# Almheiri ## Holographic QEC and the projected BH interior \[Links: [arXiv](https://arxiv.org/abs/1810.02055), [PDF](https://arxiv.org/pdf/1810.02055.pdf)\] \[Abstract: The [[0146 Quantum error correction|quantum error correction]] interpretation of AdS/CFT establishes a sense of fluidity to the bulk/boundary dictionary. We show how this property can be utilized to construct a dictionary for operators behind horizons of pure black holes. We demonstrate this within the context of the SYK model with pure black hole microstates obtained via projecting out a single side of the thermofield double (and perturbed versions thereof). Assuming an erasure subsystem code for the duality between the eternal black hole and the [[0574 Thermofield double|thermofield double]], this projection results in a rewiring of the dictionary so as to map the interior operators to the remaining boundary in a determinable way. We find this dictionary to be sensitive to the implemented projection in a manner reminiscent of previous state-dependent constructions of the black hole interior. We also comment on how the fluidity of the dictionary can be used to transfer information between two black holes connected by a [[0083 Traversable wormhole|wormhole]], relating the ideas of [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]] and the Hayden-Preskill decoding criterion.\] ## Summary - used [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]] to understand how [[0220 ER=EPR|ER=EPR]] continues to revolve the [[0195 Firewall|firewall paradox]] for a two-sided BH # Anastasiou, Araya, Arias, Olea ## Einstein-AdS action, renormalised volume/area and holographic Renyi entropies \[Links: [arXiv](https://arxiv.org/abs/1806.10708), [PDF](https://arxiv.org/pdf/1806.10708.pdf)\] \[Abstract: \] ## Refs - extensions to higher derivative gravity - for Lovelock - [[AnastasiouArayaMannOlea2021]][](https://arxiv.org/pdf/2103.14640.pdf) - 4-derivative gravity - [[AnastasiouArayaMorenoOleaRivera-Betancour2021]][](https://arxiv.org/pdf/2102.11242.pdf) ## Summary - *uses* [[0395 Volume renormalisation]] instead of [[0209 Holographic renormalisation]] to renormalise the action and apply to HEE etc # Bao, Chatwin-Davies, Remmen ## Entanglement of purification and multiboundary wormhole geometries \[Links: [arXiv](https://arxiv.org/abs/1811.01983), [PDF](https://arxiv.org/pdf/1811.01983.pdf)\] \[Abstract: We posit a geometrical description of the [[0258 Entanglement of purification|entanglement of purification ]]for subregions in a holographic CFT. The bulk description naturally generalizes the two-party case and leads to interesting inequalities among multi-party entanglements of purification that can be geometrically proven from the conjecture. Further, we study the relationship between holographic entanglements of purification in locally-AdS3 spacetimes and entanglement entropies in multi-throated wormhole geometries constructed via quotienting by isometries. In particular, we derive new holographic inequalities for geometries that are locally AdS3 relating entanglements of purification for subregions and entanglement entropies in the wormhole geometries.\] ## Summary - studies [[0258 Entanglement of purification]] in locally AdS3 spacetimes - studies [[0145 Generalised area|HEE]] in multiboundary wormholes - relates the two things above # Bao, Penington, Sorce, Wall ## Holographic tensor networks in full AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/1902.10157), [PDF](https://arxiv.org/pdf/1902.10157.pdf)\] \[Abstract: We present a general procedure for constructing tensor networks for geometric states in the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. Given a state in a large-$N$ CFT with a static, semiclassical gravitational dual, our procedure produces a tensor network for the boundary state whose internal geometry matches (a discretization of) the bulk spacetime geometry. By invoking the "holographic entanglement of purification" conjecture, our construction can be made to capture the structure of the bulk spacetime at sub-AdS scales.\] ## Refs - [[0054 Tensor network]] # Belin, de Boer, Kruthoff ## Comments on a state-operator correspondence for the torus \[Links: [arXiv](https://arxiv.org/abs/1802.00006), [PDF](https://arxiv.org/pdf/1802.00006.pdf)\] \[Abstract: We investigate the existence of a [[0025 Operator-state correspondence|state-operator correspondence]] on the torus. This correspondence would relate states of the CFT Hilbert space living on a spatial torus to the path integral over compact Euclidean manifolds with operator insertions. Unlike the states on the sphere that are associated to local operators, we argue that those on the torus would more naturally be associated to line operators. We find evidence that such a correspondence cannot exist and in particular, we argue that no compact Euclidean path integral can produce the vacuum on the torus. Our arguments come solely from field theory and formulate a CFT version of the [[0407 Horowitz-Myers conjecture|Horowitz-Myers conjecture]] for the [[0567 AdS soliton|AdS soliton]].\] ## Summary - *investigates* [[0025 Operator-state correspondence|state-operator map]] on the ==torus== - *provides* a CFT statement of [[0407 Horowitz-Myers conjecture|HM conjecture]] ## No state-operator map for torus ![[BelinDeBoerKruthoff2018_fig2.png|300]] - Needs a line operator instead of a local operator. But as long as it is lower dimensional it is cool. - Could not find a compact manifold (without operator insertion) that prepares a torus at ground state - This is implied by [[0407 Horowitz-Myers conjecture]]: the lowest energy solution with $S^1\times T^2$ is a 4d Euclidean soliton and is unique. So cannot have a compact geometry with lowest energy that prepare the torus on the boundary. # Berkooz, Isachenkov, Narovlansky, Torrents ## Towards a full solution of the large N double-scaled SYK model \[Links: [arXiv](https://arxiv.org/abs/1811.02584), [PDF](https://arxiv.org/pdf/1811.02584.pdf)\] \[Abstract: We compute the ==exact, all energy scale, 4-point function== of the large $N$ [[0503 Double-scaled SYK|double-scaled SYK]] model, by using only combinatorial tools and relating the correlation functions to sums over chord diagrams. We apply the result to obtain corrections to the maximal [[0466 Lyapunov exponent|Lyapunov exponent]] at low temperatures. We present the rules for the non-perturbative diagrammatic description of correlation functions of the entire model. The latter indicate that the model can be solved by a reduction of a quantum deformation of $SL(2)$, that generalizes the Schwarzian to the complete range of energies.\] # Bernamonti, Galli, Myers, Oppenheim ## Holographic second laws of black hole thermodynamics \[Links: [arXiv](https://arxiv.org/abs/1803.03633), [PDF](https://arxiv.org/pdf/1803.03633)\] \[Abstract: Recently, it has been shown that for out-of-equilibrium systems, there are additional constraints on thermodynamical evolution besides the ordinary second law. These form a new family of second laws of thermodynamics, which are equivalent to the monotonicity of quantum Rényi divergences. In black hole thermodynamics, the usual [[0005 Black hole second law|second law]] is manifest as the area increase theorem. Hence one may ask if these additional laws imply new restrictions for gravitational dynamics, such as for out-of-equilibrium black holes? Inspired by this question, we study these constraints within the [[0001 AdS-CFT|AdS/CFT]] correspondence. First, we show that the [[0293 Renyi entropy|Rényi]] divergence can be computed via a Euclidean path integral for a certain class of excited CFT states. Applying this construction to the boundary CFT, the Rényi divergence is evaluated as the renormalized action for a particular bulk solution of a minimally coupled gravity-scalar system. Further, within this framework, we show that there exist transitions which are allowed by the traditional second law, but forbidden by the additional thermodynamical constraints. We speculate on the implications of our findings.\] # Blake, Davison, Grozdanov, Liu ## Many-body chaos and energy dynamics in holography \[Links: [arXiv](https://arxiv.org/abs/1809.01169), [PDF](https://arxiv.org/pdf/1809.01169.pdf)\] \[Abstract: Recent developments have indicated that in addition to [[0482 Out-of-time-order correlator|out-of-time ordered correlation functions]] (OTOCs), [[0008 Quantum chaos|quantum chaos]] also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic systems. The manifestation, referred to as [[0179 Pole skipping|pole-skipping]], concerns the analytic behaviour of energy density two-point functions around a special point $\omega = i \lambda$, $k = i \lambda/v_B$ in the complex frequency and momentum plane. Here $\lambda$ and $v_B$ are the [[0466 Lyapunov exponent|Lyapunov exponent]] and [[0167 Butterfly velocity|butterfly velocity]] characterising quantum chaos. In this paper we provide an argument that the phenomenon of pole-skipping is universal for general finite temperature systems dual to Einstein gravity coupled to matter. In doing so we uncover a surprising universal feature of the linearised Einstein equations around a static black hole geometry. We also study analytically a holographic axion model where all of the features of our general argument as well as the pole-skipping phenomenon can be verified in detail.\] ## Summary - not just [[0482 Out-of-time-order correlator|OTOC]] contains info about quantum chaos: two-point function also does - in terms of [[0179 Pole skipping]] - *provides* an argument for the universality of [[0179 Pole skipping]] for Einstein coupled to matter - a surprising universal feature of linearised Einstein equations around a BH - makes connection to [[0117 Shockwave]] ## Einstein equations at the skipped pole - perturbation: $\delta g_{v v}(r, v, x)=\delta g_{v v}(r) e^{-i \omega v+i k x}$ etc - $E_{vv}$: $\left(-i \frac{d}{2} \omega h^{\prime}\left(r_{0}\right)+k^{2}\right) \delta g_{v v}^{(0)}-i(2 \pi T+i \omega)\left[\omega \delta g_{x^{i} x^{i}}^{(0)}+2 k \delta g_{v x}^{(0)}\right]$=-2 h\left(r_{0}\right)\left[T_{v r}\left(r_{0}\right) \delta g_{v v}^{(0)}-\delta T_{v v}\left(r_{0}\right)\right]$ - the RHS is found to be zero for a class class of black brane solutions (we can try to show it in general) - the left is automatically zero for special $k$ and $\omega$ # Blake, Lee, Liu ## A quantum hydrodynamical description for scrambling and many-body chaos \[Links: [arXiv](https://arxiv.org/abs/1801.00010), [PDF](https://arxiv.org/pdf/1801.00010.pdf)\] \[Abstract: \] ## Refs - one of originals for [[0179 Pole skipping]] # Blommaert, Mertens, Verschelde ## The Schwarzian Theory - A Wilson Line Perspective \[Links: [arXiv](https://arxiv.org/abs/1806.07765), [PDF](https://arxiv.org/pdf/1806.07765)\] \[Abstract: We provide a holographic perspective on correlation functions in Schwarzian quantum mechanics, as boundary-anchored Wilson line correlators in [[0050 JT gravity|Jackiw-Teitelboim gravity]]. We first study compact groups and identify the diagrammatic representation of bilocal correlators of the particle-on-a-group model as Wilson line correlators in its 2d holographic [[0557 BF theory|BF]] description. We generalize to the Hamiltonian reduction of $SL(2,R)$ and derive the Schwarzian correlation functions. [[0482 Out-of-time-order correlator|Out-of-time ordered correlators]] are determined by crossing Wilson lines, giving a [[0597 6j symbol|6j-symbol]], in agreement with [[0003 2D CFT|2d CFT]] results.\] # Bonifacio, Hinterbichler, Joyce, Rosen ## Shift Symmetries in (Anti) de Sitter Space \[Links: [arXiv](https://arxiv.org/abs/1812.08167), [PDF](https://arxiv.org/pdf/1812.08167.pdf)\] \[Abstract: We construct a class of extended [[0500 Shift symmetry|shift symmetries]] for fields of all integer spins in de Sitter (dS) and anti-de Sitter (AdS) space. These generalize the shift symmetry, galileon symmetry, and special galileon symmetry of massless scalars in flat space to all symmetric tensor fields in (A)dS space. These symmetries are parametrized by generalized Killing tensors and exist for fields with particular discrete masses corresponding to the longitudinal modes of massive fields in partially massless limits. We construct interactions for scalars that preserve these shift symmetries, including an extension of the special galileon to (A)dS space, and discuss possible generalizations to interacting massive higher-spin particles.\] # Brown, Gharibyan, Lin, Susskind, Thorlacius, Zhao ## The Case of the Missing Gates: Complexity of Jackiw-Teitelboim Gravity \[Links: [arXiv](https://arxiv.org/abs/1810.08741), [PDF](https://arxiv.org/pdf/1810.08741.pdf)\] \[Abstract: The [[0050 JT gravity|Jackiw-Teitelboim (JT) model]] arises from the dimensional reduction of charged black holes. Motivated by the holographic [[0204 Quantum complexity|complexity]] conjecture, we calculate the late-time rate of change of action of a Wheeler-DeWitt patch in the JT theory. Surprisingly, the rate vanishes. This is puzzling because it contradicts both holographic expectations for the rate of complexification and also action calculations for charged black holes. We trace the discrepancy to an improper treatment of boundary terms when naively doing the dimensional reduction. Once the boundary term is corrected, we find exact agreement with expectations. We comment on the general lessons that this might hold for holographic complexity and beyond.\] # Brown, Gharibyan, Streicher, Susskind, Thorlacius, Zhao ## Falling Toward Charged Black Holes \[Links: [arXiv](https://arxiv.org/abs/1804.04156), [PDF](https://arxiv.org/pdf/1804.04156.pdf)\] \[Abstract: The growth of the "size" of operators is an important diagnostic of [[0008 Quantum chaos|quantum chaos]]. In [[2018#Susskind (Feb, a)]] it was conjectured that the holographic dual of the size is proportional to the average radial component of the momentum of the particle created by the operator. Thus the growth of operators in the background of a black hole corresponds to the acceleration of the particle as it falls toward the horizon. In this note we will use the momentum-size correspondence as a tool to study scrambling in the field of a near-extremal charged black hole. The agreement with previous work provides a non-trivial test of the momentum-size relation, as well as an explanation of a paradoxical feature of scrambling previously discovered by [[2014#Leichenauer]]. Naively Leichenauer's result says that only the non-extremal entropy participates in scrambling. The same feature is also present in the [[0201 Sachdev-Ye-Kitaev model|SYK model]]. In this paper we find a quite different interpretation of Leichenauer's result which does not have to do with any decoupling of the extremal degrees of freedom. Instead it has to do with the buildup of momentum as a particle accelerates through the long throat of the Reissner-Nordstrom geometry.\] ## Refs - [[0326 Charged BH in holography]] # Brown, Semeniuk, Wang, Monserrat, Pickard, Grosche ## Strong coupling superconductivity in a quasiperiodic host-guest structure \[Links: [Science Advances](http://advances.sciencemag.org/content/4/4/eaao4793)\] \[Abstract: Elemental bismuth displays an unusually low carrier concentration which decreases under applied pressure. Experiments suggested that a band gap opens up at the Fermi level at a moderate pressure of about 25,000 bar, above which bismuth changes into an incommensurate host-guest structure. Because the host-guest structure does not have a unit cell, its electronic properties are difficult to model. In our work, we investigated the evolution with pressure of the electronic structure of bismuth using Density Functional Theory (DFT). We explored both the low-pressure behaviour, reproducing the semimetal to semiconductor transition, and the high-pressure behaviour. For the latter, a series of commensurate approximate structures were created, in which the band structure calculations are feasible. The calculations successfully explained several experimentally observed features mentioned above. In addition, we carried out an exhaustive investigation of the role of approximant choice and k-space grid in arriving at estimates of the plasma frequency, which was needed for analysing the experimental data.\] # Cano ## Lovelock action with non-smooth boundaries \[Links: [arXiv](https://arxiv.org/abs/1803.00172), [PDF](https://arxiv.org/pdf/1803.00172.pdf)\] \[Abstract: \] ## Summary - computes the [[0102 Hayward term|Corner term]] for Lovelock gravity, and find two types - one gives [[1993#Jacobson, Myers]] entropy - the other one is a total derivative terms and should be discarded - using a limiting procedure - computes [[0204 Quantum complexity]] ## Action - $I=\sum_{n=1}^{\lfloor D / 2\rfloor} \lambda_{n} I^{(n)}$ - $I^{(n)}=\int_{\mathcal{M}} d^{d+1} x \sqrt{|g|} \mathcal{X}_{2 n}+\sum_{k}\left[\int_{\mathcal{B}_{k}} d \Sigma \mathcal{Q}_{n}+\int_{\partial \mathcal{B}_{k}}d \sigma \mathcal{F}_{n}\right]+\sum_{l} \int_{\mathcal{C}_{l}} d \sigma 2 n \psi \hat{\mathcal{X}}_{2(n-1)}$ ## Obtaining the corner term 1. local Gaussian frame - $d s^{2}=n^{2}+h_{i j} d x^{i} d x^{j}$ - $n=N d r, \quad h_{i j} d x^{i} d x^{j}=M^{2} d \tilde{\theta}^{2}+\sigma_{A B} d x^{A} d x^{B}$ - demanding regularity at $r=0$ gives - $\left.M\right|_{r \rightarrow 0}=M(r),\left.\quad M\right|_{r=0}=0,\left.\quad \frac{\partial N}{\partial \tilde{\theta}}\right|_{r=0}=\left.\frac{\partial \sigma_{A B}}{\partial \tilde{\theta}}\right|_{r=0}=0$ - also no conical singularity at $r=0$ - $\lim _{r \rightarrow 0} \frac{\partial_{r} M}{N}=1$ 2. quantities in this coordinate - $K_{i j}=\frac{1}{2 N} \partial_{r} h_{i j}$ - non-vanishing components $K_{\tilde{\theta}}^{\tilde{\theta}}=\frac{\partial_{r} M}{M N}, \quad K_{A}^{B}=\frac{1}{2 N} \partial_{r} \sigma_{A C} \sigma^{C B}$ 3. what terms survive - $K_{\tilde{\theta}}^{\tilde{\theta}}$ diverges as $1/M$ as $r\rightarrow0$ - $\sqrt{|h|}=M \sqrt{|\sigma|}$ goes to 0 - => only terms linear in $K_{\tilde{\theta}}^{\tilde{\theta}}$ survives # Carbello-Rubio, Di Filippo, Moynihan ## Taming higher-derivative interactions and bootstrapping gravity with soft theorems \[Links: [arXiv](https://arxiv.org/abs/1811.08192), [PDF](https://arxiv.org/pdf/1811.08192.pdf)\] \[Abstract: On-shell constructibility is redefining our understanding of perturbative quantum field theory. The tree-level S-matrix of constructible theories is completely determined by a set of recurrence relations and a reduced number of scattering amplitudes. In this paper, we revisit the [[0551 On-shell recursion relations|on-shell constructibility]] of gravitational theories making use of new results on [[0009 Soft theorems|soft theorems]] and recurrence relations. We show that using a double complex shift and an all-line soft deformation allows us to relax the technical conditions for constructibility, in order to include more general propagators and higher-derivative interactions that prevent using conventional [[0058 BCFW|Britto-Cachazo-Feng-Witten]] (BCFW) shifts. From this result we extract a set of criteria that guarantee that a given gravitational action has the same tree-level S-matrix in Minkowski spacetime as [[0554 Einstein gravity|general relativity]], which implies the equivalence at all orders in perturbation theory between these classical field theories on asymptotically flat spacetimes. As a corollary we deduce that the scattering amplitudes of general relativity and unimodular gravity are the same for an arbitrary number of external particles (as long as the S-matrix of the latter is unitary), thus extending previous works that were able to deal only with $n=4$ and $n=5$ amplitudes.\] ## Main statement Let us assume that there exists a gravitational action such that: - (A) Describes two degrees of freedom that, at the linear level, correspond to massless gravitons; - (B) Has the same 3-point amplitudes as [[0554 Einstein gravity|general relativity]]; then, it follows that - (1) The [[0009 Soft theorems|soft graviton theorem]] with the standard leading, subleading and sub-subleading contributions is verified. Furthermore, if we also assume that: - (C) The propagator behaves for large (off-shell) momentum as $T_{\mu \nu \rho \sigma}(p) /\left(p^2\right)^{m / 2+1}$, where $T_{\mu \nu \rho \sigma}(p)$ represents an arbitrary tensorial structure (perhaps Lorentz violating) containing $0 \le m \ge 4$ times the product of the momentum $p$; - (D) $k$-point interaction vertices, with $k \ge 4$, have at most $I(k) ≤ I_\star(k) = 2(k − 1)$ powers of momenta, while for 3-point interaction vertices we demand that $I(3) < 4 − m/3$; then, - (2) The entire (tree-level) S-matrix is recursively constructible from the information encoded in the soft graviton theorem, and is therefore the same as in general relativity. ## Higher derivative gravity - see Sec.V.D - any theory that has a different 3-point amplitude from Einstein gravity would violate condition (D) - if condition (D) can be relaxed, then Einstein cubic gravity seems a natural candidate that is reconstructable since it can change the 3-point vertex # Cardoso, Kimura, Maselli, Senatore ## Black holes in an Effective Field Theory extension of GR \[Links: [arXiv](https://arxiv.org/abs/1808.08962), [PDF](https://arxiv.org/pdf/1808.08962.pdf)\] \[Abstract: Effective field theory methods suggest that some rather-general extensions of [[0554 Einstein gravity|General Relativity]] include, or are mimicked by, certain [[0006 Higher-derivative gravity|higher-order curvature corrections]], with coupling constants expected to be small but otherwise arbitrary. Thus, the tantalizing prospect to test the fundamental nature of gravity with gravitational-wave observations, in a systematic way, emerges naturally. Here, we build black hole solutions in such a framework and study their main properties. Once rotation is included, we find the first purely gravitational example of geometries without $\mathbb{Z}_2$-symmetry. Despite the higher-order operators of the theory, we show that linearized fluctuations of such geometries obey second-order differential equations. We find nonzero [[0581 Tidal Love numbers|tidal Love numbers]]. We study and compute the [[0325 Quasi-normal modes|quasinormal modes]] of such geometries. These results are of interest to gravitational-wave science but also potentially relevant for electromagnetic observations of the galactic center or X-ray binaries.\] # Casals, Zimmerman ## Perturbations of Extremal Kerr Spacetime: Analytic Framework and Late-time Tails \[Links: [arXiv](https://arxiv.org/abs/1801.05830), [PDF](https://arxiv.org/pdf/1801.05830.pdf)\] \[Abstract: \] ## Summary - perturbations to extremal Kerr - [[0473 Retarded Green's function]] has a branch point # Chang, Lin, Shao, Wang, Yin ## Topological Defect Lines and Renormalization Group Flows in Two Dimensions \[Links: [arXiv](https://arxiv.org/abs/1802.04445), [PDF](https://arxiv.org/pdf/1802.04445)\] \[Abstract: We consider [[0659 Topological defect line|topological defect lines]] (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the 't Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.\] # Cherman, Shifman, Unsal ## Bose-Fermi cancellations without supersymmetry \[Links: [arXiv](https://arxiv.org/abs/1812.04642), [PDF](https://arxiv.org/pdf/1812.04642.pdf)\] \[Abstract: We show that adjoint QCD features very strong Bose-Fermi cancellations in the large $N$ limit, despite the fact that it is manifestly non-supersymmetric. The difference between the bosonic and fermionic densities of states in large $N$ adjoint QCD turns out to have a 'two-dimensional' scaling $\sim \exp{(\sqrt{\ell E})}$ for large energies $E$ in finite spatial volume, where $\ell$ is a length scale associated with the curvature of the spatial manifold. In particular, all Hagedorn growth cancels, and so does the growth $\exp{(V^{1/4} E^{3/4})}$ expected in a standard local 4d theory in spatial volume $V$. In these ways, large $N$ adjoint QCD, a manifestly non-supersymmetric theory, acts similarly to supersymmetric theories. We also show that at large $N$, the vacuum energy of multi-flavor adjoint QCD is non-negative and exponentially small compared to the UV cutoff with several natural regulators.\] ## Refs - some holographic analogue: [[2023#Chen, Turiaci]] # Cheung, Liu, Remmen ## Proof of the Weak Gravity Conjecture from Black Hole Entropy \[Links: [arXiv](https://arxiv.org/abs/1801.08546), [PDF](https://arxiv.org/pdf/1801.08546.pdf)\] \[Abstract: We prove that higher-dimension operators contribute positively to the entropy of a thermodynamically stable black hole at fixed mass and charge. Our results apply whenever the dominant corrections originate at tree level from quantum field theoretic dynamics. More generally, positivity of the entropy shift is equivalent to a certain inequality relating the free energies of black holes. These entropy inequalities mandate new positivity bounds on the coefficients of higher-dimension operators. One of these conditions implies that the charge-to-mass ratio of an extremal black hole asymptotes to unity from above for increasing mass. Consequently, large extremal black holes are unstable to decay to smaller extremal black holes and the weak gravity conjecture is automatically satisfied. Our findings generalize to arbitrary spacetime dimension and to the case of multiple gauge fields. The assumptions of this proof are valid across a range of scenarios, including string theory constructions with a dilaton stabilized below the string scale.\] ## Summary - *proves* $F(\beta)<\widetilde{F}(\beta)$ for i) a thermodynamically stable black hole in ii) a theory in which the dominant contributions to higher-dimension operators are generated at tree level by massive quantum fields - using Euclidean path integral methods ## Logic - a subsystem in the same macrostate has less entropy because there is less microstate degeneracy: $\Delta S>0$ (implied by $F(\beta)<\widetilde{F}(\beta)$) - finds $\frac{q}{m}-1 \propto \Delta S$ for extremal BHs - $\Delta S\rightarrow 0$ as higher derivatives operators are decoupled at long distances (low energies) - -> for larger and larger BHs $q/m\rightarrow1$ from *above* - since $q/m>1$, [[0177 Weak gravity conjecture|WGC]] is automatically satisfied # Cook, Wang, Sperhake ## Orbiting black-hole binaries and apparent horizons in higher dimensions \[Links: [arXiv](https://arxiv.org/abs/1808.05834), [PDF](https://arxiv.org/pdf/1808.05834.pdf), [CQG](https://iopscience.iop.org/article/10.1088/1361-6382/aae995/meta)\] \[Abstract: We study gravitational wave emission and the structure and formation of [[0226 Apparent horizon|apparent horizons]] in orbiting black-hole binary systems in higher-dimensional general relativity. For this purpose we present an apparent horizon finder for use in higher dimensional numerical simulations and test the finder's accuracy and consistency in single and binary black-hole spacetimes. The black-hole binaries we model in $D=6$ dimensions complete up to about one orbit before merging or scatter off each other without formation of a common horizon. In agreement with the absence of stable circular geodesic orbits around higher-dimensional black holes, we do not find binaries completing multiple orbits without finetuning of the initial data. All binaries radiate about $0.13\,\%$ to $0.2\,\%$ of the total mass-energy in gravitational waves, over an order of magnitude below the radiated energy measured for four-dimensional binaries. The low radiative efficiency is accompanied by relatively slow dynamics of the binaries as expected from the more rapid falloff of the binding gravitational force in higher dimensions.\] # Collier, Gobeil, Maxfield, Perlmutter ## Quantum Regge Trajectories and the Virasoro Analytic Bootstrap \[Links: [arXiv](https://arxiv.org/abs/1811.05710), [PDF](https://arxiv.org/pdf/1811.05710)\] \[Abstract: Every conformal field theory (CFT) above two dimensions contains an infinite set of Regge trajectories of local operators which, at large spin, asymptote to "double-twist" composites with vanishing anomalous dimension. In two dimensions, due to the existence of local conformal symmetry, this and other central results of the conformal bootstrap do not apply. We incorporate exact stress tensor dynamics into the CFT$_2$ analytic bootstrap, and extract several implications for AdS$_3$ quantum gravity. Our main tool is the Virasoro [[0573 Crossing kernel|fusion kernel]], which we newly analyze and interpret in the [[0036 Conformal bootstrap|bootstrap]] context. The contribution to double-twist data from the Virasoro vacuum module defines a "Virasoro Mean Field Theory" (VMFT), its spectrum includes a finite number of discrete Regge trajectories, whose dimensions obey a simple formula exact in the central charge $c$ and external operator dimensions. We then show that VMFT provides a baseline for large spin universality in two dimensions: in every unitary compact CFT$_2$ with $c > 1$ and a twist gap above the vacuum, the double-twist data approaches that of VMFT at large spin $\ell$. Corrections to the large spin spectrum from individual non-vacuum primaries are exponentially small in $\sqrt{\ell}$ for fixed $c$. We analyze our results in various large $c$ limits. Further applications include a derivation of the late-time behavior of Virasoro blocks at generic $c$, a refined understanding and new derivation of heavy-light blocks, and the determination of the cross-channel limit of generic Virasoro blocks. We deduce non-perturbative results about the bound state spectrum and dynamics of quantum gravity in AdS$_3$.\] # Cotler, Jensen ## A theory of reparameterizations for AdS3 gravity \[Links: [arXiv](https://arxiv.org/abs/1808.03263), [PDF](https://arxiv.org/pdf/1808.03263.pdf)\] \[Abstract: We rewrite the Chern-Simons description of pure gravity on global AdS$_3$ and on Euclidean [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black holes as a quantum field theory on the AdS boundary. The resulting theory is (two copies of) the path integral quantization of a certain coadjoint orbit of the [[0032 Virasoro algebra|Virasoro]] group, and it should be regarded as the quantum field theory of the boundary gravitons. This theory respects all of the conformal field theory axioms except one: it is not modular invariant. The coupling constant is $1/c$ with $c$ the [[0033 Central charge|central charge]], and perturbation theory in $1/c$ encodes loop contributions in the gravity dual. The QFT is a theory of reparametrizations analogous to the Schwarzian description of nearly AdS$_2$ gravity, and has several features including: (i) it is ultraviolet-complete; (ii) the torus partition function is the vacuum Virasoro character, which is one-loop exact by a localization argument; (iii) it reduces to the Schwarzian theory upon compactification; (iv) it provides a powerful new tool for computing Virasoro blocks at large $c$ via a diagrammatic expansion. We use the theory to compute several observables to one-loop order in the bulk, including the "heavy-light" limit of the identity block. We also work out some generalizations of this theory, including the boundary theory which describes fluctuations around two-sided eternal black holes.\] ## Refs - coordinated publication with [[2018#Haehl, Rozali]] ## Summary - rewrites [[0089 Chern-Simons theory|CS theory]] of pure gravity on ==global AdS3 and BTZ== as QFT on the boundary - the boundary QFT is a theory of reparameterisation like [[0201 Sachdev-Ye-Kitaev model|SYK]] but in 2 dimensions # Delacretaz, Hartman, Hartnoll, Lewkowycz ## Thermalization, Viscosity and the Averaged Null Energy Condition \[Links: [arXiv](https://arxiv.org/abs/1805.04194), [PDF](https://arxiv.org/pdf/1805.04194.pdf)\] \[Abstract: We explore the implications of the [[0417 Averaged null energy condition|averaged null energy condition]] for thermal states of relativistic quantum field theories. A key property of such thermal states is the thermalization length. This lengthscale generalizes the notion of a mean free path beyond weak coupling, and allows finite size regions to independently thermalize. Using the [[0040 Eigenstate thermalisation hypothesis|eigenstate thermalization hypothesis]], we show that thermal fluctuations in finite size 'fireballs' can produce states that violate the averaged null energy condition if the thermalization length is too short or if the shear viscosity is too large. These bounds become very weak with a large number $N$ of degrees of freedom but can constrain real-world systems, such as the quark-gluon plasma.\] # Distler, Flauger, Horn ## Double-soft graviton amplitudes and the extended BMS charge algebra \[Links: [arXiv](https://arxiv.org/abs/1808.09965), [PDF](https://arxiv.org/pdf/1808.09965.pdf)\] \[Abstract: We discuss how scattering amplitudes in 4d Minkowski spacetime which involve multiple soft gravitons realize the algebra of [[0064 BMS group|BMS]] charges on the null boundary. In particular, we show how the commutator of two such charges is realized by the antisymmetrized consecutive soft limit of the [[0504 Double soft limits|double soft amplitude]]. The commutator is found to be robust even in the presence of quantum corrections, and the associated Lie algebra has an extension, which breaks the BMS symmetry if the BMS algebra is taken to include the [[0032 Virasoro algebra|Virasoro algebra]] of local superrotations. We discuss the implications of this structure for the existence of a 2d CFT dual description for 4d scattering amplitudes.\] # Dong ## Holographic Renyi Entropy at High Energy Density \[Links: [arXiv](https://arxiv.org/abs/1811.04081), [PDF](https://arxiv.org/pdf/1811.04081.pdf)\] \[Abstract: We show that [[0293 Renyi entropy|Renyi entropies]] of subregions can be used to distinguish when the entire system is in a microcanonical ensemble from when it is in a canonical ensemble, at least in theories holographically dual to gravity. Simple expressions are provided for these Renyi entropies in a particular thermodynamic limit with high energy density and fixed fractional size of the subregion. Holographically, the Renyi entropies are determined by the areas of cosmic branes inserted into the bulk spacetime. They differ between a microcanonical and a canonical ensemble because the two ensembles provide different boundary conditions for the gravitational theory under which cosmic branes lead to different backreacted geometries. This is in contrast to the [[0301 Entanglement entropy|von Neumann entropy]] which is more coarse-grained and does not differentiate microcanonical ensembles from canonical ensembles.\] ## Summary - in holography at least, Renyi entropies are different in microcanonical v.s. canonical ensembles, but von Neumann entropy is the same # Dong, Harlow, Marolf ## Flat entanglement spectra in fixed-area states of quantum gravity \[Links: [arXiv](https://arxiv.org/abs/1811.05382), [PDF](https://arxiv.org/pdf/1811.05382.pdf)\] \[Abstract: \] ## Summary - introduces [[0024 Fixed area states]] - explains the weird $n$-independce of [[0047 Renyi at finite n for higher derivative gravity|Renyi entropy]] in [[0054 Tensor network]] - relation to [[0048 JLMS]] # Dong, Silverstein, Torroba ## De Sitter Holography and Entanglement Entropy \[Links: [arXiv](https://arxiv.org/abs/1804.08623), [PDF](https://arxiv.org/pdf/1804.08623.pdf)\] \[Abstract: We propose a new example of entanglement knitting spacetime together, satisfying a series of checks of the corresponding [[0301 Entanglement entropy|von Neumann]] and [[0293 Renyi entropy|Renyi entropies]]. The conjectured dual of de Sitter in $d+1$ dimensions involves two coupled CFT sectors constrained by residual $d$-dimensional gravity. In the $d=2$ case, the gravitational constraints and the CFT spectrum are relatively tractable. We identify a finite portion of each CFT Hilbert space relevant for de Sitter. Its maximum energy level coincides with the transition to the universal Cardy behavior for theories with a large [[0033 Central charge|central charge]] and a sparse light spectrum, derived by Hartman, Keller, and Stoica. Significant interactions between the two CFTs, derived previously for other reasons, suggest a maximally mixed state upon tracing out one of the two sectors; we derive this by determining the holographic Renyi entropies. The resulting entanglement entropy matches the Gibbons-Hawking formula for de Sitter entropy, including the numerical coefficient. Finally, we interpret the Gibbons-Hawking horizon entropy in terms of the [[0007 RT surface|Ryu-Takayanagi entropy]], and explore the time evolution of the entanglement entropy.\] ## Refs - [[0545 de Sitter quantum gravity]] # Donnay, Puhm, Strominger ## Conformally Soft Photons and Gravitons \[Links: [arXiv](https://arxiv.org/abs/1810.05219), [PDF](https://arxiv.org/pdf/1810.05219.pdf)\] \[Abstract: The four-dimensional $S$-matrix is reconsidered as a correlator on the [[0022 Celestial sphere|celestial sphere]] at null infinity. Asymptotic particle states can be characterized by the point at which they enter or exit the celestial sphere as well as their $SL(2,\mathbb C)$ Lorentz quantum numbers: namely their conformal scaling dimension and spin $h\pm \bar h$ instead of the energy and momentum. This characterization precludes the notion of a soft particle whose energy is taken to zero. We propose it should be replaced by the notion of a conformally soft particle with $h=0$ or $\bar h=0$. For photons we explicitly construct conformally soft $SL(2,\mathbb C)$ currents with dimensions $(1,0)$ and identify them with the generator of a $U(1)$ [[0069 Kac-Moody algebra|Kac-Moody symmetry]] on the celestial sphere. For gravity the generator of celestial conformal symmetry is constructed from a $(2,0)$ $SL(2,\mathbb C)$ primary wavefunction. Interestingly, BMS supertranslations are generated by a spin-one weight $(\frac{3}{2},\frac{1}{2})$ operator, which nevertheless shares holomorphic characteristics of a conformally soft operator. This is because the right hand side of its OPE with a weight $(h,\bar h)$ operator ${\cal O}_{h,\bar h}$ involves the shifted operator ${\cal O}_{h+\frac{1}{2},\bar h+ \frac{1}{2}}$. This OPE relation looks quite unusual from the celestial CFT$_2$ perspective but is equivalent to the leading soft graviton theorem and may usefully constrain celestial correlators in quantum gravity.\] # Fishbach et al. ## A standard siren measurement of the Hubble constant from GW170817 without the electromagnetic counterpart \[Links: [arXiv](https://arxiv.org/abs/1807.05667), [PDF](https://arxiv.org/pdf/1807.05667.pdf)\] \[Abstract: \] ## Refs - [[0239 Hubble constant measurement from gravitational waves]] ## Summary - uses a single BNS event GW170817 - estimate $H_0$ by identifying a set of host galaxies within a region ## Method 1. identify a set of potential hosts 2. find the redshift for each of the potential host 3. calculate a $H_0$ for each host 4. combine to get an overall estimate # Foini, Kurchan ## The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators \[Links: [arXiv](https://arxiv.org/abs/1803.10658), [PDF](https://arxiv.org/pdf/1803.10658.pdf)\] \[Abstract: The [[0040 Eigenstate thermalisation hypothesis|Eigenstate Thermalization Hypothesis]] (ETH) implies a form for the matrix elements of local operators between eigenstates of the Hamiltonian, expected to be valid for [[0008 Quantum chaos|chaotic]] systems. Another signal of chaos is a positive [[0466 Lyapunov exponent|Lyapunov exponent]], defined on the basis of Loschmidt echo or [[0482 Out-of-time-order correlator|out-of-time-order correlators]]. For this exponent to be positive, correlations between matrix elements unrelated by symmetry, usually neglected, have to exist. The same is true for the peak of the dynamic heterogeneity length, relevant for systems with slow dynamics. These correlations, as well as those between elements of different operators, are encompassed in a generalized form of ETH.\] # Gharibyan, Hanada, Shenker, Tezuka ## Onset of Random Matrix Behavior in Scrambling Systems \[Links: [arXiv](https://arxiv.org/abs/1803.08050), [PDF](https://arxiv.org/pdf/1803.08050.pdf)\] \[Abstract: The fine grained energy spectrum of [[0008 Quantum chaos|quantum chaotic]] systems is widely believed to be described by [[0579 Random matrix theory|random matrix]] statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding time scale by the time at which the linearly growing ramp region in the spectral form factor begins. We call this time $t_{\rm ramp}$. The purpose of this paper is to study this scale in many-body quantum systems that display strong chaos, sometimes called scrambling systems. We focus on randomly coupled qubit systems, both local and $k$-local (all-to-all interactions) and the [[0201 Sachdev-Ye-Kitaev model|Sachdev--Ye--Kitaev (SYK) model]]. Using numerical results for Hamiltonian systems and analytic estimates for random quantum circuits we find the following results. For geometrically local systems with a conservation law we find $t_{\rm ramp}$ is determined by the diffusion time across the system, order $N^2$ for a 1D chain of $N$ qubits. This is analogous to the behavior found for local one-body chaotic systems. For a $k$-local system with conservation law the time is order $\log N$ but with a different prefactor and a different mechanism than the scrambling time. In the absence of any conservation laws, as in a generic random quantum circuit, we find $t_{\rm ramp} \sim \log N$, independent of connectivity.\] # Glorioso, Crossley, Liu ## A prescription for holographic Schwinger-Keldysh contour in non-equilibrium systems \[Links: [arXiv](https://arxiv.org/abs/1812.08785), [PDF](https://arxiv.org/pdf/1812.08785)\] \[Abstract: We develop a prescription for computing real-time correlation functions defined on a [[0042 Schwinger-Keldysh techniques|Schwinger-Keldysh contour]] for non-equilibrium systems using gravity. The prescription involves a new analytic continuation procedure in a black hole geometry which can be dynamical. For a system with a slowly varying horizon, the continuation enables computation of the Schwinger-Keldysh generating functional using derivative expansion, drastically simplifying calculations. We illustrate the prescription with two-point functions for a scalar operator. We then use it to derive from gravity the recently proposed non-equilibrium effective action for diffusion.\] # Glorioso, Liu ## Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics \[Links: [arXiv](https://arxiv.org/abs/1805.09331), [PDF](https://arxiv.org/pdf/1805.09331.pdf)\] \[Abstract: We review recent progress in developing effective field theories (EFTs) for non-equilibrium processes at finite temperature, including a new formulation of fluctuating [[0429 Hydrodynamics|hydrodynamics]], and a new proof of the second law of thermodynamics. There are a number of new elements in formulating EFTs for such systems. Firstly, the nature of IR variables is very different from those of a system in equilibrium or near the vacuum. Secondly, while all static properties of an equilibrium system can in principle be extracted from the partition function, there appears no such quantity which can capture all non-equilibrium properties. Thirdly, non-equilibrium processes often involve dissipation, which is notoriously difficult to deal with using an action principle. The purpose of the review is to explain how to address these issues in a pedagogic manner, with fluctuating hydrodynamics as a main example.\] # Gopalakrishnan, Zakirov ## Facilitated quantum cellular automata as simple models with nonthermal eigenstates and dynamics \[Links: [arXiv](https://arxiv.org/abs/1802.07729), [PDF](https://arxiv.org/pdf/1802.07729.pdf)\] \[Abstract: We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so their combined action constitutes a Floquet unitary. The dynamics of the models we discuss can be classically simulated, and their eigenstates classically constructed (although they are highly entangled). We consider a variety of models in both one and two dimensions, involving Clifford gates and Toffoli gates. For some of these models, we explicitly construct conserved densities; thus these models are "integrable." The other models do not seem to be integrable; yet, for some system sizes and boundary conditions, their eigenstate entanglement is strongly subthermal. Some of the models have exponentially many eigenstates in which one or more sites are "disentangled" from the rest of the system, as a consequence of reflection symmetry.\] # Gralla, Ravishankar, Zimmerman ## Semi-local Quantum Criticality and the Instability of Extremal Planar Horizons \[Links: [arXiv](https://arxiv.org/abs/1808.07053), [PDF](https://arxiv.org/pdf/1808.07053.pdf)\] \[Abstract: We show that the [[0340 Aretakis instability|Aretakis instability]] of compact extremal horizons persists in the planar case of interest to holography and discuss its connection with the emergence of "semi-local quantum criticality" in the field theory dual. In particular, the spatially localized power-law decay of this critical phase corresponds to spatially localized power-law growth of stress-energy on the horizon. For near-extremal black holes these phenomena occur transiently over times of order the inverse temperature. The boundary critical phase is characterized by an emergent temporal conformal symmetry, and the bulk instability seems to be essential to preserving the symmetry in the presence of interactions. We work primarily in the solvable example of ==charged scalar perturbations of five-dimensional (near-)extremal planar Reissner-Nordström anti-de Sitter spacetime== and argue that the conclusions hold more generally.\] ## Summary - discusses the dual of [[0340 Aretakis instability|Aretakis instability]]: *semi-local quantum criticality* ## Fourier to real space - at late times: - $G_{\partial \mathrm{B}}^{\mathrm{far}}(\tau, x, z)=\frac{1}{\ell^{3 / 2}} \int \frac{d \omega d^3 k}{(2 \pi)^4} e^{-i \omega \tau+i \vec{k} \cdot \vec{x}} \frac{D_{-} \mathscr{G}}{\left(2 \Delta_{+}-4\right) B_{+}}(-2 i \omega)^{2 h_{+}-1} R_{\mathrm{far}}^{+}(z)$ - perform the $\omega$ and $k$ integrals - $G_{\partial \mathrm{B}}^{\mathrm{far}} \sim \frac{\mathscr{C}_f}{\ell^{3 / 2} x}\left(\frac{1}{\hat{\xi} x}\right)^{3 / 2} \tau^{-1} e^{-x / \hat{\xi}} R_{\mathrm{far}}^{+}(z)|_{h=1 / 2}, \quad x \rightarrow \infty$ ## Comments - connection to zero-temperature [[0179 Pole skipping|pole skipping]] or [[2022#Horowitz, Kolanowski, Santos (Oct)]]? # Gralla, Zimmerman ## Scaling and Universality in Extremal Black Hole Perturbations \[Links: [arXiv](https://arxiv.org/abs/1804.04753), [PDF](https://arxiv.org/pdf/1804.04753.pdf)\] \[Abstract: We show that the emergent near-horizon conformal symmetry of extremal black holes gives rise to universal behavior in perturbing fields, both near and far from the black hole horizon. The scale-invariance of the near-horizon region entails power law time-dependence with three universal features: (1) the decay off the horizon is always precisely twice as fast as the decay on the horizon; (2) the special rates of $1/t$ off the horizon and $1/\sqrt{v}$ on the horizon commonly occur; and (3) sufficiently high-order transverse derivatives grow on the horizon (Aretakis instability). The results are simply understood in terms of near-horizon ($\mathrm{AdS}_2$) holography. We first show how the general features follow from symmetry alone and then go on to present the detailed universal behavior of scalar, electromagnetic, and gravitational perturbations of $d$-dimensional electrovacuum black holes.\] ## Summary - provides a scaling argument for [[0340 Aretakis instability|Aretakis instability]] # Grozdanov ## On the connection between hydrodynamics and quantum chaos in holographic theories with stringy corrections \[Links: [arXiv](https://arxiv.org/abs/1811.09641), [PDF](https://arxiv.org/pdf/1811.09641.pdf)\] \[Abstract: [[0179 Pole skipping|Pole-skipping]] is a recently discovered signature of many-body [[0008 Quantum chaos|quantum chaos]] in collective energy dynamics. It establishes a precise connection between resummed, all-order hydrodynamics and the underlying microscopic chaos. In this paper, we demonstrate the existence of pole-skipping in holographic conformal field theories with [[0006 Higher-derivative gravity|higher-derivative gravity]] duals. In particular, we first consider Einstein-Hilbert gravity deformed by curvature-squared ($R^2$) corrections and then type IIB supergravity theory with the $\alpha'^3 R^4$ term, where $\alpha'$ is set by the length of the fundamental string. The former case allows us to discuss the effects of leading-order $1/N_c$ corrections (with $N_c$ being the number of colours of the dual gauge group) and phenomenological coupling constant dependence. In Einstein-Gauss-Bonnet theory, pole-skipping turns out to be valid non-perturbatively in the Gauss-Bonnet coupling. The $\alpha'^3 R^4$ deformation enables us to study perturbative inverse 't Hooft coupling corrections ($\alpha'^3 \sim 1 / \lambda^{3/2}$) in $SU(N_c)$, $\mathcal{N} = 4$ supersymmetric Yang-Mills theory with infinite $N_c$. While the maximal [[0466 Lyapunov exponent|Lyapunov exponent]] characterising quantum chaos remains uncorrected, the [[0167 Butterfly velocity|butterfly velocity]] is shown to depend both on $N_c$ and the coupling. Several implications of the relation between hydrodynamics and chaos are discussed, including an intriguing similarity between the dependence of the butterfly velocity and the ratio of shear viscosity to entropy density on stringy corrections.\] ## Comments - checked that the results match with [[2022#Dong, Wang, Weng, Wu]] ## Summary - [[0179 Pole skipping|pole skipping]] for [[0006 Higher-derivative gravity|higher derivative gravity]] - GB and Weyl${}^4$ terms (GB is treated as a large $N$ correction while Weyl${}^4$ is considered a $\alpha^\prime$ (or large 't Hoost coupling) correction) - results: - Lyapunov: uncorrected - [[0167 Butterfly velocity|butterfly velocity]]: exact matching between [[0179 Pole skipping|pole-skipping]] and [[0117 Shockwave|shockwave]] methods ## Treating GB as $1/N$ correction - instead of treating GB as a $1/\alpha^\prime$ correction - GB makes conformal central charges $a$ and $c$ no longer equal - but there is a parameter regime in which $\lambda_{GB}$ can be associated with a $1/N$ corrections so that $(c-a) / c \sim 1 / N$ # Gutperle, Miller ## Topological interfaces in Chern-Simons theory and AdS$_3$/CFT$_2$ \[Links: [arXiv](https://arxiv.org/abs/1810.08713), [PDF](https://arxiv.org/pdf/1810.08713.pdf)\] \[Abstract: Recently, topological interfaces between three-dimensional abelian [[0089 Chern-Simons theory|Chern-Simons theories]] were constructed. In this note we investigate such topological interfaces in the context of the AdS$_3$/CFT$_2$ correspondence. We show that it is possible to connect the topological interfaces in the bulk Chern-Simons theory to topological interfaces in the dual CFT on the boundary. In addition for $[U(1)]^{2N}$ Chern-Simons theory on AdS$_3$, we show that it is possible to find boundary counter terms which lead to the $N$ conserved currents in the dual two-dimensional CFT.\] ## Summary - establishing the holography between [[0088 Topological interface|topological interface]] in $U(1)$ CS theory in the bulk and [[0065 Defect CFT|topological interface in the 2d CFT]] # Haehl, Rozali ## EFT for Chaotic CFTs \[Links: [arXiv](https://arxiv.org/abs/1808.02898), [PDF](https://arxiv.org/pdf/1808.02898.pdf)\] \[Abstract: We derive an effective field theory for general chaotic two-dimensional conformal field theories with a large central charge. The theory is a specific and calculable instance of a more general framework recently proposed in [1]. We discuss the gauge symmetries of the model and how they relate to the [[0466 Lyapunov exponent|Lyapunov]] behaviour of certain correlators. We calculate the out-of-time-ordered correlators diagnosing [[0008 Quantum chaos|quantum chaos]], as well as certain more fine-grained higher-point generalizations, using our Lorentzian effective field theory. We comment on potential future applications of the effective theory to real-time thermal physics and conformal field theory.\] ## Refs - coordinated publication with [[2018#Cotler, Jensen]] ## Summary - EFT for chaotic 2d CFT (large $c$) - a calculable example of [[2018#Blake, Lee, Liu]] ## Potential - EFT in higher dimensions? # Hamada, Shiu ## Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities \[Links: [arXiv](https://arxiv.org/abs/1801.05528), [PDF](https://arxiv.org/pdf/1801.05528.pdf)\] \[Abstract: \] ## Summary - infinitely many new [[0009 Soft theorems]] in gauge and gravity theories ## Refs - see also [[LiLinZhang2018]] - later [[2021#Strominger]] # Harlow, Jafferis ## Factorisation problem in JT \[Links: [arXiv](https://arxiv.org/abs/1804.01081), [PDF](https://arxiv.org/pdf/1804.01081.pdf)\] \[Abstract: In this note we study the 1+1 dimensional [[0050 JT gravity|Jackiw-Teitelboim gravity]] in Lorentzian signature, explicitly constructing the gauge-invariant classical phase space and the quantum Hilbert space and Hamiltonian. We also semiclassically compute the [[0162 No-boundary wavefunction|Hartle-Hawking wave function]] in two different bases of this Hilbert space. We then use these results to illustrate the gravitational version of the [[0514 Lorentzian factorisation problem|factorization problem]] of AdS/CFT: the Hilbert space of the two-boundary system tensor-factorizes on the CFT side, which appears to be in tension with the existence of gauge constraints in the bulk. In this model the tension is acute: we argue that JT gravity is a sensible quantum theory, based on a well-defined Lorentzian bulk path integral, which has no CFT dual. In bulk language, it has wormholes but it does not have black hole microstates. It does however give some hint as to what could be added to to rectify these issues, and we give an example of how this works using the SYK model. Finally we suggest that similar comments should apply to pure Einstein gravity in 2+1 dimensions, which we'd then conclude also cannot have a CFT dual, consistent with the results of Maloney and Witten.\] ## Toy model: pure Maxwell theory in 1+1 - the solution is $A_{x}=-E t+a$ where $a$ can be changed by large gauge transformations (since large gauge transformations are not gauge transformations, $a$ labels physically different states) - obviously does not factorise - no boundary dual anyways so non-factorsation is okay - but it's a sector of Einstein-Maxwell theory on two-sided BH solution in any dimensions! -> does have consequences ## JT gravity - does not factorise, using an argument similar to pure Maxwell - this means it cannot have a CFT dual, but we comment on how it can # Harlow, Ooguri (Short) \[Links: [arXiv](https://arxiv.org/abs/1810.05337), [PDF](https://arxiv.org/pdf/1810.05337.pdf)\] \[Abstract: \] ## Refs - a long one [[2018#Harlow, Ooguri (Long)]] with details - proving no [[0187 Global symmetries in QG]] in AdS/CFT <!--- - new work on extending this beyond AdS/CFT appeared afterwards (Marija mentioned during Grant's lectures) ---> # Harlow, Ooguri (Long) ## Symmetries in quantum field theory and quantum gravity \[Links: [arXiv](https://arxiv.org/abs/1810.05338), [PDF](https://arxiv.org/pdf/1810.05338.pdf)\] \[Abstract: \] ## Comments - [[2020#Liu]]: The proof is based on the quantum error correction theory of AdS/CFT: in AdS/CFT, the holographic dictionary is understood as an error correction code, where the code subspace corresponds to the low energy sector in CFT and effective field theory in the bulk. From the quantum information point of view, the no global symmetry statement is shown to be closely related to the Eastin-Knill theorem \[22–24\] in quantum error correction \[25–27\]: there is no exact covariant code associated with continuous global symmetry. # Hayden, Penington ## Learning the alpha-bits of BHs \[Links: [arXiv](https://arxiv.org/abs/1807.06041), [PDF](https://arxiv.org/pdf/1807.06041.pdf)\] \[Abstract: \] ## Refs - [[0255 Alpha bits]] # Hijano ## Semi-classical BMS${}_3$ blocks and flat holography ## Summary - constructs BMS$_3$ blocks for a 2d field theory. - generalise the monodromy method (used in AdS/CFT) - compare results with holographic computations involving probe particles - consider geodesic Feynman diagrams, evaluated in locally flat geometries generated by backreaction of heavy BMS primary operators - comment on [[0040 Eigenstate thermalisation hypothesis]] ## Extensions - Extend to unitary representations (done by himself in a later paper [[2019#Hijano]]) # Huang ## Butterfly Velocity in Quadratic Gravity \[Links: [arXiv](https://arxiv.org/abs/1804.05527), [PDF](https://arxiv.org/pdf/1804.05527.pdf)\] \[Abstract: \] ## Summary - *computes* [[0167 Butterfly velocity]] in quadratic gravity # Jahnke (Review) ## Recent developments in the holographic description of quantum chaos \[Links: [arXiv](https://arxiv.org/abs/1811.06949), [PDF](https://arxiv.org/pdf/1811.06949.pdf)\] \[Abstract: We review recent developments encompassing the description of [[0008 Quantum chaos|quantum chaos]] in holography. We discuss the characterization of quantum chaos based on the late time vanishing of [[0482 Out-of-time-order correlator|out-of-time-order correlators]] and explain how this is realized in the dual gravitational description. We also review the connections of chaos with the spreading of quantum entanglement and diffusion phenomena.\] ## Refs - [[0008 Quantum chaos]] ## 2 Classical chaos - $\frac{\partial \mathbf{X}(t)}{\partial \mathbf{X}_{0}} \sim e^{\lambda t}$ - **max exponent**: the exponent depends on the orientation in phase space ($\left\{\lambda_{1}, \lambda_{2}, \ldots, \lambda_{K}\right\}$), and usually one defines a *maximum Lyapunov exponent*: $\lambda_{\max }=\lim _{t \rightarrow \infty} \lim _{\delta \mathbf{X}_{0} \rightarrow 0} \frac{1}{t} \log \left(\frac{\delta \mathbf{X}(t)}{\delta \mathbf{X}_{0}}\right)$ - if the limit *exists* and $\lambda_\text{max}>0$ -> chaotic - n.b. at later times, the maximal exponent dominates - approach to thermal equilibrium - $G(t)=\langle\mathbf{X}(t) \mathbf{X}(0)\rangle_{\beta}-\langle\mathbf{X}\rangle_{\beta}^{2}$ - $G(t) \sim \sum_{j} b_{j} e^{-\mu_{j} t}$: *Ruelle resonances* ($\mu_i$ are complex) ## 3 Quantum chaos - promote $\{q(t), p(0)\}_{\text {P.в. }} \rightarrow \frac{1}{i \hbar}[\hat{q}(t), \hat{p}(0)]$ - to remove the sign, $C(t)=\left\langle-[W(t), V(0)]^{2}\right\rangle_{\beta}$ where $W$ and $V$ are two generic operators - to make sense of **smallness** in perturbation, find a system of large number of dof, so small means only a new dof is changed - behaviour of $C(t)$: - for $t<t_d$: $1/N_{\mathrm{dof}}$ - for $t_{d} \ll t \ll t_{*}$: $N_{\mathrm{dof}}^{-1} \exp \left(\lambda_{L} t\right)$ - for $t>t_*$: $O(1)$ - $t_d$ = **dissipation** time: controls late time thermalisation (Ruelle) and character the **two-point function**: $\langle V(0) V(t)\rangle \sim e^{-t / t_{d}}$ - **[[0482 Out-of-time-order correlator|OTOC]]**: $C(t) =\left\langle-[W(t), V(0)]^{2}\right\rangle_{\beta} =2-2\langle W(t) V(0) W(t) V(0)\rangle_{\beta}$ - $\mathrm{OTO}(t)=\left\langle\psi_{2} |\psi_{1}\right\rangle$, where $\left|\psi_{1}\right\rangle=W(-t) V(0)|\beta\rangle, \left|\psi_{2}\right\rangle=V(0) W(-t)|\beta\rangle$ - vanishing commutator <-> two states same -> large OTO; non-zero commutator <-> two states not the same -> small OTO - $V(0) W(-t)|\beta\rangle=V(0) e^{-i H t} W(0) e^{i H t}|\beta\rangle$, $V(0)$ applied last, no time to disappear; but for $W(-t) V(0)|\beta\rangle =e^{-i H t} W(0) e^{i H t} V(0)|\beta\rangle$, applying $V$ at time 0, then evolve back, then insert perturbation $W$, then evolve forward will give no rematerialisation of $V$ because small change at past gives a very different state for a chaotic system - using **BCH** formula: $W(t)=e^{i H t} W(0) e^{-i H t}=\sum_{k=0}^{\infty} \frac{(-i t)^{k}}{k !}[H[H, \ldots[H, W(0)] \ldots]]$. This makes it obvious that more and more complicated expressions contribute at higher orders in $t$ - with **local** operators: $C(t, x)=\left\langle-[V(0,0), W(t, x)]^{2}\right\rangle_{\beta}$ - $C(t, x) \sim \exp \left[\lambda_{L}\left(t-t_{*}-\frac{|x|}{v_{B}}\right)\right]$ ## 4 Holographic chaos - [[0325 Quasi-normal modes]] control the two point function $\langle V(t) V(0)\rangle_{\beta} \sim e^{-t / t_{d}}$ of the boundary theory - $t_d$ is related to the lowest QNM $\operatorname{Im}(\omega) \sim t_{d}^{-1}$ (so one can guess that QNM ~ classical Ruelle resonances) - **[[0117 Shockwave]]** - ![[Jahnke2018_fig10.png|300]] - $\left|\psi_{\text {in }}\right\rangle=W(-t) V(0) |$TFD$\rangle .$ - first create a state using $V(0)$ and then insert $W(-t)$ to affect it - ![[Jahnke2018_fig11.png|250]] - $\left|\psi_{\text {out }}\right\rangle=V(0) W(-t)|\mathrm{TFD}\rangle$ - first create the shock wave and then insert $V(0)$ - **calculating [[0482 Out-of-time-order correlator|OTOC]]** - in Rindler AdS${}_3$ with $\Delta_{W}\gg\Delta_{V}$: $\frac{\left\langle V\left(i \epsilon_{1}\right) W\left(t+i \epsilon_{2}\right) V\left(i \epsilon_{3}\right) W\left(t+i \epsilon_{4}\right)\right\rangle}{\left\langle V\left(i \epsilon_{1}\right) V\left(i \epsilon_{3}\right)\right\rangle\left\langle W\left(i \epsilon_{2}\right) W\left(i \epsilon_{4}\right)\right\rangle}=\left(\frac{1}{1-\frac{8 \pi i G_{N} \Delta_{W}}{\epsilon_{13} \epsilon_{24}^{*}} e^{\frac{2 \pi}{\beta}\left(t-\frac{|\vec{x}|}{v_{B}}\right)}}\right)^{\Delta_{V}}$ - can be obtained using Eikonal approximation ([[2014#Shenker, Stanford]]) or geodesic approximation ([[2013#Shenker, Stanford (Jun)]] and [[2014#Roberts, Stanford]]) - matches with CFT calculation [[2014#Roberts, Stanford]] - expansion - expanding gives $\mathrm{OTO}(t)=1-8 \pi i G_{\mathrm{N}} \frac{\Delta_{V} \Delta_{W}}{\epsilon_{13} \epsilon_{24}^{*}} e^{\frac{2 \pi}{\beta}\left(t-\frac{|\vec{x}|}{v_{B}}\right)}$ - therefore $C(t, \vec{x}) \sim h(t, \vec{x})$ (because $h(t, \vec{x}) \sim G_{\mathrm{N}} e^{\frac{2 \pi}{\beta}\left(t-\frac{|\vec{i}|}{v_{B}}\right)}$) - at late times, QNC controls [[0482 Out-of-time-order correlator|OTOC]] (in compact space) - $C(t) \sim e^{-2 i \omega\left(t-t_{*}-R / v_{B}\right)}$, with $\operatorname{Im}(\omega)<0$ - $R$ is diameter of compact space - bounds - bounds on Lyapunov (see [[0008 Quantum chaos]]) - bounds on butterfly velocity [[2016#Mezei]] - relation to [[0300 Mutual information]] - mutual info related to 2-point function $I(A, B) \geqslant \frac{\left(\left\langle\mathcal{O}_{L} \mathcal{O}_{R}\right\rangle-\left\langle\mathcal{O}_{L}\right\rangle\left\langle\mathcal{O}_{R}\right\rangle\right)^{2}}{2\left\langle\mathcal{O}_{L}^{2}\right\rangle\left\langle\mathcal{O}_{R}^{2}\right\rangle}$ - we can see how disturbance destroys correlation and therefore mutual information: $\left\langle\mathcal{O}_{L} \mathcal{O}_{R}\right\rangle_{W}=\left\langle\mathrm{TFD}\left|W_{R}^{\dagger} \mathcal{O}_{L} \mathcal{O}_{R} W_{R}\right| \mathrm{TFD}\right\rangle=0$ - can calculate using [[0007 RT surface]]: - if wormhole has larger area then $I=0$; - if wormhole has smaller area then $I(A, B)=\frac{1}{4 G_{\mathrm{N}}}\left[\operatorname{Area}\left(\gamma_{A}\right)+\operatorname{Area}\left(\gamma_{B}\right)-\right.$ Area $\left.\left(\gamma_{\text {wormhole }}\right)\right]>0$ - shock wave makes wormhole longer so smaller mutual info and finally 0 if too long - **entanglement velocity**: for $t_{0} \gtrsim t_{*}$, the mutual information decreases linearly with behavior controlled by $\frac{d I(A, B)}{d t_{0}}=-\frac{d S_{A \cup B}}{d t_{0}}=-v_{E} s_{\mathrm{th}} \operatorname{Area}(A \cup B)$ - bounds on entanglement velocity - $v_{E} \leqslant v_{E}^{\mathrm{Sch}}=\frac{\sqrt{d}(d-1)^{\frac{1}{2}-\frac{1}{d}}}{[2(d-1)]^{1-\frac{1}{d}}}$ conjectured in [[2013#Liu, Suh (May)]] and [[2013#Liu, Suh (Nov)]] - Just like in the case of $v_B$, the entanglement velocity in thermal CFTs does not depend on the temperature. But vE acquires a temperature dependence if we deform the CFT and move along the corresponding RG flow. In these cases, $v_E$ violate the above bound, but it remains bounded by its corresponding value at the IR fixed point, never surpassing the speed of light - chaos and **hydrodynamics** - e.g. [[0179 Pole skipping]] # Jiang, Zhang ## Surface term, corner term, and action growth in $F(R_{abcd})$ gravity theory \[Links: [arXiv](https://arxiv.org/abs/1806.10312), [PDF](https://arxiv.org/pdf/1806.10312.pdf)\] \[Abstract: \] ## Refs - [[2009#Deruelle, Sasaki, Sendouda, Yamauchi]] obtains the surface term but not the corner term - [[0138 Variational principle]] ## Conventions - $d \Sigma_{a}=\varepsilon n_{a} d \Sigma$ (see eq.17) - $n_a$ is outward pointing normal for non-null boundaries - this is consistent with Poisson 3.16 ## Alternative action - introduce $\phi_{abcd}$ and $\psi_{abcd}$ - define $I_{\text {bulk }}=\int_{\mathcal{M}} d^{d+2} x \sqrt{-g}\;\left[F\left(\phi_{a b c d}, g_{a b}\right)-\psi^{a b c d}\left(\phi_{a b c d}-R_{a b c d}\right)\right]$ - equivalent to $I_{\text {bulk }}=\int_{\mathcal{M}} d^{d+2} x \sqrt{-g}\; F\left(R_{a b c d}, g_{a b}\right)$ on shell - which is obvious: EOM for $\psi^{abcd}$ sets $\phi_{abcd}=R_{abcd}$ - EOM for $\phi$: $E_{\phi}^{a b c d}=\frac{\partial F\left(\phi_{a b c d}, g_{a b}\right)}{\partial \phi_{a b c d}}-\psi^{a b c d}$ ## Derivation of surface term by variations - it is in general hard to find a good surface term that make the variational principle well posed. With the alternative action, it is now doable - $\delta I_{\mathrm{bulk}}=\int_{\mathcal{M}} d^{d+2} x \sqrt{-g}\,\left(E_{a b} \delta g^{a b}+E_{\phi}^{a b c d} \delta \phi_{a b c d}+E_{\psi}^{a b c d} \delta \psi_{a b c d}\right)+\int_{\partial \mathcal{M}} \bar{\delta} v^{a} d \Sigma_{a}$ - $\bar \delta v^{c}=2 {\psi_{a}}^{b c d} \delta {\Gamma^{a}}_{b d}+2 \delta g_{b d} \nabla_{a} \psi^{a b c d}$ - ==$= -4 \varepsilon \Psi_{a b} \delta K^{a b}-2 D^{a}\left(\bar \delta A^{b} \Psi_{a b}\right)+\left(2 n^{a} \nabla^{e} \psi_{b e a c}+6 \varepsilon \Psi_{a b} {K^{a}}_c\right) \delta h^{b c}-2 n^{d} \psi_{c a d b} D^{a} \delta h^{b c}$== - $\Psi_{a b} \equiv \psi_{a c b d} n^{c} n^{d}$, $\bar \delta {A}^{a}=-\varepsilon {h^{a}}_{b} \delta g^{b c} n_{c}$ - require ==$\delta \Psi_{ab}=\delta h_{ab}=0$== and forget about corner terms (a total derivative on the boundary) => $\int_{\Sigma} \bar\delta v^{a} d \Sigma_{a}=-4 \delta\left(\int_{\Sigma} \Psi_{a b} K^{a b} d \Sigma\right)$ - => need to add surface term ==$I_{\text {surf }}=4 \int_{\partial \mathcal{M}} \Psi_{a b} K^{a b} d \Sigma$== - now it seems that every term is linear in $f$, so it does not seem possible that perturbatively one can get a different answer. - NO. metric and everything else are expanded ## Derivation of corner term - a total derivative in the boundary variation - $n_{a} \bar\delta v^{a} \ni -2 D^{a}\left(\bar\delta A^{b} \Psi_{a b}\right)$ - require $I_\text{corner}$ s.t. $\delta I_{\text {comer }}=2 \sum_{s}\left(\varepsilon \int_{\partial \Sigma_{s}} \bar\delta A^{b} \Psi_{b a} d S^{a}\right)$ # Jonay, Huse, Nahum ## Coarse-grained dynamics of operator and state entanglement \[Links: [arXiv](https://arxiv.org/abs/1803.00089), [PDF](https://arxiv.org/pdf/1803.00089.pdf)\] \[Abstract: We give a detailed theory for the leading coarse-grained dynamics of [[0301 Entanglement entropy|entanglement entropy]] of states and of operators in generic short-range interacting quantum many-body systems. This includes operators spreading under Heisenberg time evolution, which we find are much less entangled than "typical" operators of the same spatial support. Extending previous conjectures based on random circuit dynamics, we provide evidence that the leading-order entanglement dynamics of a given chaotic system are determined by a function $\mathcal{E}(v)$, which is model-dependent, but which we argue satisfies certain general constraints. In a minimal membrane picture, $\mathcal{E}(v)$ is the "surface tension" of the membrane and is a function of the membrane's orientation $v$ in spacetime. For one-dimensional (1D) systems this surface tension is related by a Legendre transformation to an entanglement entropy growth rate $\Gamma(\partial S/\partial x)$ which depends on the spatial "gradient" of the entanglement entropy $S(x,t)$ across the cut at position $x$. We show how to extract the entanglement growth functions numerically in 1D at infinite temperature using the concept of the operator entanglement of the time evolution operator, and we discuss possible universality of $\mathcal{E}$ at low temperatures. Our theoretical ideas are tested against and informed by numerical results for a quantum-chaotic 1D spin Hamiltonian. These results are relevant to the broad class of chaotic many-particle systems or field theories with spatially local interactions, both in 1D and above.\] ## Refs - [[0433 Membrane theory of entanglement dynamics]] # Kitaev, Suh ## Statistical mechanics of a two-dimensional black hole \[Links: [arXiv](https://arxiv.org/abs/1808.07032), [PDF](https://arxiv.org/pdf/1808.07032)\] \[Abstract: The dynamics of a nearly-AdS2 spacetime with boundaries is reduced to two particles in the anti-de Sitter space. We determine the class of physically meaningful wavefunctions, and prescribe the statistical mechanics of a black hole. We demonstrate how wavefunctions for a two-sided black hole and a regularized notion of trace can be used to construct thermal partition functions, and more generally, arbitrary density matrices. We also obtain correlation functions of external operators.\] # Kravchuk, Simmons-Duffin ## Light-ray operators in conformal field theory \[Links: [arXiv](https://arxiv.org/abs/1805.00098), [PDF](https://arxiv.org/pdf/1805.00098.pdf)\] \[Abstract: We argue that every CFT contains light-ray operators labeled by a continuous spin $J$. When $J$ is a positive integer, [[0450 Light-ray operators|light-ray operators]] become integrals of local operators over a null line. However for non-integer $J$, light-ray operators are genuinely nonlocal and give the analytic continuation of CFT data in spin described by Caron-Huot. A key role in our construction is played by a novel set of intrinsically Lorentzian integral transforms that generalize the [[0039 Shadow transform|shadow transform]]. Matrix elements of light-ray operators can be computed via the integral of a double-commutator against a [[0031 Conformal block|conformal block]]. This gives a simple derivation of Caron-Huot's Lorentzian OPE inversion formula and lets us generalize it to arbitrary four-point functions. Furthermore, we show that light-ray operators enter the Regge limit of CFT correlators, and generalize conformal Regge theory to arbitrary four-point functions. The average null energy operator is an important example of a light-ray operator. Using our construction, we find a new proof of the [[0417 Averaged null energy condition|average null energy condition (ANEC)]], and furthermore generalize the ANEC to continuous spin.\] # Kusuki ## Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity \[Links: [arXiv](https://arxiv.org/abs/1810.01335), [PDF](https://arxiv.org/pdf/1810.01335.pdf)\] \[Abstract: The [[0619 Lightcone OPE|light cone OPE]] limit provides a significant amount of information regarding the conformal field theory (CFT), like the high-low temperature limit of the partition function. We started with the light cone bootstrap in the *general* CFT${}_2$ with $c>1$. For this purpose, we needed an explicit asymptotic form of the Virasoro conformal blocks in the limit $z \to 1$, which was unknown until now. In this study, we computed it in general by studying the pole structure of the *[[0573 Crossing kernel|fusion matrix]]* (or the crossing kernel). Applying this result to the light cone bootstrap, we obtained the universal total twist (or equivalently, the universal binding energy) of two particles at a large angular momentum. In particular, we found that the total twist is saturated by the value $\frac{c-1}{12}$ if the total Liouville momentum exceeds beyond the BTZ threshold. This might be interpreted as a black hole formation in AdS${}_3$. As another application of our light cone singularity, we studied the [[0522 Entanglement dynamics|dynamics of entanglement]] after a global [[0558 Quantum quench|quench]] and found a Renyi phase transition as the replica number was varied. We also investigated the dynamics of the 2nd [[0293 Renyi entropy|Renyi entropy]] after a local quench. We also provide a universal form of the Regge limit of the Virasoro conformal blocks from the analysis of the light cone singularity. This Regge limit is related to the general $n$-th Renyi entropy after a local quench and [[0482 Out-of-time-order correlator|out of time ordered correlators]].\] # Leichenauer, Levine, Shahbazi-Moghaddam ## Energy is entanglement \[Links: [arXiv](https://arxiv.org/abs/1802.02584), [PDF](https://arxiv.org/pdf/1802.02584.pdf)\] \[Abstract: We compute the local second variation of the [[0301 Entanglement entropy|von Neumann entropy]] of a region in theories with a gravity dual. For null variations our formula says that the diagonal part of the [[0405 Quantum null energy condition|Quantum Null Energy Condition]] is saturated in every state, thus providing an equivalence between energy and entropy. We prove that the formula holds at leading order in $1/N$, and further argue that it will not be affected at higher orders. We conjecture that the QNEC is saturated in all interacting theories. We also discuss the special case of free theories, and the implications of our formula for the [[0417 Averaged null energy condition|Averaged Null Energy Condition]], [[0243 Quantum focusing conjecture|Quantum Focusing Conjecture]], and gravitational equations of motion. We show that the leading-order gravitational equations of motion, Einstein's equations, are equivalent to leading-order saturation of the QFC for Planck-width deformations.\] ## Summary - saturation of [[0405 Quantum null energy condition]] implies energy is just vN entropy # Lewkowycz, Parrikar ## The Holographic Shape of Entanglement and Einstein’s Equations \[Links: [arXiv](https://arxiv.org/abs/1802.10103), [PDF](https://arxiv.org/pdf/1802.10103.pdf)\] \[Abstract: \] ## Summary - double deformation: shape of boundary region and state - a more derivation of [[0007 RT surface]] without using replica trick - [[0302 Gravity from entanglement]] and vice versa ## CFT entropy deformation - $\delta \delta_{V} S=\lim _{B \rightarrow 0} \int_{-\infty}^{\infty} \frac{d s}{4 \sinh ^{2}\left(\frac{s+i \epsilon}{2}\right)} \oint_{\partial R_{B}} V^{\mu} n^{\nu} \delta\left\langle\rho_{R}^{-i s / 2 \pi}: T_{\mu \nu}: \rho_{R}^{i s / 2 \pi}\right\rangle$ ## Bulk entropy - the boundary entropy can be calculated via $\delta \delta_{V} S=\frac{\delta \delta_{V} A_{e x t}}{4 G_{N}}$ - n.b. this goes the other way as well: if this equation holds, then linearised Einstein equation must hold; but since the region is arbitrary, non-linear Einstein equation must hold ## Higher derivatives - claims that the techniques still apply # Maldacena, Qi ## Eternal traversable wormhole \[Links: [arXiv](https://arxiv.org/abs/1804.00491), [PDF](https://arxiv.org/pdf/1804.00491.pdf)\] \[Abstract: We construct a nearly-AdS$_2$ solution describing an eternal [[0083 Traversable wormhole|traversable wormhole]]. The solution contains negative null energy generated by quantum fields under the influence of an external coupling between the two boundaries. In parallel, we discuss two [[0201 Sachdev-Ye-Kitaev model|SYK]] systems coupled by a relevant interaction. The physics of the two cases is very similar. They both share a "gravitational" subsector which is identical. The solution within this subsector sets the stage for dynamics which is almost conformal invariant. We study this system in detail, both in gravity and in the SYK model. The coupled SYK models have an interesting phase diagram at finite temperature, displaying the usual [[0012 Hawking-Page transition|Hawking-Page transition]] between the thermal AdS phase at low temperature and the black hole phase at high temperature. Interestingly, these two phases are continuously connected in the microcannonical ensemble.\] ## Refs - 3d example [[2023#Harvey, Jensen]] # Marolf ## Microcanonical Path Integrals and the Holography of small Black Hole Interiors \[Links: [arXiv](https://arxiv.org/abs/1808.00394), [PDF](https://arxiv.org/pdf/1808.00394.pdf)\] \[Abstract: We use a microcanonical path integral closely related to that introduced by Brown and York in 1992 to add new entries to the [[0001 AdS-CFT|AdS/CFT dictionary]] concerning the interiors of small black holes. Stationary points of such path integrals are also stationary points of more standard canonical-type path integrals with fixed boundary metric, but the condition for dominance is now maximizing [[0007 RT surface|Hubeny-Rangamani-Takayanagi entropy]] at fixed energy. As a result, such path integrals can bring to the fore saddles that fail to dominate in more familiar contexts. We use this feature to argue that the standard Kruskal-like two-sided extension of small AdS black holes with energy $E_0$ is dual to a microcanonical version of the thermofield double state for AdS black holes that maximize the microcanonical bulk entropy at this energy. We also comment on entanglement in such states and on quantum effects that become large when the energy-width of the microcanonical ensemble is sufficiently small.\] ## Refs - [[0438 Small black holes in AdS]] # Meltzer ## Higher Spin ANEC and the Space of CFTs \[Links: [arXiv](https://arxiv.org/abs/1811.01913), [PDF](https://arxiv.org/pdf/1811.01913)\] \[Abstract: We study the positivity properties of the leading Regge trajectory in higher-dimensional, unitary, conformal field theories (CFTs). These conditions correspond to higher spin generalizations of the [[0417 Averaged null energy condition|averaged null energy condition]] (ANEC). By studying higher spin ANEC, we will derive new bounds on the dimensions of charged, spinning operators and prove that if the [[0493 Conformal collider bounds|Hofman-Maldacena bounds]] are saturated, then the theory has a [[0621 Higher-spin conserved currents in CFT|higher spin symmetry]]. We also derive new, general bounds on CFTs, with an emphasis on theories whose spectrum is close to that of a generalized free field theory. As an example, we consider the Ising CFT and show how the OPE structure of the leading Regge trajectory is constrained by causality. Finally, we use the analytic bootstrap to perform additional checks, in a large class of CFTs, that higher spin ANEC is obeyed at large and finite spin. In the process, we calculate corrections to large spin OPE coefficients to one-loop and higher in [[0122 Holographic CFT|holographic CFTs]].\] # Mezei ## Membrane theory of entanglement dynamics from holography \[Links: [arXiv](https://arxiv.org/abs/1803.10244), [PDF](https://arxiv.org/pdf/1803.10244.pdf)\] \[Abstract: Recently, a [[0433 Membrane theory of entanglement dynamics|minimal membrane description of the entanglement dynamics]] of large regions in generic [[0008 Quantum chaos|chaotic]] systems was conjectured in [[2018#Jonay, Huse, Nahum]]. Analytic results in random circuits and spin chain numerics support this theory. We show that the results found by the author in [[2016#Mezei]] about the dynamics of [[0301 Entanglement entropy|entanglement entropy]] in theories with a [[0001 AdS-CFT|holographic]] dual can be reformulated in terms of the same minimal membrane, providing strong evidence that the membrane theory describes all chaotic systems. We discuss the implications of our results for tensor network approaches to holography and the [[0209 Holographic renormalisation|holographic renormalization group]].\] ## Summary - this is the original paper for holographically understanding the [[0433 Membrane theory of entanglement dynamics|membrane theory of entanglement dynamics]] - connecting [[2016#Mezei]] and [[2018#Jonay, Huse, Nahum]] # Mukhametzhanov, Zhiboedov ## Analytic Euclidean Bootstrap \[Links: [arXiv](https://arxiv.org/abs/1808.03212), [PDF](https://arxiv.org/pdf/1808.03212.pdf)\] \[Abstract: We solve crossing equations analytically in the deep Euclidean regime. Large scaling dimension $\Delta$ tails of the weighted spectral density of primary operators of given spin in one channel are matched to the Euclidean OPE data in the other channel. Subleading $1\over \Delta$ tails are systematically captured by including more operators in the Euclidean OPE in the dual channel. We use dispersion relations for conformal partial waves in the complex $\Delta$ plane, the Lorentzian inversion formula and complex tauberian theorems to derive this result. We check our formulas in a few examples (for CFTs and scattering amplitudes) and find perfect agreement. Moreover, in these examples we observe that the large $\Delta$ expansion works very well already for small $\Delta \sim 1$. We make predictions for the 3d Ising model. Our analysis of dispersion relations via complex tauberian theorems is very general and could be useful in many other contexts.\] # Nayak, Shukla, Soni, Trivedi, Vishal ## On the Dynamics of Near-Extremal Black Holes \[Links: [arXiv](https://arxiv.org/abs/1802.09547), [PDF](https://arxiv.org/pdf/1802.09547.pdf)\] \[Abstract: We analyse the dynamics of near-extremal Reissner-Nordström black holes in asymptotically four-dimensional Anti-de Sitter space (AdS$_4$). We work in the spherically symmetric approximation and study the thermodynamics and the response to a ==probe scalar field==. We find that the behaviour of the system, at low energies and to leading order in our approximations, is well described by the [[0050 JT gravity|Jackiw-Teitelboim (JT) model]] of gravity. In fact, this behaviour can be understood from symmetry considerations and arises due to the breaking of time reparametrisation invariance. The JT model has been analysed in considerable detail recently and related to the behaviour of the [[0201 Sachdev-Ye-Kitaev model|SYK model]]. Our results indicate that features in these models which arise from symmetry considerations alone are more general and present quite universally in near-extremal black holes.\] # Parker, Cao, Avdoshkin, Scaffidi, Altman ## A Universal Operator Growth Hypothesis \[Links: [arXiv](https://arxiv.org/abs/1812.08657), [PDF](https://arxiv.org/pdf/1812.08657)\] \[Abstract: We present a [[0665 Universal Operator Growth Hypothesis|hypothesis]] for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate $\alpha$ in generic systems, with an extra logarithmic correction in 1d. The rate $\alpha$ --- an experimental observable --- governs the exponential growth of operator complexity in a sense we make precise. This exponential growth even prevails beyond semiclassical or large-$N$ limits. Moreover, $\alpha$ upper bounds a large class of operator complexity measures, including the [[0482 Out-of-time-order correlator|out-of-time-order correlator]]. As a result, we obtain a sharp bound on [[0466 Lyapunov exponent|Lyapunov exponents]] $\lambda_L \leq 2 \alpha$, which complements and improves the known universal low-temperature bound $\lambda_L \leq 2 \pi T$. We illustrate our results in paradigmatic examples such as non-integrable spin chains, the [[0201 Sachdev-Ye-Kitaev model|Sachdev-Ye-Kitaev model]], and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants.\] # Pook-Kolb, Birnholtz, Krishnan, Schnetter ## The existence and stability of marginally trapped surfaces \[Links: [arXiv](https://arxiv.org/abs/1811.10405), [PDF](https://arxiv.org/pdf/1811.10405.pdf)\] \[Abstract: \] ## Summary - gives a method for finding minimal surfaces ([[0298 MOTS]]) on [[0285 Brill-Lindquist initial data]] - implemented in Einstein toolkit - gives area plots for different mass ratios as a function of distance parameter ## Refs - [[0298 MOTS]] - later papers - [[2021#Pook-Kolb, Hennigar, Booth]] - [[BoothHennigarPook-Kolb2021]] # Rodina ## Scattering Amplitudes from Soft Theorems and Infrared Behavior \[Links: [arXiv](https://arxiv.org/abs/1807.09738), [PDF](https://arxiv.org/pdf/1807.09738.pdf)\] \[Abstract: We prove that [[0009 Soft theorems|soft theorems]] uniquely fix scattering amplitudes in a wide range of theories, including Yang-Mills, gravity, the non-linear sigma model, Dirac-Born-Infeld, dilaton effective theories, extended theories like NLSM$\oplus \phi^3$ or BI$\oplus$YM, as well as some higher derivative corrections to these theories. We conjecture the same is true even when imposing more general soft behavior, simply by assuming the existence of soft operators, or by imposing gauge invariance/the Adler zero only up to a finite order in soft expansions. Besides reproducing known amplitudes, this analysis reveals a new higher order correction to the NLSM, and two interesting facts: the subleading theorem for the dilaton, and the subsubleading theorem for DBI follow automatically from the more leading theorems. These results provide motivation that [[0060 Asymptotic symmetry|asymptotic symmetries]] contain enough information to fully fix a holographic S-matrix.\] # Saad, Shenker, Stanford ## A semiclassical ramp in SYK and in gravity \[Links: [arXiv](https://arxiv.org/abs/1806.06840), [PDF](https://arxiv.org/pdf/1806.06840.pdf)\] \[Abstract: In finite entropy systems, real-time partition functions do not decay to zero at late time. Instead, assuming random matrix universality, suitable averages exhibit a growing "ramp" and "plateau" structure. Deriving this non-decaying behavior in a large $N$ collective field description is a challenge related to one version of the [[0131 Information paradox|black hole information problem]]. We describe a candidate semiclassical explanation of the ramp for the [[0201 Sachdev-Ye-Kitaev model|SYK]] model and for black holes. In SYK, this is a two-replica nonperturbative saddle point for the large $N$ collective fields, with zero action and a compact zero mode that leads to a linearly growing ramp. In the black hole context, the solution is a two-sided black hole that is periodically identified under a Killing time translation. We discuss but do not resolve some puzzles that arise.\] # Stieberger, Taylor (Dec) ## Symmetries of celestial amplitudes \[Links: [arXiv](https://arxiv.org/abs/1812.01080), [PDF](https://arxiv.org/pdf/1812.01080.pdf)\] \[Abstract: Celestial amplitudes provide holographic imprints of four-dimensional scattering processes in terms of conformal correlation functions on a two-dimensional sphere describing Minkowski space at null infinity. We construct the generators of Poincare and conformal groups in the celestial representation and discuss how these symmetries are manifest in the amplitudes.\] ## Refs - [[0010 Celestial holography]] ## Summary - *translates* 4D Poincare and conformal symmetries to 2D language - *constructs* symmetry generators in 2D ## Generators ### Lorentz $\begin{array}{ll}L_{1} \equiv M_{23}+i M_{10}=\left(1-z^{2}\right) \partial_{z}-2 z h, & -M_{23}+i M_{10}=\bar{L}_{1} \\ L_{2} \equiv M_{20}+i M_{13}=\left(1+z^{2}\right) \partial_{z}+2 z h, & -M_{20}+i M_{13}=\bar{L}_{2} \\ L_{3} \equiv M_{21}+i M_{03}=2\left(z \partial_{z}+h\right), & -M_{21}+i M_{03}=\bar{L}_{3},\end{array}$ ### Translations $\begin{aligned}P_{0}=&\left(1+|z|^{2}\right) e^{\left(\partial_{h}+\partial_{\bar{h}}\right) / 2}\\ P_{1}=&(z+\bar{z}) e^{\left(\partial_{h}+\partial_{\bar{h}}\right) / 2}\\ P_{2}=&-i(z-\bar{z}) e^{\left(\partial_{h}+\partial_{\bar{h}}\right) / 2}\\ P_{3}=&\left(1-|z|^{2}\right) e^{\left(\partial_{h}+\partial_{\bar{h}}\right) / 2}\end{aligned}$ ## Commutators $\begin{aligned}\left[L_{1}, L_{2}\right] &=2 L_{3} \\\left[L_{2}, L_{3}\right] &=2 L_{1} \\\left[L_{3}, L_{1}\right] &=-2 L_{2} \end{aligned}$ # Susskind (Feb, a) ## Why do Things Fall? \[Links: [arXiv](https://arxiv.org/abs/1802.01198), [PDF](https://arxiv.org/pdf/1802.01198.pdf)\] \[Abstract: This is the first of several short notes in which I will describe phenomena that illustrate GR=QM. In it I explain that the gravitational attraction that a black hole exerts on a nearby test object is a consequence of a fundamental law of quantum mechanics---the tendency for [[0204 Quantum complexity|complexity]] to grow. It will also be shown that the Einstein bound on velocities is closely related to the [[0474 Chaos bound|quantum-chaos bound]] of [[2015#Maldacena, Shenker, Stanford|Maldacena, Shenker, and Stanford]].\] # Witten (Mar, Review) ## Notes On Some Entanglement Properties Of Quantum Field Theory \[Links: [arXiv](https://arxiv.org/abs/1803.04993), [PDF](https://arxiv.org/pdf/1803.04993.pdf)\] ## 1. Introduction ## 2. The [[0164 Reeh–Schlieder theorem|Reeh-Schlieder theorem]] # Witten (Oct) ## Open strings on the Rindler horizon \[Links: [arXiv](https://arxiv.org/abs/1810.11912), [PDF](https://arxiv.org/pdf/1810.11912.pdf)\] \[Abstract: It has been proposed that a certain $Z_N$ orbifold, analytically continued in $N$, can be used to describe the thermodynamics of Rindler space in string theory. In this paper, we attempt to implement this idea for the open-string sector. The most interesting result is that, although the orbifold is tachyonic for positive integer $N$, the tachyon seems to disappear after analytic continuation to the region that is appropriate for computing $\operatorname{Tr} \rho^{\mathcal{N}}$, where $\rho$ is the density matrix of Rindler space and Re $\mathcal{N}>1$. Analytic continuation of the full orbifold conformal field theory remains a challenge, but we find some evidence that if such analytic continuation is possible, the resulting theory is a logarithmic conformal field theory, necessarily nonunitary.\] ## Summary - in String Theory the usual replica trick does not work because there is no known CFT whose target space is an $n$-fold cover of $\mathbb{R}^2$, branched over the origin; but can use an orbifold with opening angle of $2\pi/n$ (so formally we compute $Tr \rho^{1/n}$) - problem: $Tr \rho^{1/n}$ can be divergent for $\Re(1/n)<1$ ## String calculation The 1-loop contribution to $Tr\rho^{1/N}$ comes from a WS that is an annulus (in the open string case) : $\left.\log \operatorname{Tr} \rho^{1 / N}\right|_{1}=\frac{1}{2} \int_{0}^{\infty} \frac{\mathrm{d} T}{T} Z_{N}(T)$ # Yang ## The Quantum Gravity Dynamics of Near Extremal Black Holes \[Links: [arXiv](https://arxiv.org/abs/1809.08647), [PDF](https://arxiv.org/pdf/1809.08647)\] \[Abstract: We study the quantum effects of Near-Extremal black holes near their horizons. The gravitational dynamics in such backgrounds are closely connected to a particle in AdS$_2$ with constant electric field. We use this picture to solve the theory exactly. We will give a formula to calculate all correlation functions with quantum gravity backreactions as well as the exact [[0345 Wheeler-DeWitt (WdW) equation|Wheeler-DeWitt wavefunction]]. Using the WdW wavefunction, we investigate the [[0204 Quantum complexity|complexity]]0 growth in quantum gravity.\] # Yuan ## Simplicity in AdS perturbative dynamics \[Links: [arXiv](https://arxiv.org/abs/1801.07283), [PDF](https://arxiv.org/pdf/1801.07283.pdf)\] \[Abstract: We investigate analytic properties of loop-level perturbative dynamics in pure AdS, with the scalar effective theories with non-derivative couplings as a prototype. Explicit computations reveal certain (perhaps unexpected) simplicity regarding the pole structure of the results, in both the Mellin amplitude and a closely related object that we call Mellin pre-amplitude. Correspondingly we propose a pair of conjectures for arbitrary diagrams at all loops, based on non-trivial evidence up to two loops (and higher loops in a special class of diagrams). We also inspect the structure of residues at poles in the physical channels for several one-loop examples up to a 4-point box, as well as a two-loop double-triangle diagram. These analyses are performed using the recursive construction of Mellin (pre-)amplitudes recently prescribed in [arXiv:1710.01361](https://arxiv.org/abs/1710.01361), for which we provide detailed derivation and generalization in this paper. Along the way we derive a set of alternative diagrammatic rules for tree (pre-)amplitudes, which are better suited to our loop construction. On the mathematical aspect we share some new thoughts on improving the contour analysis of multi-dimensional Mellin integrals, which are the essential ingredients that make our approach practical.\] ## Refs - may help understand [[0105 AdS amplitudes]] - earlier paper [[Yuan2017]] on loop calculation in AdS ## Summary - ==loop level== dynamics in ==pure AdS== for ==scalar effective field theories== - find simplicity in the pole structure of Mellin amplitudes and Mellin **pre-amplitudes** - two conjectures for arbitrary diagrams at all loops - alternative diagrammatic rules for tree (pre-)amplitudes, better suited to loop constructions