of both coupling constant and coordinates $z$ and $\bar z$ ## Comments - Appendix B contains prescription to find the correct action that gives a good variational principle ## Notations - conical angle $2\pi m$ where $m$ is any positive real number smaller than unity - because we need $m<1$ so the next to leading order in $h_{ij}$ is $\hat o(r)$ - also consistent with end of p.33 ## App. A: Einstein variation - NEED to choose a *family* of metrics (in terms of an expansion) (A.1) - turns out that Einstein equation constrains it to a certain form (so we could start with this more constrained form to begin with) - **Well-defined variation principle** with ==BC fixing the conical angle== - $E_{ij,pqs}=0$: - $pq=s=0$: trivial - else: allows to solve for $h_{ij,pqs}$ in terms of lower order quantities - $E_{z\bar z,pqs}=0$: - $pq=s=0$: trivial - else: used to solve for $T_{pqs}$ in terms of lower order quantities - $E_{zi,pqs}=0$: (and c.c.) - $p=s=0$: trivial - else: used to solve for $U_{i,pqs}$ in terms of lower order quantities - $E_{zz,pqs}=0$: - $p=0, s\le 1$: trivial - $p>0, q=s=0$: can solve for the trace $h^{ij}{}_{,000}h_{ij,p00}$ - else: guaranteed by Bianchi identities - **finiteness of action**: - $g_{\mu \nu}=\left.g_{\mu \nu}\right|_{r=0}+\hat{o}(r), \quad \Gamma_{\mu \nu}^{\rho}=\frac{\hat{o}(r)}{r}, \quad R_{\nu \rho \sigma}^{\mu}=\frac{\hat{o}(r)}{r^{2}}$ so the action is integrable near $r=0$ - **vanishing of boundary term**: - $\delta \tilde{I}[g]=\frac{1}{16 \pi G} \lim _{\epsilon \rightarrow 0^{+}}\left[\int_{r \geq \epsilon} d^{d+1} x \sqrt{g}\left(G^{\mu \nu}+\Lambda g^{\mu \nu}\right) \delta g_{\mu \nu}\right.$\left.+\left.\int_{\partial} d^{d} X \sqrt{\gamma} n^{\mu}\left(\nabla^{\nu} \delta g_{\mu \nu}-\nabla_{\mu} \delta g_{\nu}^{\nu}\right)\right|_{r=\epsilon}\right]$ - but $\nabla_{\rho} \delta g_{\mu \nu}=\frac{\hat{o}(r)}{r}$, $\sqrt{\gamma} \sim r$ and $n^{\mu} \sim r^{0}$, so this the boundary term vanishes - n.b. this varying requires fixing the BC (fixed conical angle); if varying wrt to the conical angel we get an area term ## Expansion - $d s^{2}=d z d \bar{z}+T \frac{(\bar{z} d z-z d \bar{z})^{2}}{z \bar{z}}+h_{i j} d y^{i} d y^{j}+2 i U_{j} d y^{j}(\bar{z} d z-z d \bar{z})$ - for Einstein: - $T=\sum_{p, q, s=0 \atop p q>0 \text { or } s>0}^{\infty} T_{p q s} z^{\frac{p}{m}} \bar{z}^{\frac{q}{m}}(z \bar{z})^{s}$ - $U_{i}=\sum_{p, q, s=0}^{\infty} U_{i, p q s} z^{\frac{p}{m}} \bar{z}^{\frac{q}{m}}(z \bar{z})^{s}$ - $h_{i j}=\sum_{p, q, s=0}^{\infty} h_{i j, p q s} z^{\frac{p}{m}} \bar{z}^{\frac{q}{m}}(z \bar{z})^{s}$ - n.b. $T$ does not have a constant term - in general: - $T^{(\vec{n})}=\sum_{p, q, s=0 \atop p q>0 \text { or } s>n}^{\infty} T_{p q s}^{(\vec{n})} z^{\frac{p}{m}} \bar{z}^{\frac{q}{m}}(z \bar{z})^{s-n}$ - $U_{i}^{(\vec{n})}=\sum_{p, q, s=0 \atop p q>0 \text { or } s \geq n}^{\infty} U_{i, p q s}^{(\vec{n})} z^{\frac{p}{m}} \bar{z}^{\frac{q}{m}}(z \bar{z})^{s-n}$ - $h_{i j}^{(\vec{n})}=\sum_{p, q, s=0 \atop p q>0 \text { or } s \geq n}^{\infty} h_{i j, p q s}^{(\vec{n})} z^{\frac{p}{m}} \bar{z}^{\frac{q}{m}}(z \bar{z})^{s-n}$ - n.b. none of these have a constant term (at order $\vec n$) - where $n=\sum_{k=1}^{\infty} n_{k}\left(\frac{D_{k}}{2}-1\right)$ - $D_k$ = total number of derivatives in the term with coefficient $\lambda_k$ - e.g. $D=4$ for four-derivative terms # Dutta, Faulkner ## A canonical purification for the entanglement wedge cross-section \[Links: [arXiv](https://arxiv.org/abs/1905.00577), [PDF](https://arxiv.org/pdf/1905.00577.pdf)\] \[Abstract: \] ## Summary - *introduces* [[0166 Reflected entropy]] - *shows* it is twice of entanglement wedge cross section # Engelhardt, Horowitz ## A Holographic Argument for the Penrose Inequality in AdS \[Links: [arXiv](https://arxiv.org/abs/1903.00555), [PDF](https://arxiv.org/pdf/1903.00555.pdf)\] \[Abstract: We give a holographic argument in favor of the AdS [[0476 Penrose inequality|Penrose inequality]], which conjectures a lower bound on the total mass in terms of the area of [[0226 Apparent horizon|apparent horizons]]. This inequality is often viewed as a test of [[0221 Weak cosmic censorship|cosmic censorship]]. We further find a connection between the area law for apparent horizons and the Penrose inequality. Finally, we show that the argument also applies to solutions with charge, resulting in a charged Penrose inequality in AdS.\] # Fan, Fotopoulos, Taylor ## Soft limits of Yang-Mills amplitudes and conformal correlators \[Links: [arXiv](https://arxiv.org/abs/1903.01676), [PDF](https://arxiv.org/pdf/1903.01676.pdf)\] \[Abstract: : We study tree-level celestial amplitudes in Yang-Mills theory -- [[0079 Mellin transform|Mellin transforms]] of multi-gluon scattering amplitudes that convert them into the correlators of conformal primary fields on two-dimensional [[0022 Celestial sphere|celestial sphere]]. By using purely field-theoretical methods, we show that the [[0390 Conformally soft theorems|soft conformal limit]] of celestial amplitudes, in which one of the primary field operators associated to gauge bosons becomes a dimension one current, is dominated by the contributions of low-energy soft particles. This result confirms conclusions reached by using Yang-Mills theory formulated in curvilinear coordinates, as pioneered by Strominger. By using well-known [[0078 Collinear limit|collinear limits]] of Yang-Mills amplitudes, we derive the [[0114 Celestial OPE|OPE]] rules for the primary fields and the holomorphic currents arising in the conformally soft limit. The [[0106 Ward identity|Ward identities]] following from OPE have the same form as the identities derived by using [[0009 Soft theorems|soft theorems]].\] ## Summary - shows that the soft conformal limit of celestial amplitudes, in which one of the primary field operators associated to gauge bosons becomes a dim-1 current, is dominated by the contribution of low-energy soft particles - confirms conclusions reached by doing YM in curvilinear coordinates - use collinear limits of amplitudes => OPEs rules for ==primary fields and the holomorphic currents== ## Refs - subleading collinear limit: [[2015#Stieberger, Taylor (Aug)]] - precursor to [[2019#Pate, Raclariu, Strominger, Yuan]] - collinear limits = OPE for ==gluons== in this paper ## Warning - extra factors of $g(\lambda_i)$ in (3.1) for [[0079 Mellin transform|Mellin transform]] ## Sec. 4: [[0030 Operator product expansion|OPE]] - currents associated with conformally soft gauge bosons - $j^{a}(z)=\mathcal{O}_{0+}^{a}(z, \bar{z}), \quad \bar{j}^{a}(\bar{z})=\mathcal{O}_{0-}^{a}(z, \bar{z})$ - 0 means $\lambda=0$ - OPE - $j^{a}(z) \mathcal{O}_{\lambda J}^{b}(w, \bar{w})=\frac{1}{z-w} \sum_{c} f^{a b c} \mathcal{O}_{\lambda J}^{c}(w, \bar{w})+\ldots$ - $\bar{j}^{a}(\bar{z}) \mathcal{O}_{\lambda J}^{b}(w, \bar{w})=\frac{1}{\bar{z}-\bar{w}} \sum_{c} f^{a b c} \mathcal{O}_{\lambda J}^{c}(w, \bar{w})+\ldots$ - $j^{a}(z) j^{b}(w)=\frac{1}{z-w} \sum_{c} f^{a b c} j^{c}(w)+\ldots$ # Fitzpatrick, Huang, Li ## Probing universalities in $d>2$ CFTs: from BHs to shock waves \[Links: [arXiv](https://arxiv.org/abs/1907.10810), [PDF](https://arxiv.org/pdf/1907.10810.pdf)\] \[Abstract: \] ## Refs - [[0129 Dual of shockwaves]] ## Summary - computes correlation function on a [[0117 Shockwave]] background to all orders in a large central charge expansion - **geodesic limit**: ANEC exponentitates in the multi-stress-tensor sector - ... ## Correlator across the shock wave - $G_{\text {Eik }}(z, \bar{z})=\frac{\Gamma(2 \Delta)}{\Gamma^{2}(\Delta-1)} \int_{H_{3}} \frac{d^{3} \mathbf{x}}{(-2 \mathbf{q} \cdot \mathbf{x}+h(\mathbf{x} \cdot \mathbf{p})+i \epsilon)^{2 \Delta}}$ - $h(\mathbf{x} \cdot \mathbf{p})=A z^{-3}{ }_{2} F_{1}\left(3, \frac{5}{2}, 5, \frac{1}{z}\right)$ # Fotopoulos, Stieberger, Taylor, Zhu ## Extended BMS algebra of CCFT \[Links: [arXiv](https://arxiv.org/abs/1912.10973), [PDF](https://arxiv.org/pdf/1912.10973.pdf)\] \[Abstract: \] ## Summary - [[0063 Symmetry of CCFT]] = extended BMS - use soft and collinear theorems of EYM to derive OPE of BMS field operators - stress tensor (given by shadow transform of soft graviton operator) implements **superrotations** in the [[0032 Virasoro algebra|Virasoro]] subalgebra of $\mathfrak{b m s}_{4}$ - makes sense at stress tensor in an usual 2d CFT is just the Virasoro generator - **supertranslations**: obtained from translation along lightcone by commuting with stress tensor - also originates from a soft graviton and generates a flow of conformal dimensions - all supertranslations can be assembled into a single primary conformal field operator on [[0022 Celestial sphere]] # Fotopoulos, Taylor ## Primary Fields in Celestial CFT \[Links: [arXiv](https://arxiv.org/abs/1906.10149), [PDF](https://arxiv.org/pdf/1906.10149.pdf)\] \[Abstract: \] ## Refs ## Summary - *derives* the [[0030 Operator product expansion]] between stress tensor and gluon - *shows* that they transform as [[0032 Virasoro algebra|Virasoro primaries]] # Freidel, Hopfmuller, Riello ## Asymptotic renormalization in flat space: symplectic potential and charges of electromagnetism \[Links: [arXiv](https://arxiv.org/abs/1904.04384), [PDF](https://arxiv.org/pdf/1904.04384.pdf)\] \[Abstract: \] - [[0209 Holographic renormalisation]] # Fu, Marolf ## Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/1909.02505), [PDF](https://arxiv.org/pdf/1909.02505.pdf)\] \[Abstract: We use Euclidean path integrals to explore the set of bulk asymptotically AdS spacetimes with good CFT duals. We consider simple bottom-up models of bulk physics defined by [[0554 Einstein gravity|Einstein-Hilbert gravity]] coupled to thin domain walls and restrict to solutions with spherical symmetry. The cosmological constant is allowed to change across the domain wall, modeling more complicated Einstein-scalar systems where the scalar potential has multiple minima. In particular, the cosmological constant can become positive in the interior. However, in the above context, we show that inflating bubbles are never produced by smooth Euclidean saddles to asymptotically AdS path integrals. The obstacle is a direct parallel to the well-known obstruction to creating inflating universes by tunneling from flat space. In contrast, we do find good saddles that create so-called [[0281 Bag-of-gold spacetime|"bag-of-gold" geometries]] which, in addition to their single asymptotic region, also have an additional large semi-classical region located behind both past and future event horizons. Furthermore, without fine-tuning model parameters, using multiple domain walls we find Euclidean geometries that create arbitrarily large bags-of-gold inside a black hole of fixed horizon size, and thus at fixed [[0004 Black hole entropy|Bekenstein-Hawking entropy]]. Indeed, with our symmetries and in our class of models, such solutions provide the unique semi-classical saddle for appropriately designed (microcanonical) path integrals. This strengthens a classic tension between such spacetimes and the CFT density of states, similar to that in the [[0131 Information paradox|black hole information problem]].\] ## Summary - these spacetimes can exhibit a pathology related to [[0131 Information paradox|information paradox]] - review thin-wall formalism for AlAdS - no AlAdS spacetimes with inflating interiors - construct bag-of-gold - large number of domain walls -> large bags-of-gold inside BH with fixed horizon size # Geiller, Jai-akson ## Extended actions, dynamics of edge modes, and entanglement entropy \[Links: [arXiv](https://arxiv.org/abs/1912.06025), [PDF](https://arxiv.org/pdf/1912.06025.pdf)\] \[Abstract: In this work we propose a simple and systematic framework for including [[0556 Edge mode|edge modes]] in gauge theories on manifolds with boundaries. We argue that this is necessary in order to achieve the factorizability of the path integral, the Hilbert space and the phase space, and that it explains how edge modes acquire a boundary dynamics and can contribute to observables such as the [[0301 Entanglement entropy|entanglement entropy]]. Our construction starts with a boundary action containing edge modes. In the case of Maxwell theory for example this is equivalent to coupling the gauge field to boundary sources in order to be able to factorize the theory between subregions. We then introduce a new variational principle which produces a systematic boundary contribution to the symplectic structure, and thereby provides a covariant realization of the extended phase space constructions which have appeared previously in the literature. When considering the path integral for the extended bulk + boundary action, integrating out the bulk degrees of freedom with chosen boundary conditions produces a residual boundary dynamics for the edge modes, in agreement with recent observations concerning the contribution of edge modes to the entanglement entropy. We put our proposal to the test with the familiar examples of Chern-Simons and BF theory, and show that it leads to consistent results. This therefore leads us to conjecture that this mechanism is generically true for any gauge theory, which can therefore all be expected to posses a boundary dynamics. We expect to be able to eventually apply this formalism to gravitational theories.\] ## Refs - [[0044 Extended phase space]] - [[0556 Edge mode]] - [[2017#Geiller (Mar)]] ## Summary - introduce a new ==variational principle== which produces a systematic boundary contribution to the symplectic structure, and thereby provides a ==covariant== realization of the [[0044 Extended phase space|extended phase space]] constructions - examples: Chern-Simons and BF theory - discusses path integral as well ## Corner term - argues that the corner term naturally serves as the edge modes needed to add to the symplectic potential - exactly like in [[2019#Harlow, Wu]] - but did not explain why or whether this is always enough to make the symplectic structure diffeo-invariant # Ghosh, Maxfield, Turiaci ## A universal Schwarzian sector in two-dimensional conformal field theories \[Links: [arXiv](https://arxiv.org/abs/1912.07654), [PDF](https://arxiv.org/pdf/1912.07654.pdf)\] \[Abstract: We show that an extremely generic class of two-dimensional conformal field theories (CFTs) contains a sector described by the Schwarzian theory. This applies to theories with no additional symmetries and large [[0033 Central charge|central charge]], but does not require a [[0001 AdS-CFT|holographic]] dual. Specifically, we use [[0036 Conformal bootstrap|bootstrap]] methods to show that in the grand canonical ensemble, at low temperature with a chemical potential sourcing large angular momentum, the density of states and correlation functions are determined by the Schwarzian theory, up to parametrically small corrections. In particular, we compute [[0482 Out-of-time-order correlator|out-of-time-order correlators]] in a controlled approximation. For holographic theories, these results have a gravitational interpretation in terms of large, near-extremal rotating [[0086 Banados-Teitelboim-Zanelli black hole|BTZ black holes]], which have a near horizon throat with nearly AdS$_2 \times S^1$ geometry. The Schwarzian describes strongly coupled gravitational dynamics in the throat, which can be reduced to [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] interacting with a ==$U(1)$ field associated to transverse rotations, coupled to matter==. We match the physics in the throat to observables at the AdS$_3$ boundary, reproducing the CFT results.\] # Gralla, Ravishankar, Zimmerman ## Horizon Instability of the Extremal BTZ Black Hole \[Links: [arXiv](https://arxiv.org/abs/https://arxiv.org/abs/1911.11164), [PDF](https://arxiv.org/pdf/https://arxiv.org/abs/1911.11164.pdf)\] \[Abstract: \] ## Refs - earlier [[2018#Gralla, Ravishankar, Zimmerman]]: planar BH ## Summary - studies [[0473 Retarded Green's function]] of scalar on extremal BTZ - relates [[0340 Aretakis instability]] to properties of the [[0473 Retarded Green's function]] # Grozdanov, Kovtun, Starinets, Tadic (Apr, Short) ## On the convergence of the gradient expansion in hydrodynamics \[Links: [arXiv](https://arxiv.org/abs/1904.01018), [PDF](https://arxiv.org/pdf/1904.01018.pdf)\] \[Abstract: \] ## Refs - long [[2019#Grozdanov, Kovtun, Starinets, Tadic (Apr, Long)]] # Grozdanov, Kovtun, Starinets, Tadic (Apr, Long) ## The complex life of hydrodynamic modes \[Links: [arXiv](https://arxiv.org/abs/1904.12862), [PDF](https://arxiv.org/pdf/1904.12862.pdf)\] \[Abstract: \] ## Summary - studies a connection between the non-zeroness of convergence ratio and [[0179 Pole skipping]] # Guevara ## Notes on conformal soft theorems and recursion relations in gravity \[Links: [arXiv](https://arxiv.org/abs/1906.07810), [PDF](https://arxiv.org/pdf/1906.07810.pdf)\] \[Abstract: Celestial amplitudes are flat-space amplitudes which are [[0079 Mellin transform|Mellin-transformed]] to correlators living on the [[0022 Celestial sphere|celestial sphere]]. In this note we present a recursion relation, based on a tree-level [[0058 BCFW|BCFW recursion]], for gravitational celestial amplitudes and use it to explore the notion of [[0390 Conformally soft theorems|conformal softness]]. As the BCFW formula exponentiates in the soft energy, it leads directly to conformal soft theorems in an exponential form. These appear from a soft piece of the amplitude characterized by a discrete family of singularities with weights $\Delta=1-\mathbb{Z}_+$. As a byproduct, in the case of the MHV sector we provide a direct celestial analogue of [[2012#Hodges|Hodges]]' recursion formula at all multiplicities.\] ## Summary - *uses* a [[0010 Celestial holography|celestial]] [[0058 BCFW|BCFW]] to explore the notion of [[0390 Conformally soft theorems|conformal soft theorems]] - *provides* a direct celestial analogue of [[2012#Hodges]]'s formula at all multiplicities (for [[0061 Maximally helicity violating amplitudes|MHV]] amplitudes) ## Simplification for [[0061 Maximally helicity violating amplitudes|MHV]] - in general $\mathcal{M}_{n+1}=\mathcal{M}_{n+1}^{c}+\mathcal{M}_{n+1}^{n c}+\mathcal{M}_{n+1}^{\infty}$ - but the last two terms are zero for MHV - $\mathcal{M}_{n+1}^{c}=\frac{\kappa}{2} \sum_{i=1}^{n-1} \frac{[s i]\langle n i\rangle^{2}}{\langle s i\rangle\langle n s\rangle^{2}}$\mathcal{M}_{n}\left(\ldots,\left\{\lambda_{i}, \tilde{\lambda}_{i}+\frac{\langle n s\rangle}{\langle n i\rangle} \tilde{\lambda}_{s}\right\}, \ldots,\left\{\lambda_{n}, \tilde{\lambda}_{n}+\frac{\langle i s\rangle}{\langle i n\rangle} \tilde{\lambda}_{s}\right\}\right)$ - alternative form: $\mathcal{M}_{n+1}^{\mathrm{MHV}}=\frac{\kappa}{2} \sum_{i=1}^{n-2} \frac{[s i]\langle n i\rangle\langle(n-1) i\rangle}{\langle s i\rangle\langle n s\rangle\langle(n-1) s\rangle}$ $\mathcal{M}_{n}^{\mathrm{MHV}}\left(\ldots,\left\{\lambda_{i}, \tilde{\lambda}_{i}+\frac{\langle n s\rangle}{\langle n i\rangle} \tilde{\lambda}_{s}\right\}, \ldots,\left\{\lambda_{n}, \tilde{\lambda}_{n}+\frac{\langle i s\rangle}{\langle i n\rangle} \tilde{\lambda}_{s}\right\}\right)$ ## Mellin transform - $\int_{0}^{\infty} d \omega \omega^{\Delta-1} \times \frac{e^{-\mathcal{J} \omega}}{\omega}=\Gamma(\Delta-1) \mathcal{J}^{\Delta-1}$\asymp \frac{1}{\Delta-1}-\frac{\mathcal{J}}{\Delta}+\frac{\mathcal{J}^{2} / 2}{\Delta+1}+\ldots$ # Halder ## Global Symmetry and Maximal Chaos \[Links: [arXiv](https://arxiv.org/abs/1908.05281), [PDF](https://arxiv.org/pdf/1908.05281.pdf)\] \[Abstract: In this note we study chaos in generic quantum systems with a global symmetry generalizing seminal work [arXiv:1503.01409](https://arxiv.org/abs/1503.01409) by [[2015#Maldacena, Shenker, Stanford|Maldacena, Shenker and Stanford]]. We conjecture a bound on instantaneous chaos exponent in a thermodynamic ensemble at temperature $T$ and chemical potential $\mu$ for the continuous global symmetry under consideration. For local operators which could create excitation up to some fixed charge, the bound on [[0466 Lyapunov exponent|chaos (Lyapunov) exponent]] is independent of chemical potential $\lambda_L \leq \frac{2 \pi T}{ \hbar}$. On the other hand when the operators could create excitation of arbitrary high charge, we find that exponent must satisfy $\lambda_L \leq \frac{2 \pi T}{(1-|\frac{\mu}{\mu_c}|) \hbar}$, where $\mu_c$ is the maximum value of chemical potential for which the thermodynamic ensemble makes sense. As specific examples of quantum mechanical systems we consider conformal field theories. In a generic conformal field theory with internal $U(1)$ symmetry living on a cylinder the former bound is applicable, whereas in more interesting examples of holographic two dimensional conformal field theories dual to [[0554 Einstein gravity|Einstein gravity]], we argue that later bound is saturated in presence of a non-zero chemical potential for rotation.\] # Harlow, Wu ## Covariant phase space with boundaries \[Links: [arXiv](https://arxiv.org/abs/1906.08616), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: The [[0019 Covariant phase space|covariant phase space]] method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically treat total derivatives and boundary terms, which has led to some confusion about how exactly to apply the formalism in the presence of boundaries. In particular the original construction of the canonical Hamiltonian relies on the assumed existence of a certain boundary quantity "$Bquot;, whose physical interpretation has not been clear. We here give an algorithmic procedure for applying the covariant phase space formalism to field theories with spatial boundaries, from which the term in the Hamiltonian involving $B$ emerges naturally. Our procedure also produces an additional boundary term, which was not present in the original literature and which so far has only appeared implicitly in specific examples, and which is already nonvanishing even in general relativity with sufficiently permissive boundary conditions. The only requirement we impose is that at solutions of the equations of motion the action is stationary modulo future/past boundary terms under arbitrary variations obeying the spatial boundary conditions; from this the symplectic structure and the Hamiltonian for any diffeomorphism that preserves the theory are unambiguously constructed. We show in examples that the Hamiltonian so constructed agrees with previous results. We also show that the [[0360 Poisson bracket|Poisson bracket]] on covariant phase space directly coincides with the [[0150 Peierls bracket|Peierls bracket]], without any need for non-covariant intermediate steps, and we discuss possible implications for the [[0004 Black hole entropy|entropy]] of dynamical black hole horizons.\] ## Refs - kind of like an OG for [[0324 Covariant edge mode|covariant edge mode]] - extension to null boundaries [[ShiWangXiuZhang2020]] - exactly the same idea but in the context of [[0044 Extended phase space|extended phase space]] was used in [[2019#Geiller, Jai-akson]] ## Summary - shows that [[0150 Peierls bracket|Peierls bracket]] coincides with Poisson bracket for general Lagrangian field theories (Peierls showed it for two-derivative theories) ## Charge - $H_{\xi}=\int_{\delta \Sigma}\left(Q_{\epsilon}+\xi \cdot \ell-X_{\xi} \cdot C\right)+\text { constant }$ ## GR - $C=c \cdot \epsilon_{\partial M}$ - $\left.X_{\xi} \cdot C\right|_{\partial \Sigma}=\frac{1}{16 \pi G}\left(\tau^{\alpha} n^{\beta}+\tau^{\beta} n^{\alpha}\right) \nabla_{\alpha} \xi_{\beta} \epsilon_{\partial \Sigma}$ # Hernandez-Cuenca ## The Holographic Entropy Cone for Five Regions \[Links: [arXiv](https://arxiv.org/abs/1903.09148), [PDF](https://arxiv.org/pdf/1903.09148.pdf)\] \[Abstract: Even though little is known about the quantum entropy cone for $N\geq4$ subsystems, holographic techniques allow one to get a handle on the subspace of entropy vectors corresponding to states with gravity duals. For static spacetimes and $N$ boundary subsystems, this space is a convex polyhedral cone known as the [[0259 Holographic entropy cone|holographic entropy cone]] $\mathcal{C}_N$ for $N$ regions. While an explicit description of $\mathcal{C}_N$ was accomplished for all $N\leq4$ in the initial study, the information given about larger N was only partial already for $\mathcal{C}_5$. This letter provides a complete construction of $\mathcal{C}_5$ by exhibiting graph models for every extreme ray orbit generating the cone defined by all proven holographic entropy inequalities for $N=5$. The question of whether there exist additional inequalities for 5 parties is thus settled with a negative answer. The conjecture that $\mathcal{C}_5$ coincides with the analogous cone for dynamical spacetimes is supported by demonstrating that the information quantities defining its facets are primitive.\] # Horowitz, Marolf, Santos, Wang ## Creating a traversable wormhole \[Links: [arXiv](https://arxiv.org/abs/1904.02187), [CQG](https://iopscience.iop.org/article/10.1088/1361-6382/ab436f)\] \[Abstract: We argue that one can nucleate a [[0083 Traversable wormhole|traversable wormhole]] via a nonperturbative process in quantum gravity. To support this, we construct spacetimes in which there are instantons giving a finite probability for a test cosmic string to break and produce two particles on its ends. One should be able to replace the particles with small black holes with only small changes to the spacetime away from the horizons. The black holes are then created with their horizons identified, so this is an example of nucleating a wormhole. Unlike previous examples where the created black holes accelerate apart, in our case they remain essentially at rest. This is important since wormholes become harder and harder to make traversable as their mouths become widely separated, and since traversability can be destroyed by Unruh radiation. In our case, back-reaction from quantum fields can make the wormhole traversable.\] ## Summary [[0083 Traversable wormhole|Traversable wormholes]], wormholes that allow one to enter from one side and exit from the other, have been recently discovered and studied. The examples that have been found prior to this work are all eternal traversable wormholes, i.e. they exist at all times. In this work, the possibility of creating them was studied and examples found. # Horowitz, Wang ## Gravitational corner conditions in holography \[Links: [arXiv](https://arxiv.org/abs/1909.11703), [PDF](https://arxiv.org/pdf/1909.11703.pdf), [JHEP](https://link.springer.com/article/10.1007%2FJHEP01%282020%29155)\] \[Abstract: Contrary to popular belief, asymptotically anti-de Sitter solutions of gravitational theories cannot be obtained by taking initial data (satisfying the constraints) on a spacelike surface, and choosing an arbitrary conformal metric on the timelike boundary at infinity. There are an infinite number of [[0475 Corner conditions|corner conditions]] that also must be satisfied where the initial data surface hits the boundary. These are well known to mathematical relativists, but to make them more widely known we give a simple explanation of why these conditions exist and discuss some of their consequences. An example is given which illustrates their power. Some implications for holography are also mentioned.\] ## Related work - follow-up: [[2020#Horowitz, Wang]] - [[2021#Ecker, van der Schee, Mateos, Casalderrey-Solana]]: dynamic boundary evolution # Hijano ## Flat space physics from AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/1905.02729), [PDF](https://arxiv.org/pdf/1905.02729.pdf)\] \[Abstract: \] ## Summary - Relate *flat-space S-matrix* to *CFT correlators*. - Compare [[0098 BMS blocks]] for BMS_3 using bootstrap with this paper (obtaining by taking the flat limit). - Obtain known results (2-pt correlators) in conical geometries (non vacuum CFT state). ## S-matrix - limit of CFT correlators ## Massive v.s. massless - massive: [[PaulosPenedonesToledoVanReesVieira2016]] - massless: ref.8,12,13,15 ## Relation to other papers - In 2018 it had non-unitary representation [[2018#Hijano]] - later paper [[2020#Hijano, Neuenfeld]]: obtain soft photon theorems in flat space from CFT # Himwich, Strominger ## Celestial Current Algebra from Low's Subleading Soft Theorem \[Links: [arXiv](https://arxiv.org/abs/1901.01622), [PDF](https://arxiv.org/pdf/1901.01622.pdf)\] \[Abstract: The leading [[0009 Soft theorems|soft photon theorem]] implies that four-dimensional scattering amplitudes are controlled by a two-dimensional (2D) $U(1)$ Kac-Moody symmetry that acts on the [[0022 Celestial sphere|celestial sphere]] at null infinity ($\mathcal{I}$). This celestial $U(1)$ current is realized by components of the electromagnetic vector potential on the boundaries of $\mathcal{I}$. Here, we develop a parallel story for Low's subleading soft photon theorem. It gives rise to a second celestial current, which is realized by vector potential components that are subleading in the large radius expansion about the boundaries of $\mathcal{I}$. The subleading soft photon theorem is reexpressed as a celestial [[0106 Ward identity|Ward identity]] for this second current, which involves novel shifts by one unit in the conformal dimension of charged operators.\] # Hung, Wong ## Entanglement branes and factorization in conformal field theory \[Links: [arXiv](https://arxiv.org/abs/1912.11201), [PDF](https://arxiv.org/pdf/1912.11201)\] \[Abstract: In this work, we consider the question of local Hilbert space factorization in 2D conformal field theory. Generalizing previous work on entanglement and open-closed TQFT, we interpret the factorization of CFT states in terms of path integral processes that split and join the Hilbert spaces of circles and intervals. More abstractly, these processes are cobordisms of an extended CFT which are defined purely in terms of the OPE data. In addition to the usual sewing axioms, we impose an entanglement boundary condition that is satisfied by the vacuum Ishibashi state. This choice of entanglement boundary state leads to reduced density matrices that sum over super-selection sectors, which we identify as the CFT edge modes. Finally, we relate our factorization map to the co-product formula for the CFT symmetry algebra, which we show is equivalent to a Boguliubov transformation in the case of a free boson.\] # Iizuka, Ishibashi, Maeda ## Conformally invariant ANEC from AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/1911.02654), [PDF](https://arxiv.org/pdf/1911.02654.pdf)\] \[Abstract: We study the compatibility of the AdS/CFT duality with the bulk and boundary causality, and derive a conformally invariant averaged null energy condition (CANEC) for quantum field theories in 3 and 5-dimensional curved boundaries. This is the generalization of the [[0417 Averaged null energy condition|averaged null energy condition]] (ANEC) in Minkowski spacetime to curved boundaries, where null energy is averaged along the null line with appropriate weight for conformal invariance. For this purpose we take, as our guiding principle, the no-bulk-shortcut theorem of [[0477 Gao-Wald theorem|Gao and Wald]], which essentially asserts that when going from one point to another on the boundary, one cannot take a "shortcut through the bulk". We also discuss the relationship between bulk vs boundary causality and the [[0221 Weak cosmic censorship|weak cosmic censorship]].\] ## Remarks - ANEC here is for the *boundary* field theory ## Summary - holographically derives CANEC for 3-dimensional boundary, which is static Einstein universe with constant curvature - also does it for deformed boundary # Iliesiu ## On 2D gauge theories in Jackiw-Teitelboim gravity \[Links: [arXiv](https://arxiv.org/abs/1909.05253), [PDF](https://arxiv.org/pdf/1909.05253.pdf)\] \[Abstract: The low-energy behavior of near-extremal black holes can be understood from the near-horizon AdS$_2$ region. In turn, this region is effectively described by using [[0050 JT gravity|Jackiw-Teitelboim gravity]] coupled to [[0071 Yang-Mills|Yang-Mills]] theory through the two-dimensional metric and the dilaton field. We show that such a two-dimensional model of gravity coupled to gauge fields is soluble for an arbitrary choice of gauge group and gauge couplings. Specifically, we determine the partition function of the theory on two-dimensional surfaces of arbitrary genus and with an arbitrary number of boundaries. When solely focusing on the contribution from surfaces with disk topology, we show that the gravitational gauge theory is described by the Schwarzian theory coupled to a particle moving on the gauge group manifold. When considering the contribution from all genera, we show that the theory is described by a particular double-scaled matrix integral, where the elements of the matrix are functions that map the gauge group manifold to complex or real numbers. Finally, we compute the expectation value of various diffeomorphism invariant observables in the gravitational gauge theory and find their exact boundary description.\] # Iliesiu, Pufu, Verlinde, Wang ## An exact quantization of Jackiw-Teitelboim gravity \[Links: [arXiv](https://arxiv.org/abs/1905.02726), [PDF](https://arxiv.org/pdf/1905.02726)\] \[Abstract: We propose an exact quantization of two-dimensional [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] by formulating the JT gravity theory as a [[0557 BF theory|2D gauge theory]] placed in the presence of a loop defect. The gauge group is a certain central extension of $PSL(2, \mathbb{R})$ by $\mathbb{R}$. We find that the exact partition function of our theory when placed on a Euclidean disk matches precisely the finite temperature partition function of the Schwarzian theory. We show that observables on both sides are also precisely matched: correlation functions of boundary-anchored Wilson lines in the bulk are given by those of bi-local operators in the Schwarzian theory. In the gravitational context, the Wilson lines are shown to be equivalent to the world-lines of [[0654 JT with matter|massive particles in the metric formulation of JT gravity]].\] # Jensen ## Scrambling in nearly thermalized states at large central charge \[Links: [arXiv](https://arxiv.org/abs/1906.05852), [PDF](https://arxiv.org/pdf/1906.05852.pdf)\] \[Abstract: We study 2d conformal field theory (CFT) at large [[0033 Central charge|central charge]] $c$ and finite temperature $T$ with heavy operators inserted at spatial infinity. The heavy operators produce a nearly thermalized steady state at an effective temperature $T_{\rm eff}\leq T$. Under some assumptions, we find an effective Schwarzian-like description of these states and, when they exist, their gravity duals. We use this description to compute the [[0466 Lyapunov exponent|Lyapunov exponents]] for light operators to be $2\pi T_{\rm eff}$, so that scrambling is suppressed by the heavy insertions.\] # Johnson ## Non-Perturbative JT Gravity \[Links: [arXiv](https://arxiv.org/abs/1912.03637), [PDF](https://arxiv.org/pdf/1912.03637.pdf)\] \[Abstract: Recently, [[2019#Saad, Shenker, Stanford|Saad, Shenker and Stanford]] showed how to define the genus expansion of [[0050 JT gravity|Jackiw-Teitelboim]] quantum gravity in terms of a double-scaled Hermitian [[0197 Matrix model|matrix model]]. However, the model's non-perturbative sector has fatal instabilities at low energy that they cured by procedures that render the physics non-unique. This might not be a desirable property for a system that is supposed to capture key features of quantum black holes. Presented here is a model with identical perturbative physics at high energy that instead has a stable and unambiguous non-perturbative completion of the physics at low energy. An explicit examination of the full spectral density function shows how this is achieved. The new model, which is based on complex matrix models, also allows for the straightforward inclusion of spacetime features analogous to Ramond-Ramond fluxes. Intriguingly, there is a deformation parameter that connects this non-perturbative formulation of JT gravity to one which, at low energy, has features of a super JT gravity.\] # Kapec, Mahajan, Stanford ## Matrix ensembles with global symmetries and 't Hooft anomalies from 2d gauge theory \[Links: [arXiv](https://arxiv.org/abs/1912.12285), [PDF](https://arxiv.org/pdf/1912.12285.pdf)\] \[Abstract: The Hilbert space of a quantum system with internal global symmetry $G$ decomposes into sectors labelled by irreducible representations of $G$. If the system is [[0008 Quantum chaos|chaotic]], the energies in each sector should separately resemble ordinary [[0579 Random matrix theory|random matrix theory]]. We show that such "sector-wise" random matrix ensembles arise as the boundary dual of two-dimensional gravity with a $G$ gauge field in the bulk. Within each sector, the eigenvalue density is enhanced by a nontrivial factor of the dimension of the representation, and the ground state energy is determined by the quadratic Casimir. We study the consequences of 't Hooft anomalies in the matrix ensembles, which are incorporated by adding specific topological terms to the gauge theory action. The effect is to introduce projective representations into the decomposition of the Hilbert space. Finally, we consider ensembles with $G$ symmetry and time reversal symmetry, and analyze a simple case of a mixed anomaly between time reversal and an internal $\mathbb{Z}_2$ symmetry.\] ## Bulk calculations Due to the topological nature of the gauge theory in 2d, the full bulk partition function factorises:$Z_g\left(\beta_1, r_1 ; \ldots ; \beta_n, r_n\right)=Z_g^{\text {grav }}\left(\beta_1, \ldots, \beta_n\right) Z_g^{\text {gauge }}\left(\beta_1, r_1 ; \ldots ; \beta_n, r_n\right).$Without the gauge theory in the bulk, the gravity theory is dual to a [[0197 Matrix model|random matrix model]] without global symmetry. On the disk and trumpet, the gauge theory answers are given by:$\begin{aligned} Z_D^{\text {gauge }}(\beta, r) & =\frac{\operatorname{dim}(r)^2}{\operatorname{vol}(G)} e^{-\beta c_2(r) / 2}, \\ Z_T^{\text {gauge }}\left(\beta, r ; r^{\prime}\right) & =\delta_{r, r^{\prime}} \operatorname{dim}(r) e^{-\beta c_2(r) / 2}.\end{aligned}$On a genus-$g$ surface with $n$ boundaries, it is given by $Z_g^{\text {gauge }}\left(\beta_1, r_1 ; \ldots ; \beta_n, r_n\right)=\delta_{r_1, \ldots, r_n}\left(\operatorname{dim}\left(r_1\right)\right)^n\left(\frac{\operatorname{vol}(G)}{\operatorname{dim}\left(r_1\right)}\right)^{2 g+n-2} \prod_{j=1}^n e^{-\beta_j c_2\left(r_1\right) / 2}.$Here $c_2$ is a constant that indicates a shifted ground state energy relative to the pure-gravity answer. # Kulaxizi, Ng, Parnachev ## Subleading eikonal, AdS/CFT and double stress tensors \[Links: [arXiv](https://arxiv.org/abs/1907.00867), [PDF](https://arxiv.org/pdf/1907.00867.pdf)\] \[Abstract: \] ## Remarks - mentioned by [[2019#Fitzpatrick, Huang, Li]] - current paper contains equation (7) of that paper - but current paper is not a shock wave calculation - caveat: an earlier paper [[KulaxiziNgParnachev2018]] computes the four point function where the two heavy operators create a thermal state, so the bulk dual is just test particles travelling on a black hole background - this is not the [[0129 Dual of shockwaves]] # Kusuki, Miyaji ## Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block \[Links: [arXiv](https://arxiv.org/abs/1905.02191), [PDF](https://arxiv.org/pdf/1905.02191.pdf)\] \[Abstract: We explore the structures of light cone and Regge limit singularities of $n$-point Virasoro conformal blocks in $c>1$ two-dimensional conformal field theories with no chiral primaries, using [[0573 Crossing kernel|fusion matrix]] approach. These CFTs include not only holographic CFTs dual to classical gravity, but also their full quantum corrections, since this approach allows us to explore full $1/c$ corrections. As the important applications, we study time dependence of Renyi entropy after a local [[0558 Quantum quench|quench]] and [[0482 Out-of-time-order correlator|out-of-time ordered correlator]] (OTOC) at late time. We first show that, the $n$-th ($n>2$) [[0293 Renyi entropy|Renyi entropy]] after a local quench in our CFT grows logarithmically at late time, for any $c$ and any conformal dimensions of excited primary. In particular, we find that this behavior is independent of $c$, contrary to the expectation that the finite $c$ correction fixes the late time Renyi entropy to be constant. We also show that the constant part of the late time Renyi entropy is given by a monodromy matrix. We also investigate OTOCs by using the monodromy matrix. We first rewrite the monodromy matrix in terms of fusion matrix explicitly. By this expression, we find that the OTOC decays exponentially in time, and the decay rates are divided into three patterns, depending on the dimensions of external operators. We note that our result is valid for any $c>1$ and any external operator dimensions. Our monodromy matrix approach can be generalized to the [[0562 Liouville theory|Liouville theory]] and we show that the Liouville OTOC approaches constant in the late time regime. We emphasize that, there is a number of other applications of the fusion and the monodromy matrix approaches, such as solving the [[0036 Conformal bootstrap|conformal bootstrap]] equation. Therefore, it is tempting to believe that the fusion and monodromy matrix approaches provide a key to understanding the [[0001 AdS-CFT|AdS/CFT]] correspondence.\] # Law, Zlotnikov ## Poincare constraints on celestial amplitudes \[Links: [arXiv](https://arxiv.org/abs/2008.02331), [PDF](https://arxiv.org/pdf/2008.02331.pdf)\] \[Abstract: \] ## Remarks - this paper is before [[2019#Pate, Raclariu, Strominger, Yuan]] but some results in that paper were made public by Strominger in a talk ## Summary - derives constraints to celestial amplitudes by Poincare symmetry (c.f. part of [[0123 BMS bootstrap]]) - parallel approach to [[2017#Pasterski, Shao, Strominger (Jan)]] - instead of performing integral transform of amplitudes (hard) - work with celestial basis directly - ==for 2, 3, 4-pt. massless external particles of various spin & massive external scalars== - in specific 3-pt massive scalar cases, the recursion relations can be solved - reproduce known results ## App. A - repeats [[PasterskiShaoStrominger201706]] for 3-pt gluon amplitude (which was done in (2,2) signature) in Minkowski (1,3) signature (which is now distribution valued and derived in (4.20)). # Li, Troost ## Pure and twisted holography \[Links: [arXiv](https://arxiv.org/abs/1911.06019), [PDF](https://arxiv.org/pdf/1911.06019.pdf)\] \[Abstract: \] ## Refs - [[0130 Twisted holography]] ## Summary - topologically twist both sides # May, Penington, Sorce ## Holographic scattering requires a connected entanglement wedge \[Links: [arXiv](https://arxiv.org/abs/1912.05649), [PDF](https://arxiv.org/pdf/1912.05649.pdf)\] \[Abstract: In AdS/CFT, there can exist local 2-to-2 bulk scattering processes even when local scattering is not possible on the boundary; these have previously been studied in connection with boundary correlation functions. We show that boundary regions associated with these scattering configurations must have $O(1/G_N)$ [[0300 Mutual information|mutual information]], and hence a connected entanglement wedge. One of us previously argued for this statement from the boundary theory using operational tools in quantum information theory. We improve that argument to make it robust to small errors and provide a proof in the bulk using [[0408 Raychaudhuri equation|focusing arguments]] in [[0554 Einstein gravity|general relativity]]. We also provide a direct link to [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]] by showing that the bulk scattering region must lie inside the connected entanglement wedge. Our construction implies the existence of nonlocal quantum computation protocols that are exponentially more efficient than the optimal protocols currently known.\] # Maxfield ## Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap \[Links: [arXiv](https://arxiv.org/abs/1906.04416), [PDF](https://arxiv.org/pdf/1906.04416.pdf)\] \[Abstract: Any unitary compact two-dimensional CFT with $c>1$ and no symmetries beyond [[0032 Virasoro algebra|Virasoro]] has a parametrically large density of primary states at large spin for $\bar{h}>\bar{h}_\text{extr}\sim \frac{c-1}{24}$, of a universal form determined by [[0612 Modular invariance|modular invariance]]. By including the contribution of light primary operators and multi-twist composites constructed from them in the modular bootstrap, we find that $\bar{h}_\text{extr}$ receives corrections in a large spin expansion, which we compute at finite $c$. The analysis uses a formulation of the modular S-transform as a Fourier transform acting on the density of primary states. For theories with gravitational duals, $\bar{h}_\text{extr}$ is interpreted as the extremality bound of rotating [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black holes, receiving quantum corrections which we compute at one loop by prohibiting naked singularities in the quantum-corrected geometry. This gravity result is reproduced by modular bootstrap in a semiclassical $c\to\infty$ limit.\] # McCormick ## On the charged Riemannian Penrose inequality with charged matter \[Links: [arXiv](https://arxiv.org/abs/1907.07967), [PDF](https://arxiv.org/pdf/1907.07967.pdf)\] \[Abstract: Throughout the literature on the charged Riemannian [[0476 Penrose inequality|Penrose inequality]], it is generally assumed that there is no charged matter present; that is, the electric field is divergence-free. The aim of this article is to clarify when the charged Riemannian Penrose inequality holds in the presence of charged matter, and when it does not. First we revisit Jang's proof of the charged Riemannian Penrose inequality to show that under suitable conditions on the charged matter, this argument still carries though. In particular, a charged Riemannian Penrose inequality is obtained from this argument when charged matter is present provided that the charge density does not change sign. Moreover, we show that such hypotheses on the sign of the charge are in fact required by constructing counterexamples to the charged Riemannian Penrose inequality when these conditions are violated. We conclude by comparing this counterexample to another version of the Riemannian Penrose inequality with charged matter existing in the literature.\] # Mertens, Turiaci ## Defects in Jackiw-Teitelboim Quantum Gravity \[Links: [arXiv](https://arxiv.org/abs/1904.05228), [PDF](https://arxiv.org/pdf/1904.05228)\] \[Abstract: We classify and study defects in 2d [[0050 JT gravity|Jackiw-Teitelboim gravity]]. We show these are holographically described by a deformation of the Schwarzian theory where the reparametrization mode is integrated over different coadjoint orbits of the [[0032 Virasoro algebra|Virasoro group]]. We show that the quantization of each coadjoint orbit is connected to 2d [[0562 Liouville theory|Liouville CFT]] between branes with insertions of Verlinde loop operators. We also propose an interpretation for the exceptional orbits. We use this perspective to solve these deformations of the Schwarzian theory, computing their partition function and correlators. In the process, we define two geometric observables: the horizon area operator $\Phi_h$ and the geodesic length operator $L(\gamma)$. We show this procedure is structurally related to the deformation of the particle-on-a-group quantum mechanics by the addition of a chemical potential. As an example, we solve the low-energy theory of complex [[0201 Sachdev-Ye-Kitaev model|SYK]] with a $U(1)$ symmetry and generalize to the non-abelian case.\] # Mezei, Sarosi ## Chaos in the butterfly cone \[Links: [arXiv](https://arxiv.org/abs/1908.03574), [PDF](https://arxiv.org/pdf/1908.03574.pdf)\] \[Abstract: \] ## Summary - *defines* a velocity-dependent [[0466 Lyapunov exponent]] (a generalisation) - *shows* a bound on the velocity-dependent [[0466 Lyapunov exponent]]: $\lambda(\mathbf{v}) \leq 2 \pi T\left(1-|\mathbf{v}| / v_{B}\right)$ - *discusses* difference between maximal and non-maximal [[0008 Quantum chaos]] # Mezei, Virrueta (Dec) ## Exploring the Membrane Theory of Entanglement Dynamics \[Links: [arXiv](https://arxiv.org/abs/1912.11024), [PDF](https://arxiv.org/pdf/1912.11024.pdf)\] \[Abstract: Recently an [[0433 Membrane theory of entanglement dynamics|effective membrane theory]] valid in a "hydrodynamic limit" was proposed to describe entanglement dynamics of [[0008 Quantum chaos|chaotic systems]] based on results in random quantum circuits and [[0001 AdS-CFT|holographic gauge theories]]. In this paper, we show that this theory is robust under a large set of generalizations. In generic quench protocols we find that the membrane couples geometrically to [[0429 Hydrodynamics|hydrodynamics]], joining quenches are captured by branes in the effective theory, and the entanglement of time evolved local operators can be computed by probing a time fold geometry with the membrane. We also demonstrate that the structure of the effective theory does not change under finite coupling corrections holographically dual to [[0006 Higher-derivative gravity|higher derivative gravity]] and that subleading orders in the hydrodynamic expansion can be incorporated by including higher derivative terms in the effective theory.\] ## Summary - extends [[2018#Mezei]] on [[0433 Membrane theory of entanglement dynamics|entanglement membrane theory]] to - [[0006 Higher-derivative gravity|higher-derivative gravity]] - more general initial states: implemented using a hydrodynamic expansion in the long-wavelength limit ## Motivation - the [[0518 Quasiparticle model|quasiparticle model]] is good for integrable systems but not good enough for chaotic systems - it is important to know if the [[0433 Membrane theory of entanglement dynamics|membrane]] theory is rigid under corrections to the theory and for more general initial states ## Higher-derivative corrections - general four-derivative theories considered - simplification: in the scaling limit, the [[0425 Gauss-Bonnet gravity|GB]] term in [[0145 Generalised area|HEE]] is always subleading - reproduces the [[0167 Butterfly velocity|butterfly velocity]] in [[2016#Mezei, Stanford]] exactly ## Coordinates - Kruskal - $d s^2=2 A(u v) d u d v+B(u v) d x^2-2 A(u v) h(x) \delta(u) d u^2$ - transformation - $u_{L, R}=\pm e^{-\frac{2 \pi}{\beta} t_{L, R}}, \quad u v=-e^{\frac{4 \pi}{\beta} z_*(z)}, \quad z_*(z) \equiv \int^z \frac{d z^{\prime}}{a\left(z^{\prime}\right) b\left(z^{\prime}\right)}$ - outgoing EF - $d s_{L, R}^2=\frac{1}{z^2}\left[-a(z) d t_{L, R}^2+\frac{2}{b(z)} d z d t_{L, R}+d x^2\right]$ # Murthy, Srednicki (Jun, a) ## Structure of chaotic eigenstates and their entanglement entropy \[Links: [arXiv](https://arxiv.org/abs/1906.04295), [PDF](https://arxiv.org/pdf/1906.04295.pdf)\] \[Abstract: We consider a chaotic many-body system (i.e., one that satisfies the [[0040 Eigenstate thermalisation hypothesis|eigenstate thermalization hypothesis]]) that is split into two subsystems, with an interaction along their mutual boundary, and study the entanglement properties of an energy eigenstate with nonzero energy density. When the two subsystems have nearly equal volumes, we find a universal correction to the [[0301 Entanglement entropy|entanglement entropy]] that is proportional to the square root of the system's heat capacity (or a sum of capacities, if there are conserved quantities in addition to energy). This phenomenon was first noted by Vidmar and Rigol in a specific system; our analysis shows that it is generic, and expresses it in terms of thermodynamic properties of the system. Our conclusions are based on a refined version of a model of a chaotic eigenstate originally due to Deutsch, and analyzed more recently by Lu and Grover.\] # Murthy, Srednicki (Jun, b) ## Bounds on chaos from the eigenstate thermalization hypothesis \[Links: [arXiv](https://arxiv.org/abs/1906.10808), [PDF](https://arxiv.org/pdf/1906.10808.pdf)\] \[Abstract: We show that the known bound on the growth rate of the [[0482 Out-of-time-order correlator|out-of-time-order four-point correlator]] in chaotic many-body quantum systems follows directly from the general structure of operator matrix elements in systems that obey the [[0040 Eigenstate thermalisation hypothesis|eigenstate thermalization hypothesis]]. This ties together two key paradigms of thermal behavior in isolated many-body quantum systems.\] # Nandan, Schreiber, Volovich, Zlotnikov ## Conformal amplitudes: Conformal partial waves and soft limits \[Links: [arXiv](https://arxiv.org/abs/1904.10940), [PDF](https://arxiv.org/pdf/1904.10940.pdf)\] \[Abstract: Massless scattering amplitudes in four-dimensional Minkowski spacetime can be [[0079 Mellin transform|Mellin transformed]] to correlation functions on the [[0022 Celestial sphere|celestial sphere]] at null infinity called [[0262 Celestial amplitude calculations|celestial amplitudes]]. We study various properties of massless four-point scalar and gluon celestial amplitudes such as [[0020 Conformal partial wave decomposition|conformal partial wave decomposition]], crossing relations and optical theorem. As a byproduct, we derive the analog of the single and [[0504 Double soft limits|double]] [[0009 Soft theorems|soft]] limits for all gluon celestial amplitudes.\] ## Summary - derives various properties of ==4-pt. scalar and gluon== celestial amplitudes: - [[0020 Conformal partial wave decomposition|partial waves]] - [[0021 Crossing symmetry|crossing]] - optical theorem - (by-product) analog of single and double soft limits for all ==gluon== celestial amplitudes ## The expansion - $\tilde{A}_{4}(z, \bar{z})=i \sum_{J=0}^{\infty}{}^\prime \int_{\mathcal{C}} d \Delta \Psi_{h_{i}, \bar{h}_{i}}^{h, \bar{h}}(z, \bar{z}) \frac{(1-2 h)(2 \bar{h}-1)}{(2 \pi)^{2}}\left\langle\tilde{A}_{4}(z, \bar{z}), \Psi_{h_{i}, \bar{h}_{i}}^{h, \bar{h}}(z, \bar{z})\right\rangle$ - $\sum^\prime$ means that the $J = 0$ term contributes with weight $1/2$ - conformal partial waves are known - $\Psi_{h_{i}, \bar{h}_{i}}^{h, \bar{h}}(z, \bar{z})=c_{1}^{\prime} F_{+}(z, \bar{z})+c_{2}^{\prime} F_{-}(z, \bar{z})$ - to actually calculate - find poles in the $\Delta$ plane to know what terms to include - "One can use e.g. the integral representation of the conformal partial wave (A.3) (given by eq. (7) in \[23\]) to make sure that the half-circle integration at infinity vanishes" - then just do the inner product calculations # Okuyama, Sakai ## JT gravity, KdV equations and macroscopic loop operators \[Links: [arXiv](https://arxiv.org/abs/1911.01659), [PDF](https://arxiv.org/pdf/1911.01659)\] \[Abstract: We study the thermal partition function of [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] in asymptotically Euclidean AdS$_2$ background using the [[0197 Matrix model|matrix model]] description recently found by [[2019#Saad, Shenker, Stanford|Saad, Shenker and Stanford]]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. We have computed both these expansions up to very high orders using this method. It turns out that we can take a low temperature limit with the ratio of the temperature and the genus counting parameter held fixed. We find the first few orders of the expansion of the free energy in a closed form in this scaling limit. We also study numerically the behavior of the eigenvalue density and the Baker-Akhiezer function using the results in the scaling limit.\] # Palti (Review) ## The Swampland: Introduction and Review \[Links: [arXiv](https://arxiv.org/abs/1903.06239), [PDF](https://arxiv.org/pdf/1903.06239.pdf)\] \[Abstract: \] - [[0184 Swampland]] - [[0183 Swampland distance conjecture]] # Pate, Raclariu, Strominger ## Conformally Soft Theorem in Gauge Theory \[Links: [arXiv](https://arxiv.org/abs/1904.10831), [PDF](https://arxiv.org/pdf/1904.10831.pdf)\] \[Abstract: \] ## Caveat - conformal soft theorem cannot be obtained from low energy effective theory ## Sec.3 A conjecture > A perturbative quantum deformation of a classical four-dimensional Minkowskian quantum field theory exists if and only if the celestial amplitudes $\widetilde{\mathcal{A}}_{J_{1} \ldots J_{n}}\left(\lambda_{i}, z_{i}, \bar{z}_{i}\right)$ exist # Pate, Raclariu, Strominger, Yuan ## Celestial operator products of gluons and gravitons \[Links: [arXiv](https://arxiv.org/abs/1910.07424), [PDF](https://arxiv.org/pdf/1910.07424.pdf)\] \[Abstract: The [[0030 Operator product expansion|operator product expansion (OPE)]] on the celestial sphere of conformal primary gluons and gravitons is studied. [[0060 Asymptotic symmetry|Asymptotic symmetries]] imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein-Yang-Mills theory, that these recursion relations are so constraining that they completely fix the leading [[0114 Celestial OPE|celestial OPE]] coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents.\] ## Refs - extends the [[0114 Celestial OPE|celestial OPE]] calculation for gluons (YM) in [[2019#Fan, Fotopoulos, Taylor]] to graviton plus gluons (EYM) ## Summary - [[0030 Operator product expansion|OPE]] of *conformal* primary gluons and gravitons - c.f. BMS primaries in [[2020#Banerjee, Ghosh, Gonzo]] - [[0060 Asymptotic symmetry|AS]] imply recursion relations between products of operators whose conformal weights differ by half-integers - ==tree-level EYM theory== - leading OPE coefficients completely fixed ## Bulk <-> [[0010 Celestial holography|CCFT]] - Poles in celestial OPE for *massless* particles <-> [[0078 Collinear limit|collinear]] singularities in momentum space - related by [[0079 Mellin transform|Mellin transform]] ## EYM - with some analyticity assumptions, [[0060 Asymptotic symmetry|AS]] completely determine (at least) all the *conformal primary* OPE coefficients of the *leading poles* in OPE. - checked that messier calculations using Feynman diagrams give same result ## Determining allowed terms - using 3-pt vertex - see App. A - for Einstein gravity, $d_V=5$ # Penington (May) ## Entanglement Wedge Reconstruction and the Information Paradox \[Links: [arXiv](https://arxiv.org/abs/1905.08255), [PDF](https://arxiv.org/pdf/1905.08255)\] \[Abstract: When absorbing boundary conditions are used to evaporate a black hole in [[0001 AdS-CFT|AdS/CFT]], we show that there is a phase transition in the location of the quantum [[0007 RT surface|Ryu-Takayanagi surface]], at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time $\beta/2\pi \log S_{BH}$ into the past. We can immediately derive the [[0131 Information paradox|Page curve]], using the Ryu-Takayanagi formula, and the [[0217 Hayden-Preskill decoding criterion|Hayden-Preskill decoding criterion]], using [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]]. Because part of the interior is now encoded in the early Hawking radiation, the decreasing [[0301 Entanglement entropy|entanglement entropy]] of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a [[0195 Firewall|firewall]]. By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the [[0004 Black hole entropy|Bekenstein-Hawking entropy]], and show that this is sufficient state dependence to avoid the AMPSS typical-state [[0195 Firewall|firewall paradox]].\] ## Remarks - one of the two first papers in solving the [[0131 Information paradox|information paradox]], along with [[2019#Almheiri, Engelhardt, Marolf, Maxfield]] ## Assumptions - assumes that, from the bulk perspective, the Hawking radiation continues to be purified by the interior modes, even late in the evaporation - assume that semi-classical physics is good, as long as BH is larger than Planck (EFT is valid) ## Conclusions - only a non-perturbatively small amount of information escapes the BH before Page time, but they are important for allowing information to escape later - [[0217 Hayden-Preskill decoding criterion|Hayden-Preskill]] is true - Page curve is derived - no [[0195 Firewall|firewall]] # Penington, Shenker, Stanford, Yang ## Replica wormholes and the black hole interior \[Links: [arXiv](https://arxiv.org/abs/1911.11977), [PDF](https://arxiv.org/pdf/1911.11977.pdf)\] \[Abstract: Recent work has shown how to obtain the Page curve of an evaporating black hole from holographic computations of [[0301 Entanglement entropy|entanglement entropy]]. We show how these computations can be justified using the replica trick, from geometries with a spacetime wormhole connecting the different replicas. In a simple model, we study the Page transition in detail by summing replica geometries with different topologies. We compute related quantities in less detail in more complicated models, including [[0050 JT gravity|JT gravity]] coupled to conformal matter and the [[0201 Sachdev-Ye-Kitaev model|SYK model]]. Separately, we give a direct gravitational argument for entanglement wedge reconstruction using an explicit formula known as the Petz map; again, a spacetime wormhole plays an important role. We discuss an interpretation of the wormhole geometries as part of some ensemble average implicit in the gravity description.\] # Puhm ## Conformally Soft Theorem In Gravity \[Links: [arXiv](https://arxiv.org/abs/1905.09799), [PDF](https://arxiv.org/pdf/1905.09799.pdf)\] \[Abstract: A central feature of scattering amplitudes in gravity or gauge theory is the existence of a variety of [[0009 Soft theorems|energetically soft theorems]] which put constraints on the amplitudes. Celestial amplitudes which are obtained from momentum-space amplitudes by a [[0079 Mellin transform|Mellin transform]] over the external particle energies cannot obey the usual energetically soft theorems. Instead, the symmetries of the celestial sphere imply that the scattering of conformally soft particles whose conformal weights under the 4D Lorentz group $SL(2,C)$ are taken to zero obey special relations. Such conformally soft theorems have recently been found for gauge theory. Here, I show conformally soft factorization of celestial amplitudes for gravity and identify it as the celestial analogue of Weinberg's soft graviton theorem.\] # Saad ## Late time correlation functions, baby universes, and ETH in JT \[Links: [arXiv](https://arxiv.org/abs/1910.10311), [PDF](https://arxiv.org/pdf/1910.10311.pdf)\] \[Abstract: \] ## Summary - correlation functions of fields *outside* the BH probe BH microstates - e.g. thermal [[0103 Two-point functions|2-point function]] oscillates around a decay, ramp, plateau diagram <- similar to a theory described by an [[0154 Ensemble averaging]] of Hamiltonians - [[0050 JT gravity]] and [[0197 Matrix model]] - the bulk description - emitting and absorbing [[0051 Baby universes]] ## Refs - [[0154 Ensemble averaging]] - [[0050 JT gravity]] # Saad, Shenker, Stanford ## JT gravity as a matrix integral \[Links: [arXiv](https://arxiv.org/abs/1903.11115), [PDF](https://arxiv.org/pdf/1903.11115.pdf)\] \[Abstract: We present exact results for partition functions of [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] on two-dimensional surfaces of arbitrary genus with an arbitrary number of boundaries. The boundaries are of the type relevant in the NAdS${}_2$/NCFT${}_1$ correspondence. We show that the partition functions correspond to the genus expansion of a certain [[0197 Matrix model|matrix integral]]. A key fact is that Mirzakhani's recursion relation for Weil-Petersson volumes maps directly onto the Eynard-Orantin "topological recursion" formulation of the loop equations for this matrix integral. The matrix integral provides a (non-unique) nonperturbative completion of the genus expansion, sensitive to the underlying discreteness of the matrix eigenvalues. In matrix integral descriptions of noncritical strings, such effects are due to an infinite number of disconnected worldsheets connected to [[0156 D-brane|D-branes]]. In JT gravity, these effects can be reproduced by a sum over an infinite number of disconnected geometries -- a type of D-brane logic applied to spacetime.\] # Speranza ## Geometrical tools for embedding fields, submanifolds, and foliations \[Links: [arXiv](https://arxiv.org/abs/1904.08012), [PDF](https://arxiv.org/pdf/1904.08012.pdf)\] \[Abstract: \] ## Refs - [[0044 Extended phase space]] - [[0556 Edge mode]] # Sperhake, Cook, Wang ## The high-energy collision of black holes in higher dimensions \[Links: [arXiv](https://arxiv.org/abs/1909.02997), [PRD](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.100.104046)\] \[Abstract: We compute the gravitational wave energy $E_{\rm rad}$ radiated in head-on collisions of equal-mass, nonspinning black holes in up to $D=8$ dimensional asymptotically flat spacetimes for boost velocities $v$ up to about $90\,\%$ of the speed of light. We identify two main regimes: Weak radiation at velocities up to about $40\,\%$ of the speed of light, and exponential growth of $E_{\rm rad}$ with $v$ at larger velocities. Extrapolation to the speed of light predicts a limit of $12.9\,\% (10.1,~7.7,~5.5,~4.5)\,\%$. of the total mass that is lost in gravitational waves in $D=4 (5,\,6,\,7,\,8)$ spacetime dimensions. In agreement with perturbative calculations, we observe that the radiation is minimal for small but finite velocities, rather than for collisions starting from rest. Our computations support the identification of regimes with super Planckian curvature outside the black-hole horizons reported by Okawa, Nakao, and Shibata [Phys.~Rev.~D {\bf 83} 121501(R) (2011)].\] ## Summary How much energy is lost in the form of gravitational waves when two black holes collide at high speeds? In this work, we find that the answer depends on the spacetime dimension. Roughly speaking, less is lost in higher dimensions. However, some features seem to be independent of the dimension. For example, below 40% of the speed of light, the percentage loss as gravitational waves seems to decrease slightly with the speed, while above this speed, it seems to increase exponentially with the speed. Evidence for super Planckian curvature outside black hole horizons is also reported in this paper. # Stanford, Witten ## JT Gravity and the Ensembles of Random Matrix Theory \[Links: [arXiv](https://arxiv.org/abs/1907.03363), [PDF](https://arxiv.org/pdf/1907.03363.pdf)\] \[Abstract: We generalize the recently discovered [[0471 String-matrix duality|relationship]] between [[0050 JT gravity|JT gravity]] and double-scaled [[0197 Matrix model|random matrix theory]] to the case that the boundary theory may have ==time-reversal symmetry== and may have ==fermions with or without supersymmetry==. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer "torsion." Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.\] # Suh ## Dynamics of black holes in Jackiw-Teitelboim gravity \[Links: [arXiv](https://arxiv.org/abs/1912.00861), [PDF](https://arxiv.org/pdf/1912.00861)\] \[Abstract: We present a general solution for correlators of external boundary operators in black hole states of [[0050 JT gravity|Jackiw-Teitelboim gravity]]. We use the Hilbert space constructed using the particle-with-spin interpretation of the Jackiw-Teitelboim action, which consists of wavefunctions defined on Lorentzian AdS$_2$. The density of states of the gravitational system appears in the amplitude for a boundary particle to emit and reabsorb matter. Up to self-interactions of matter, a general correlator can be reduced in an energy basis to a product of amplitudes for interactions and Wilson polynomials mapping between boundary and bulk interactions.\] # Takayanagi, Tamaoka ## Gravity Edges Modes and Hayward Term \[Links: [arXiv](https://arxiv.org/abs/1912.01636), [PDF](https://arxiv.org/pdf/1912.01636.pdf)\] \[Abstract: We argue that corner contributions in gravity action ([[0102 Hayward term|Hayward term]]) capture the essence of gravity [[0556 Edge mode|edge modes]], which lead to gravitational area entropies, such as the [[0004 Black hole entropy|black hole entropy]] and [[0145 Generalised area|HEE]]. We explain how the Hayward term and the corresponding edge modes in gravity are explained by holography from two different viewpoints. One is an extension of [[0001 AdS-CFT|AdS/CFT]] to general spacetimes and the other is the [[0181 AdS-BCFT|AdS/BCFT]] formulation. In the final part, we explore how gravity edge modes and its entropy show up in string theory by considering open strings stuck to a Rindler horizon.\] ## Summary - [[0102 Hayward term|corner term]] captures [[0556 Edge mode|edge modes]] - two ways to explain it: AdS/CFT and AdS/[[0181 AdS-BCFT|BCFT]] # Wu ## Higher curvature corrections to pole-skipping \[Links: [arXiv](https://arxiv.org/abs/1909.10223), [PDF](https://arxiv.org/pdf/1909.10223.pdf)\] \[Abstract: Recent developments have revealed a new phenomenon, i.e. the residues of the poles of the holographic retarded two point functions of generic operators vanish at certain complex values of the frequency and momentum. This so-called [[0179 Pole skipping|pole-skipping]] phenomenon can be determined [[0001 AdS-CFT|holographically]] by the near horizon dynamics of the bulk equations of the corresponding fields. In particular, the pole-skipping point in the upper half plane of complex frequency has been shown to be closed related to many-body [[0008 Quantum chaos|chaos]], while those in the lower half plane also places universal and nontrivial constraints on the two point functions. In this paper, we study the effect of [[0006 Higher-derivative gravity|higher curvature]] corrections, i.e. the stringy correction and Gauss-Bonnet correction, to the (lower half plane) pole-skipping phenomenon for generic scalar, vector, and metric perturbations. We find that at the pole-skipping points, the frequencies $\omega_n=−i2\pi nT$ are not explicitly influenced by both $R^2$ and $R^4$ corrections, while the momenta $k_n$ receive corresponding corrections.\] ## Summary - GB and stringy corrections to *lower-half plane* [[0179 Pole skipping]] - finds that the frequencies $\omega_{n}=-i 2 \pi n T$ are *not* changed by $R^2$ and $R^4$ corrections, but $k_ns do # Zaffaroni (Lectures) ## Lectures on AdS Black Holes, Holography and Localization \[Links: [arXiv](https://arxiv.org/abs/1902.07176), [PDF](https://arxiv.org/pdf/1902.07176.pdf)\] \[Abstract: In these lectures I review some recent progresses in [[0248 Black hole microstates|counting the number of microstates]] of AdS supersymmetric black holes in dimensions equal or greater than four using [[0001 AdS-CFT|holography]]. The counting is obtained by applying [[0186 Localisation|localization]] and [[0197 Matrix model|matrix model]] techniques to the dual field theory. I cover in details the case of dyonic AdS$_4$ black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS$_5$ black holes.\] # 1908.06060 ## A gravitational-wave measurement of the Hubble constant following the second observing run of Advanced LIGO and Virgo \[Links: [arXiv](https://arxiv.org/abs/1908.06060), [PDF](https://arxiv.org/pdf/1908.06060.pdf)\] \[Abstract: \] ## Refs - [[0239 Hubble constant measurement from gravitational waves]] ## Summary - uses 7 events including 1 BNS (same as in [[2017#1710.05835]]) and 6 BBH - 4 with high SNR (> 12): GW150914, GW151226, GW170608, and GW170814 (the last one particularly loud and well localised due to Dark Energy Survey) - 2 needed for consistency with assumed population model: GW170104 and GW170809