# Adamo, Bu, Casali, Sharma ## Celestial operator products from the worldsheet \[Links: [arXiv](https://arxiv.org/abs/2111.02279), [PDF](https://arxiv.org/pdf/2111.02279.pdf)\] \[Abstract: We compute the [[0030 Operator product expansion|operator product expansions]] of gluons and gravitons in celestial CFT from the worldsheet OPE of vertex operators of four-dimensional [[0348 Ambitwistor strings|ambitwistor string theories]]. Remarkably, the worldsheet OPE localizes on the short-distance singularity between vertex operator insertions which in turn coincides with the OPE limit of operator insertions on the celestial sphere. The worldsheet CFT dynamically produces known [[0114 Celestial OPE|celestial OPE]] coefficients -- as well as infinite towers of $SL(2,\mathbb{R})$ descendant contributions to the celestial OPE -- without any truncations or approximations. We obtain these results for all helicities and incoming/outgoing configurations. Furthermore, the worldsheet OPE encodes the infinite-dimensional symmetry algebras associated with the conformally soft sectors of gauge theory and gravity. We provide explicit operator realizations of the currents generating these symmetries on ambitwistor space in terms of vertex operators for soft gluons and gravitons, also computing their actions on hard particles of all helicities. Lastly, we show that the worldsheet OPE for momentum eigenstates produces the [[0078 Collinear limit|collinear splitting functions]] of gluons and gravitons.\] ## Summary - *finds* that the limit where worldsheet insertion points collide is directly related to the collision of insertion points on the celestial sphere; that the worldsheet OPE localizes onto these configurations; and that the expression for the worldsheet OPE exactly reproduces the structure of the OPE in CCFT ## Background - [[0348 Ambitwistor strings|ambitwistor strings]] give the right scattering amplitudes (in the conformal primary basis as well as in momentum space) - "the fully-fledged scattering equations only emerge after computing a fully on-shell correlation function in the worldsheet CFT of the ambitwistor string. The calculations we perform in this paper are basically off-shell: we consider the full worldsheet OPE between vertex operators, without reference to any larger correlator or the rest of the path integral." - "Hence, it is not a priori clear that the worldsheet OPE should localize to the boundary of the moduli space (i.e., where worldsheet insertion points coincide) or have anything to do with the OPE limit of operator insertions on the celestial sphere" # Agarwal, Magnea, Signorile-Signorile, Tripathi ## The Infrared Structure of Perturbative Gauge Theories \[Links: [arXiv](https://arxiv.org/abs/2112.07099), [PDF](https://arxiv.org/pdf/2112.07099.pdf)\] \[Abstract: [[0295 Infrared divergences in scattering amplitude|Infrared divergences]] in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are explored, and high-precision phenomenological applications demand an ever more refined understanding. This review aims to provide a pedagogical overview of the subject. We briefly cover some of the early historical results, we provide some simple examples of low-order applications in the context of perturbative QCD, and discuss the necessary tools to extend these results to all perturbative orders. Finally, we describe recent developments concerning the calculation of soft anomalous dimensions in multi-particle scattering amplitudes at high orders, and we provide a brief introduction to the very active field of infrared subtraction for the calculation of differential distributions at colliders.\] # Agon, Pedraza ## Quantum bit threads and holographic entanglement \[Links: [arXiv](https://arxiv.org/abs/2105.08063), [PDF](https://arxiv.org/pdf/2105.08063.pdf)\] \[Abstract: Quantum corrections to [[0007 RT surface|holographic entanglement entropy]] require knowledge of the bulk quantum state. In this paper, we derive a novel dual prescription for the generalized entropy that allows us to interpret the leading quantum corrections in a geometric way with minimal input from the bulk state. The equivalence is proven using tools borrowed from convex optimization. The new prescription does not involve bulk surfaces but instead uses a generalized notion of a flow, which allows for possible sources or sinks in the bulk geometry. In its discrete version, our prescription can alternatively be interpreted in terms of a set of Planck-thickness bit threads, which can be either classical or quantum. This interpretation uncovers an aspect of the generalized entropy that admits a neat information-theoretic description, namely, the fact that the quantum corrections can be cast in terms of entanglement distillation of the bulk state. We also prove some general properties of our prescription, including nesting and a quantum version of the max multiflow theorem. These properties are used to verify that our proposal respects known inequalities that a [[0301 Entanglement entropy|von Neumann entropy]] must satisfy, including subadditivity and [[0218 Strong subadditivity|strong subadditivity]], as well as to investigate the fate of the holographic monogamy. Finally, using the [[0019 Covariant phase space|Iyer-Wald formalism]] we show that for cases with a local [[0416 Modular Hamiltonian|modular Hamiltonian]] there is always a canonical solution to the program that exploits the property of bulk locality. Combining with previous results by Swingle and Van Raamsdonk, we show that the consistency of this special solution requires the semi-classical Einstein's equations to hold for any consistent perturbative bulk quantum state.\] ## Related - [[2021#Akers, Hernandez-Cuenca, Rath]] - [[0211 Bit thread]] # Akers, Faulkner, Lin, Rath ## Reflected entropy in random tensor networks \[Links: [arXiv](https://arxiv.org/abs/2112.09122), [PDF](https://arxiv.org/pdf/2112.09122.pdf)\] \[Abstract: In holographic theories, the [[0166 Reflected entropy|reflected entropy]] has been shown to be dual to the area of the [[0319 Entanglement wedge cross-section|entanglement wedge cross section]]. We study the same problem in random [[0054 Tensor network|tensor networks]] demonstrating an equivalent duality. For a single random tensor we analyze the important non-perturbative effects that smooth out the discontinuity in the reflected entropy across the Page phase transition. By summing over all such effects, we obtain the reflected entanglement spectrum analytically, which agrees well with numerical studies. This motivates a prescription for the analytic continuation required in computing the reflected entropy and its [[0293 Renyi entropy|Rényi]] generalization which resolves an order of limits issue previously identified in the literature. We apply this prescription to hyperbolic tensor networks and find answers consistent with holographic expectations. In particular, the random tensor network has the same non-trivial tripartite entanglement structure expected from holographic states. We furthermore show that the reflected Rényi spectrum is not flat, in sharp contrast to the usual Rényi spectrum of these networks. We argue that the various distinct contributions to the reflected entanglement spectrum can be organized into approximate superselection sectors. We interpret this as resulting from an effective description of the canonically purified state as a superposition of distinct tensor network states. Each network is constructed by doubling and gluing various candidate entanglement wedges of the original network. The superselection sectors are labelled by the different cross-sectional areas of these candidate entanglement wedges.\] ## Summary - uses a simple tensor model and relates it to a multi-boundary wormhole # Akers, Hernandez-Cuenca, Rath ## Quantum Extremal Surfaces and the Holographic Entropy Cone \[Links: [arXiv](https://arxiv.org/abs/2108.07280), [PDF](https://arxiv.org/pdf/2108.07280.pdf)\] \[Abstract: Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the [[0007 RT surface|Ryu-Takayanagi (RT) formula]] defines the [[0259 Holographic entropy cone|Holographic Entropy Cone]] (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the [[0212 Quantum extremal surface|Quantum Extremal Surface]] (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.\] ## Refs - [[2021#Agon, Pedraza]] ## Summary - extending [[0259 Holographic entropy cone]] to include quantum fields - we see that by varying the restrictions on the quantum contribution $S_{bulk}$, constrained [[0212 Quantum extremal surface|QES]] cones nicely interpolate between the “classical” HEC and the fully quantum entropy cone - n.b. the constrained QES must be bigger than HEC because removing the quantum fields create a classical state which belongs to the HEC ## Two types of constraints - HEC constraint: require quantum fields to satisfy HEC - finds that the result QES cones = HEC - can be understood as a doubly holographic thing - MMI constraints: bulk fields to satisfy MMI *for arbitrary subregions* - finds that this implies MMI for the boundary - => the MMI-constrained QES cone is at least as small as the cone obtained by imposing all instances of MMI on quantum entropies, i.e., the MMI cone. ## The question - by choosing the bulk matter to have arbitrary entanglement structures, there are no entropy constraints on the boundary quantum state other than the universal ones obeyed by quantum states (such as strong subadditivity) - => hence the interesting question to ask is what effect entropic constraints on the bulk matter fields have on the entanglement structure of the boundary state ## Bulk state inequalities v.s. boundary - in general, any given $n$-party holographic entropy inequality holds for SQES so long as the bulk state satisfies a certain $n^\prime$-party inequality for $n^\prime\gg n$, where $n^\prime$ is generally doubly-exponential in $n$ # Akers, Penington ## Quantum minimal surfaces from quantum error correction \[Links: [arXiv](https://arxiv.org/abs/2109.14618), [PDF](https://arxiv.org/pdf/2109.14618.pdf)\] \[Abstract: We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an equivalence previously shown by Harlow; in particular, we do not require the entanglement wedge to be the same for all states in the code space. In developing this theorem, we construct an emergent bulk geometry for general quantum codes, defining "areas" associated to arbitrary logical subsystems, and argue that this definition is "functionally unique." We also formalize a definition of bulk reconstruction that we call "state-specific product unitary" reconstruction. This definition captures the [[0146 Quantum error correction|quantum error correction]] (QEC) properties present in holographic codes and has potential independent interest as a very broad generalization of QEC; it includes most traditional versions of QEC as special cases. Our results extend to approximate codes, and even to the "non-isometric codes" that seem to describe the interior of a black hole at late times.\] ## Summary - generalised [[2016#Harlow]] ## Issues with Harlow's version and improvement - fixed EW - an issue if bulk entropy is important - i.e. the EW should depend on the state/code subspace - improvement - allow EW to change - so there is a minimisation procedure, like the RT ## Definition of area - first choose a set of points in the bulk $\{b_i\}$ and a boundary region $B$; then add some reference qubits on the boundary that purifies the chosen bulk qubits; then define the area corresponding to a boundary subregion $B$ and $\{b_i\}$ to be the entropy corresponding to the union of $B$ and the reference qubits that purify the qubits on the EW of $B$ - not a conventional way to think about area but this is needed when the surface is non-minimal - later to get the entropy we need to minimise over all choices of $\{b_i\}$: $S(B)=\operatorname{min}_{\{b_i\}}A_B(\{b_i\})+S(\{b_i\})$ # Almheiri, Lin ## The entanglement wedge of unknown couplings \[Links: [arXiv](https://arxiv.org/abs/2111.06298), [PDF](https://arxiv.org/pdf/2111.06298.pdf)\] \[Abstract: \] ## Refs - follow up: [[DasPalSarkar2022]][](https://arxiv.org/pdf/2203.14988.pdf) ## Summary - *considers* a BH in a superposition of states corresponding to different boundary couplings, entangled with a reference which keeps track of those couplings # Anous, Belin, de Boer, Liska ## OPE statistics from higher-point crossing \[Links: [arXiv](https://arxiv.org/abs/2112.09143), [PDF](https://arxiv.org/pdf/2112.09143)\] \[Abstract: We present new [[0663 OPE statistics|asymptotic formulas]] for the distribution of OPE coefficients in conformal field theories. These formulas involve products of four or more coefficients and include light-light-heavy as well as heavy-heavy-heavy contributions. They are derived from crossing symmetry of the six and higher point functions on the plane and should be interpreted as non-Gaussianities in the statistical distribution of the OPE coefficients. We begin with a formula for arbitrary operator exchanges (not necessarily primary) valid in any dimension. This is the first asymptotic formula constraining heavy-heavy-heavy OPE coefficients in $d>2$. For two-dimensional CFTs, we present refined asymptotic formulas stemming from exchanges of quasi-primaries as well as Virasoro primaries.\] # Atanasov, Ball, Melton, Raclariu, Strominger ## (2, 2) scattering and the celestial torus \[Links: [arXiv](https://arxiv.org/abs/2101.09591), [PDF](https://arxiv.org/pdf/2101.09591.pdf)\] \[Abstract: Analytic continuation from Minkowski space to (2,2) split signature spacetime has proven to be a powerful tool for the study of scattering amplitudes. Here we show that, under this continuation, null infinity becomes the product of a null interval with a [[0250 Celestial torus|celestial torus]] (replacing the [[0022 Celestial sphere|celestial sphere]]) and has only one connected component. Spacelike and timelike infinity are time-periodic quotients of AdS$_3$. These three components of infinity combine to an $S^3$ represented as a toric fibration over the interval. Privileged scattering states of scalars organize into $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ conformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.\] ## Refs - this paper introduces [[0250 Celestial torus]] - root [[0010 Celestial holography]] - [[Talk202102031254 Andy Strominger Celestial torus]] ## The topology - only one null infinity <- topology is $S^3$ - $S^3$ is foliated or fibrated like: ![[Talk202102031254_fibration.png|150]] - at one end, one circle contracts, and at the other end, the other circle contracts - so a cross-section is a torus ## The norm - (Shu-Heng Shao) is there a norm - (Andy) avoided talking about it in the paper - really want to talk about some scattering physics, not really needed to have a complete basis: complete for what? ## Partition function - although Lorentzian torus, can still do partition function - might be able to add cosmic string etc to deform the torus - would be interesting to find the partition function # Atanasov, Melton, Raclariu, Strominger ## Conformal Block Expansion in Celestial CFT \[Links: [arXiv](https://arxiv.org/abs/2104.13432), [PDF](https://arxiv.org/pdf/2104.13432.pdf)\] \[Abstract: The 4D 4-point scattering amplitude of massless scalars via a massive exchange is expressed in a basis of conformal primary particle wavefunctions. This celestial amplitude is expanded in a basis of 2D conformal partial waves on the unitary principal series, and then rewritten as a sum over 2D [[0031 Conformal block|conformal blocks]] via contour deformation. The conformal blocks include intermediate exchanges of spinning light-ray states, as well as scalar states with positive integer conformal weights. The conformal block prefactors are found as expected to be quadratic in the [[0114 Celestial OPE|celestial OPE]] coefficients.\] ## Refs - talk at [[Rsc0025 Celestial workshop 2021]] ## Summary - *uses* [[0020 Conformal partial wave decomposition|partial wave expansion]] of [[2019#Nandan, Schreiber, Volovich, Zlotnikov]] to - *derive* [[0031 Conformal block]] expansion for ==$\phi^3$== theory ## Why Klein space - CCFT lives on (1,1) signature -> allow continuous and imaginary spins (found in the conformal decomposition) ## Content - (1) Intro - (2) Preliminaries - (3) massless 4-point scalar mediated by massive scalar exchange in conformal primary basis - (4) review completeness properties of partial waves on the unitary principal series - (5) transform the celestial amplitude to that basis, deform the contour integral over the unitary principal series and derive the conformal block expansion from pole contributions - (6) infinite mass limit; contact ## Method - Mellin transform - $\mathcal{A}\left(z_{i}, \bar{z}_{i} ; \Delta_{i}\right)=K\left(z_{i}, \bar{z}_{i}\right) X(z, \beta) \int_{0}^{\infty} d \omega \omega^{\beta-1} \mathcal{M}\left(\omega^{2},-z \omega^{2}\right)$ - put it into this form - $\mathcal{A}\left(z_{i}, \bar{z}_{i} ; \Delta_{i}\right)=I_{13-24}\left(z_{i}, \bar{z}_{i}\right) f(z, \bar{z})$ - where $I_{13-24}$ the conformally covariant structure symmetric under 1-3 2-4 exchanges ## Eigenfunctions of Casimir operator - conformal symmetry => blocks are eigenfunctions of conformal Casimir acting on 1 and 3 - $\left(\mathcal{D}_{z}+\mathcal{D}_{\bar{z}}\right) k_{h, \bar{h}}(z, \bar{z})=[h(h-1)+\bar{h}(\bar{h}-1)] k_{h, \bar{h}}(z, \bar{z})$ - a complete, orthogonal basis of solutions - $\Psi_{h, \bar{h}}(z, \bar{z})=\Psi_{h}(z) \Psi_{\bar{h}}(\bar{z})$ - where $\mathcal{D}_{z} \Psi_{h}(z)=h(h-1) \Psi_{h}(z), \quad \mathcal{D}_{\bar{z}} \Psi_{\bar{h}}(\bar{z})=\bar{h}(\bar{h}-1) \Psi_{\bar{h}}(\bar{z})$ - symmetry under $h\to 1-h$ implies they are linear combinations of conformal blocks and their shadows - [ ] why? - a generic set of eigenfunction - with real eigenvalues $\alpha^{2}-\frac{1}{4}$ and $h=\frac{1}{2}+\alpha, \alpha \in i \mathbb{R}$ - $\Psi_{\alpha}(z)=A k_{1 / 2+\alpha}(z)+B k_{1 / 2-\alpha}(z), \quad \alpha \in i \mathbb{R}$ - boundary condition $\Psi(1)=1$ -> fixed $A$ and $B$ - -> $\Psi_{\alpha}=\frac{1}{2}\left(Q(\alpha) k_{1 / 2+\alpha}(z)+Q(-\alpha) k_{1 / 2-\alpha}(z)\right)$ - $Q(\alpha)=\frac{2 \Gamma(-2 \alpha) \Gamma\left(1-h_{13}+h_{24}\right)}{\Gamma\left(\frac{1}{2}-\alpha-h_{13}\right) \Gamma\left(\frac{1}{2}-\alpha+h_{24}\right)}$ ## Scalar scattering - $\mathcal{M}(s, t)=-g^{2}\left(\frac{1}{s-m^{2}}+\frac{1}{t-m^{2}}+\frac{1}{-t-s-m^{2}}\right)$ (eq.3.1) ## 5 Conformal block expansion - two types of particles exchanged - integer mode - light transform - Light transform: the exchanged particle is a light transformed state - $\frac{\left\langle\mathcal{O}_{1} L\left[\mathcal{O}_{\Delta, J}\right] \mathcal{O}_{3}\right\rangle\left\langle\mathcal{O}_{2} L\left[\mathcal{O}_{\Delta, J}\right] \mathcal{O}_{4}\right\rangle}{\left\langle L\left[\mathcal{O}_{\Delta, J}\right] L\left[\mathcal{O}_{\Delta, J}\right]\right\rangle}$ # Balasubramanian, Craps, Khramtsov, Shaghoulian ## Submerging islands through thermalization \[Links: [arXiv](https://arxiv.org/abs/2107.14746), [PDF](https://arxiv.org/pdf/2107.14746.pdf)\] \[Abstract: We illustrate scenarios in which [[0304 Hawking radiation|Hawking radiation]] collected in finite regions of a reservoir provides temporary access to the interior of black holes through transient entanglement "[[0213 Islands|islands]]". Whether these islands appear and the amount of time for which they dominate - sometimes giving way to a thermalization transition - is controlled by the amount of radiation we probe. In the first scenario, two reservoirs are coupled to an eternal black hole. The second scenario involves two holographic quantum gravitating systems at different temperatures interacting through a Rindler-like reservoir, which acts as a heat engine maintaining thermal equilibrium. The latter situation, which has an intricate phase structure, describes two eternal black holes radiating into each other through a shared reservoir.\] ## Summary - *considers* a finite subregion - *demonstrates* a scenario where there is a ==transient island== providing temporary access to the BH interior ## Refs - [[0131 Information paradox]] # Balasubramanian, Kar, Ugajin ## Entanglement between two gravitating universes \[Links: [arXiv](https://arxiv.org/abs/2104.13383), [PDF](https://arxiv.org/pdf/2104.13383.pdf)\] \[Abstract: We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the $n^{\text{th}}$ [[0293 Renyi entropy|Rényi entropy]] includes a wormhole between the $n$ copies of the gravitating universe, leading to a standard "[[0213 Islands|island formula]]" for [[0301 Entanglement entropy|entanglement entropy]] consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the [[0555 Gravitational path integral|path integral]] is now dominated by a novel wormhole with $2n$ boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by $\mathbb{Z}_n$ replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a "swap wormhole", a geometry in which the boundaries of the two universes are glued together by a "swaperator". This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes -- a realization of the [[0220 ER=EPR|ER=EPR]] idea. The new wormhole restores unitarity of quantum information.\] # Ball, Narayanan, Salzer, Strominger ## Perturbatively exact $w_{1+\infty}$ asymptotic symmetry of quantum self-dual gravity \[Links: [arXiv](https://arxiv.org/abs/2111.10392), [PDF](https://arxiv.org/pdf/2111.10392.pdf)\] \[Abstract: The infinite tower of positive-helicity soft gravitons in any minimally coupled, tree-level, asymptotically flat four-dimensional (4D) gravity was recently shown to generate a $w_{1+\infty}$ asymptotic symmetry algebra. It is natural to ask whether this classical algebra acquires quantum corrections at loop level. We explore this in quantum [[0234 Self-dual gravity|self-dual gravity]], whose amplitudes acquire known one-loop exact all-plus helicity quantum corrections. We show using collinear splitting formulae that, remarkably, the $w_{1+\infty}$ algebra persists in quantum self-dual gravity without corrections.\] ## Summary - [[0328 w(1+infinity)|w(1+infinity)]] algebra persists at loop order in [[0234 Self-dual gravity|SDGR]] - reason: the exact collinear splitting function for SDGR is the same as tree-level [[0554 Einstein gravity|Einstein gravity]], essentially because the three-point amplitudes of self-dual gravity are tree-exact ## Results At tree level: $M_{n}^{\text {tree }}\left(1^{h_{1}}, 2^{h_{2}}, 3^{h_{3}}, \ldots, n^{h_{n}}\right) \stackrel{1 \| 2}{\longrightarrow} \sum_{h_{P}=\pm} \operatorname{Split}_{h_{P}}^{\text {tree }}\left(t, 1^{h_{1}}, 2^{h_{2}}\right) \times M_{n-1}^{\text {tree }}\left(P^{-h_{P}}, 3^{h_{3}}, \ldots, n^{h_{n}}\right)$$\begin{aligned} &\text {Split}_{+}^{\text {tree}}\left(t, 1^{+}, 2^{+}\right)=0 \\ &\text {Split}_{-}^{\text {tree}}\left(t, 1^{+}, 2^{+}\right)=\frac{-\kappa}{2 t(1-t)} \frac{[12]}{\langle 12\rangle}=\frac{-\kappa}{2 t(1-t)} \frac{\bar{z}_{12}}{z_{12}} \end{aligned}$At loop level: $M_{n}^{1\text {-loop}}\left(1^{+}, 2^{+}, \ldots, n^{+}\right) \rightarrow \frac{-\kappa}{2 t(1-t)} \frac{[12]}{\langle 12\rangle} M_{n-1}^{1-\text { loop }}\left(P^{+}, \ldots, n^{+}\right)$ Conclusion: exactly the same splitting function even after including loop effects. ## Comments - the regular terms of the [[0114 Celestial OPE|OPE]] can still differ from other theories with [[0328 w(1+infinity)|w symmetry]]: see [[2023#Banerjee, Kulkarni, Paul (Jan)]] # Banerjee, Ghosh, Paul ## (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes \[Links: [arXiv](https://arxiv.org/abs/2108.04262), [PDF](https://arxiv.org/pdf/2108.04262.pdf)\] \[Abstract: In this paper we continue our study of the tree level [[0061 Maximally helicity violating amplitudes|MHV]] graviton scattering amplitudes from the point of view of celestial holography. In [[2020#Banerjee, Ghosh, Paul]] we showed that the [[0114 Celestial OPE|celestial OPE]] of two gravitons in the MHV sector can be written as a linear combination of $\overline{SL(2,\mathbb C)}$ current algebra and supertranslation descendants. In this note we show that the OPE is in fact manifestly invariant under the infinite dimensional [[0032 Virasoro algebra|Virasoro algebra]] as is expected for a 2-D CFT. This is consistent with the conjecture that the holographic dual in 4-D asymptotically flat space time is a 2-D CFT. Since we get only one copy of the Virasoro algebra we can conclude that the holographic dual theory which computes the MHV amplitudes is a chiral CFT with a host of other infinite dimensional global symmetries including $\overline{SL(2,\mathbb C)}$ current algebra, supertranslations and subsubleading soft graviton symmetry. We also discuss some puzzles related to the appearance of the Virasoro symmetry.\] ## Refs - [[0114 Celestial OPE]] ## Summary - investigates the [[0032 Virasoro algebra|Virasoro algebra]] of the MHV graviton amplitudes, which goes beyond the wedge algebra of [[0328 w(1+infinity)|w(1+infinity)]] studied in [[2021#Himwich, Pate, Singh]] ## Use of null states - (A.1) $\left.G_{\Delta_1}^{+}(z, \bar{z}) G_{\Delta_2}^{+}(0)\right|_{\mathcal{O}\left(z^2\right)}$ contains $L_{-1}$ - (A.2) and (A.3) allows $L_{-1}(\cdots)$ to be expressible in terms of other descendants # Banerjee, Ghosh, Samal ## Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes \[Links: [arXiv](https://arxiv.org/abs/2104.02546), [PDF](https://arxiv.org/pdf/2104.02546.pdf)\] \[Abstract: In [[2020#Banerjee, Ghosh, Paul]] it was shown that supertranslation and $\overline{SL(2,\mathbb C)}$ current algebra symmetries, corresponding to leading and subleading [[0009 Soft theorems|soft graviton theorems]], are enough to determine the tree level [[0061 Maximally helicity violating amplitudes|MHV]] graviton scattering amplitudes. In this note we clarify the role of subsubleading soft graviton theorem in this context.\] ## Refs - root [[0010 Celestial holography]] - earlier work [[2020#Banerjee, Ghosh]] ## Summary - *shows* new null states appear as a result of subsubleading soft symmetry - but they contain no additional information - *shows* that OPE is invariant under subsubleading symmetry, as expected # Banerjee, Mandal, Rudra, Saha ## Equivalence of JT Gravity and Near-extremal Black Hole Dynamics in Higher Derivative Theory \[Links: [arXiv](https://arxiv.org/abs/2110.04272), [PDF](https://arxiv.org/pdf/2110.04272.pdf)\] \[Abstract: Two derivative [[0050 JT gravity|Jackiw Teitelboim gravity]] theory captures the near horizon dynamics of higher dimensional near extremal black holes, which is governed by a Schwarzian action at the boundary in the near horizon region. The partition function corresponding to this boundary action correctly gives the statistical entropy of the near extremal black hole. In this paper, we study the thermodynamics of spherically symmetric four dimensional near extremal black holes in presence of arbitrary perturbative four derivative corrections. We find that the near horizon dynamics is again captured by a JT like action with a particular namely square of Ricci scalar higher derivative modification. Effectively the theory is described by a boundary Schwarzian action which gets suitably modified due to the presence of the higher derivative interactions. Near extremal entropy, free energy also get corrected accordingly.\] ## Summary - [[0006 Higher-derivative gravity]] at the near horizon region of near-extremal BH reduces to [[0050 JT gravity]] plus higher derivative corrections # Bao, Chatwin-Davies, Remmen ## Entanglement Wedge Cross Section Inequalities from Replicated Geometries \[Links: [arXiv](https://arxiv.org/abs/2106.02640), [PDF](https://arxiv.org/pdf/2106.02640.pdf)\] \[Abstract: We generalize the constructions for the multipartite reflected entropy in order to construct spacetimes capable of representing multipartite entanglement wedge cross sections of differing party number as [[0007 RT surface|Ryu-Takayanagi surfaces]] on a single replicated geometry. We devise a general algorithm for such constructions for arbitrary party number and demonstrate how such methods can be used to derive novel inequalities constraining mulipartite [[0319 Entanglement wedge cross-section|entanglement wedge cross sections]].\] ## Summary - use [[0007 RT surface|RT]] surfaces in replicated geometries to find relations regarding entanglement wedge cross section (eq.12,15,18) # Bao, Harper, Remmen ## Holevo information of black hole mesostates \[Links: [arXiv](https://arxiv.org/abs/2103.06888), [PDF](https://arxiv.org/pdf/2103.06888.pdf)\] \[Abstract: We define a bulk wormhole geometry interpolating between horizons of differing size and determine characteristics of the HRT surface in these geometries. This construction is dual to black hole mesostates, an intermediate coarse-graining of states between black hole microstates and the full black hole state. We analyze the distinguishability of these objects using the recently derived holographic [[0268 Holevo information|Holevo information]] techniques, demonstrating novel phase transition behavior for such systems.\] ## Summary - *constructs* wormholes interpolating between horizons of different sizes - which is dual to mesostates - *analyses* distinguishability of these objects - *using* [[0268 Holevo information]] techniques - *demonstrating* novel phase transitions ## Prerequisites - mesostates - [[SorkinSudarsky1999]][](https://arxiv.org/abs/gr-qc/9902051) # Belin, Colin-Ellerin ## Bootstrapping Quantum Extremal Surfaces I: The Area operator \[Links: [arXiv](https://arxiv.org/abs/2107.07516), [PDF](https://arxiv.org/pdf/2107.07516.pdf)\] \[Abstract: [[0212 Quantum extremal surface|Quantum extremal surfaces]] are central to the connection between quantum information theory and quantum gravity and they have played a prominent role in the recent progress on the [[0131 Information paradox|information paradox]]. We initiate a program to systematically link these surfaces to the microscopic data of the dual conformal field theory, namely the scaling dimensions of local operators and their [[0030 Operator product expansion|OPE]] coefficients. We consider CFT states obtained by acting on the vacuum with single-trace operators, which are dual to one-particle states of the bulk theory. Focusing on AdS$_3$/CFT$_2$, we compute the CFT [[0301 Entanglement entropy|entanglement entropy]] to second order in the large c expansion where quantum extremality becomes important and match it to the expectation value of the bulk area operator. We show that to this order, the Virasoro identity block contributes solely to the area operator.\] ## Summary - try to link QES to CFT data - scaling dimensions of local operators and OPE coefficients - restriction - acting on vacuum by single trace <-> single particle bulk states - can show in this case that a dictionary between geometric aspects of the quantum extremal surface and the microscopic data of the CFT can be made precise # Belin, de Boer, Liska ## Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes \[Links: [arXiv](https://arxiv.org/abs/2110.14649), [PDF](https://arxiv.org/pdf/2110.14649.pdf)\] \[Abstract: The [[0040 Eigenstate thermalisation hypothesis|Eigenstate Thermalization Hypothesis]] makes a prediction for the statistical distribution of matrix elements of simple operators in energy eigenstates of chaotic quantum systems. As a leading approximation, off-diagonal matrix elements are described by Gaussian random variables but higher-point correlation functions enforce non-Gaussian corrections which are further exponentially suppressed in the entropy. In this paper, we investigate non-Gaussian corrections to the statistical distribution of heavy-heavy-heavy [[0030 Operator product expansion|OPE]] coefficients in [[0008 Quantum chaos|chaotic]] two-dimensional conformal field theories. Using the [[0032 Virasoro algebra|Virasoro]] crossing kernels, we provide asymptotic formulas involving arbitrary numbers of OPE coefficients from modular invariance on genus-$g$ surfaces. We find that the non-Gaussianities are further exponentially suppressed in the entropy, much like the ETH. We discuss the implication of these results for products of CFT partition functions in gravity and [[0278 Euclidean wormholes|Euclidean wormholes]]. Our results suggest that there are new connected wormhole geometries that dominate over the genus-two wormhole.\] # Belin, de Boer, Nayak, Sonner ## Generalized Spectral Form Factors and the Statistics of Heavy Operators \[Links: [arXiv](https://arxiv.org/abs/2111.06373), [PDF](https://arxiv.org/pdf/2111.06373.pdf)\] \[Abstract: The [[0062 Spectral form factor|spectral form factor]] is a powerful probe of quantum chaos that diagnoses the statistics of energy levels, but is blind to other features of a theory such as matrix elements of operators or [[0030 Operator product expansion|OPE]] coefficients in conformal field theories. In this paper, we introduce generalized spectral form factors: new probes of [[0008 Quantum chaos|quantum chaos]] sensitive to the dynamical data of a theory. These quantities can be studied using an effective theory of quantum chaos. We focus our attention on a particular combination of heavy-heavy-heavy OPE coefficients that generalizes the genus-2 partition function of two-dimensional CFTs, for which we define a spectral form factor. We probe heavy-heavy-heavy OPE coefficients and find statistical correlations that agree with the OPE Randomness Hypothesis: these coefficients have a random matrix component in the ergodic regime. The EFT of quantum chaos predicts that the genus-2 spectral form factor displays a ramp and a plateau. Our results suggest that this is a common property of generalized spectral form factors.\] # Belin, Myers, Ruan, Sarosi, Speranza ## Does Complexity Equal Anything? \[Links: [arXiv](https://arxiv.org/abs/2111.02429), [PDF](https://arxiv.org/pdf/2111.02429.pdf)\] \[Abstract: We present a new infinite class of gravitational observables in asymptotically Anti-de Sitter space living on codimension-one slices of the geometry, the most famous of which is the volume of the maximal slice. We show that these observables display universal features for the thermofield-double state: they grow linearly in time at late times and reproduce the switch-back effect in [[0117 Shockwave|shock wave]] geometries. We argue that any member of this class of observables is an equally viable candidate as the extremal volume for a gravitational dual of [[0204 Quantum complexity|complexity]].\] # Berkooz, Sharon, Silberstein, Urbach ## The onset of quantum chaos in disordered CFTs \[Links: [arXiv](https://arxiv.org/abs/2111.06108), [PDF](https://arxiv.org/pdf/2111.06108.pdf)\] \[Abstract: We study the [[0466 Lyapunov exponent|Lyapunov exponent]] $\lambda_L$ in quantum field theories with spacetime-independent disorder interactions. Generically $\lambda_L$ can only be computed at isolated points in parameter space, and little is known about the way in which [[0008 Quantum chaos|chaos]] grows as we deform the theory away from weak coupling. In this paper we describe families of theories in which the disorder coupling is an exactly marginal deformation, allowing us to follow $\lambda_L$ from weak to strong coupling. We find surprising behaviors in some cases, including a discontinuous transition into chaos. We also derive self-consistency equations for the two- and four-point functions for products of $N$ nontrivial CFTs deformed by disorder at leading order in $1/N$.\] ## Refs - follow-up: [[2023#Kalloor, Sharon]] # Bhattacharyya, Dhivakar, Dinda, Kundu, Patra, Roy ## An entropy current and the second law in higher derivative theories of gravity \[Links: [arXiv](https://arxiv.org/abs/2105.06455), [PDF](https://arxiv.org/pdf/2105.06455.pdf)\] \[Abstract: We construct a proof of the [[0005 Black hole second law|second law]] of [[0127 Black hole thermodynamics|thermodynamics]] in an arbitrary diffeomorphism invariant theory of gravity working within the approximation of linearized dynamical fluctuations around stationary black holes. We achieve this by establishing the existence of an entropy current defined on the horizon of the dynamically perturbed black hole in such theories. By construction, this entropy current has non-negative divergence, suggestive of a mechanism for the dynamical black hole to approach a final equilibrium configuration via entropy production as well as the spatial flow of it on the null horizon. This enables us to argue for the second law in its strongest possible form, which has a manifest locality at each space-time point. We explicitly check that the form of the entropy current that we construct in this paper exactly matches with previously reported expressions computed considering specific four derivative theories of [[0006 Higher-derivative gravity|higher curvature gravity]]. Using the same set up we also provide an alternative proof of the physical process version of the first law applicable to arbitrary higher derivative theories of gravity.\] ## Refs - motivated by [[2015#Wall (Essay)]] and its follow-up in [[2019#Bhattacharya, Bhattacharyya, Dinda, Kundu]] - [[0005 Black hole second law]] ## Main result - $\left.\mathcal{E}_{v v}\right|_{r=0}=\partial_{v}\left[\frac{1}{\sqrt{h}} \partial_{v}\left(\sqrt{h} \mathcal{J}^{v}\right)+\frac{1}{\sqrt{h}} \partial_{i}\left(\sqrt{h} \mathcal{J}^{i}\right)\right]+T_{v v}+\mathcal{O}\left(\epsilon^{2}\right)$ - $\mathcal{J}$ is the entropy current: - $\mathcal{J}^v$ is the entropy density - $\mathcal{J}^i$ is the 3-current ## Issues with [[2015#Wall (Essay)]] - it has an issue at the very leading order in amplitude expansion: - the zero boost-weight sector of the “time-time” component of the equations of motion doesn’t acquire the desired form - -> had to invoke first law to save it - it was local in time but not space: has to integrate over a cross-section of the horizon - fixed in [[2019#Bhattacharya, Bhattacharyya, Dinda, Kundu]] ## Coordinate choice - $d s^{2}=2 d v d r-g_{v v}(r, v, x) d v^{2}+2 g_{r i}(r, v, x) d v d x^{i}+h_{i j}(r, v, x) d x^{i} d x^{j}$ - $g_{r v}=1, g_{r r}=0, g_{r i}=0,\left.g_{v v}\right|_{r=0}=0,\left.\partial_{r} g_{v v}\right|_{r=0}=0,\left.g_{v i}\right|_{r=0}=0$ - more detail in sec.2.1 - even more detail in app.A of [[2016#Bhattacharyya, Haehl, Kundu, Loganayagam, Rangamani]] ## Separation of Einstein and matter - $\mathcal{E}_{\mu \nu}=E_{\mu \nu}+T_{\mu \nu}$ - $E_{\mu\nu}$ contains *only* metric and derivatives; everything else belongs to $T_{\mu\nu}$ # Blake, Davison ## Chaos and pole-skipping in rotating black holes \[Links: [arXiv](https://arxiv.org/abs/2111.11093), [PDF](https://arxiv.org/pdf/2111.11093.pdf)\] \[Abstract: \] ## Summary - works out [[0179 Pole skipping]] in Kerr-AdS - establishes that whenever the [[0117 Shockwave]] equation is satisfied there is an extra mode (for the leading pole) ## Spherical v.s. planar - with Kerr-AdS, can no longer use $e^{ikx}$ in the Fourier expansion - but replaced by some angular profile - shown that when angular profile satisfies the shockwave equation, there is pole-skipping ## Comments - the relation between [[0117 Shockwave]] and [[0179 Pole skipping]] is by direct comparison between the equations, thus not necessarily applicable in more general situations (e.g. [[0006 Higher-derivative gravity]]) - if it needs the angular profile to satisfy the shockwave equation, does it mean that there might no be lower-half plane pole-skipping points (which has no relation to shockwave)? -> no. there are lower-half plane points, which need to solve other angular profiles (which would be singular somewhere, but ok: there are analytic continuation) # Blake, Liu ## On systems of maximal quantum chaos \[Links: [arXiv](https://arxiv.org/abs/2102.11294), [PDF](https://arxiv.org/pdf/2102.11294.pdf)\] \[Abstract: A remarkable feature of [[0008 Quantum chaos|chaos]] in many-body quantum systems is the existence of a bound on the [[0466 Lyapunov exponent|quantum Lyapunov exponent]]. An important question is to understand what is special about maximally chaotic systems which saturate this bound. Here we provide further evidence for the 'hydrodynamic' origin of chaos in such systems, and discuss hallmarks of maximally chaotic systems. We first provide evidence that a [[0519 Hydrodynamic effective theory of chaos|hydrodynamic effective field theory of chaos]] we previously proposed should be understood as a theory of maximally chaotic systems. We then emphasize and make explicit a signature of maximal chaos which was only implicit in prior literature, namely the suppression of exponential growth in commutator squares of generic few-body operators. We provide a general argument for this suppression within our chaos effective field theory, and illustrate it using [[0201 Sachdev-Ye-Kitaev model|SYK]] models and [[0001 AdS-CFT|holographic]] systems. We speculate that this suppression indicates that the nature of operator scrambling in maximally chaotic systems is fundamentally different to scrambling in non-maximally chaotic systems. We also discuss a simplest scenario for the existence of a maximally chaotic regime at sufficiently large distances even for non-maximally chaotic systems.\] ## Summary - discusses features of maximal [[0008 Quantum chaos|chaos]] - the [[0519 Hydrodynamic effective theory of chaos|hydrodynamic EFT]] proposed in [[2018#Blake, Lee, Liu]] is maximally chaotic - proposes to use "hydrodynamic" as a defining feature of maximal chaos ## Hallmarks of maximal chaos - commutator square is zero (only [[0482 Out-of-time-order correlator|OTOC]] grows but two of them cancel in the commutator squared) - “hydrodynamic” in nature: stress tensor dominates ## Questions - $[W,V]^2=0$. How about $[W,V]$ itself? Higher powers? ## Refs - [[0519 Hydrodynamic effective theory of chaos]] - extension to non-maximally chaotic systems in [[GaoLiu2023 # Blommaert, Iliesiu, Kruthoff ## Gravity factorised \[Links: [arXiv](https://arxiv.org/abs/2111.07863), [PDF](https://arxiv.org/pdf/2111.07863.pdf)\] \[Abstract: We find models of two-dimensional gravity that resolve the [[0249 Factorisation problem|factorization puzzle]] and have a discrete spectrum, whilst retaining a semiclassical description. A novelty of these models is that they contain non-trivially correlated spacetime branes or, equivalently, nonlocal interactions in their action. Such nonlocal correlations are motivated in the low-energy gravity theory by integrating out UV degrees of freedom. Demanding factorization fixes almost all brane correlators, and the exact geometric expansion of the partition function collapses to only two terms: the black hole saddle and a subleading ''half-wormhole'' geometry, whose sum yields the desired discrete spectrum. By mapping the insertion of correlated branes to a certain double-trace deformation in the dual matrix integral, we show that factorization and discreteness also persist non-perturbatively. While in our model all wormholes completely cancel, they are still computationally relevant: self-averaging quantities, like the Page curve, computed in the original theory with wormholes, accurately approximate observables in our theory, which accounts for UV corrections. Our models emphasize the importance of correlations between different disconnected components of spacetime, providing a possible resolution to the factorization puzzle in any number of dimensions.\] ## Summary - finds a particular model (a ==deformation== to [[0050 JT gravity]]) that gives [[0249 Factorisation problem|factorisation]] - the deformed theory is dual to a single member of the ensemble ## The deformation - inserts two branes ## The cancellation - all connected components cancel - a lower order term in the deformation but with higher topology (in each section) might cancel with a higher order contribution (more branes) with fewer genus in each section ## Extensions - [[Idea202111171550 Multi-local deformation]] # Bobrick, Martire ## Introducing Physical Warp Drives \[Links: [arXiv](https://arxiv.org/abs/2102.06824), [PDF](https://arxiv.org/pdf/2102.06824.pdf)\] \[Abstract: The Alcubierre [[0263 Warp drives|warp drive]] is an exotic solution in general relativity. It allows for superluminal travel at the cost of enormous amounts of matter with negative mass density. For this reason, the Alcubierre warp drive has been widely considered unphysical. In this study, we develop a model of a general warp drive spacetime in classical relativity that encloses all existing warp drive definitions and allows for new metrics without the most serious issues present in the Alcubierre solution. We present the first general model for subluminal positive-energy, spherically symmetric warp drives; construct superluminal warp-drive solutions which satisfy quantum inequalities; provide optimizations for the Alcubierre metric that decrease the negative energy requirements by two orders of magnitude; and introduce a warp drive spacetime in which space capacity and the rate of time can be chosen in a controlled manner. Conceptually, we demonstrate that any warp drive, including the Alcubierre drive, is a shell of regular or exotic material moving inertially with a certain velocity. Therefore, any warp drive requires propulsion. We show that a class of subluminal, spherically symmetric warp drive spacetimes, at least in principle, can be constructed based on the physical principles known to humanity today.\] # Brandhuber, Brown, Gowdy, Spence, Travaglini ## Celestial superamplitudes \[Links: [arXiv](https://arxiv.org/abs/2105.10263), [PDF](https://arxiv.org/pdf/2105.10263.pdf)\] \[Abstract: We study [[0010 Celestial holography|celestial]] amplitudes in (super) Yang-Mills theory using a parameterisation of the spinor helicity variables where their overall phase is not fixed by the little group action. In this approach the spin constraint $h-\bar{h}=J$ for celestial conformal primaries emerges naturally from a new [[0079 Mellin transform|Mellin transform]], and the action of conformal transformations on celestial amplitudes is derived. Applying this approach to $\mathcal{N}\!=\!4$ super Yang-Mills, we show how the appropriate definition of on-shell superspace coordinates leads naturally to a formulation of chiral celestial superamplitudes and a representation of the generators of the four-dimensional superconformal algebra on the celestial sphere, which by construction annihilate all tree-level celestial superamplitudes.\] ## Summary - [[0289 Celestial superamplitudes]] - *introduces* a new (chiral) [[0079 Mellin transform|Mellin transform]] ## Signature - done in Minkowski: little group is compact - in split signature, get divergence ## Little group scaling - [[0373 Spinor helicity formalism|spinor helicity formalism]] does not implement it nicely (without being *ad hoc*), but little group scaling can be useful to bootstrap amplitudes -> we want little group - solution: add a complex prefactor to spinors # Bu ## Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet \[Links: [arXiv](https://arxiv.org/abs/2111.15584), [PDF](https://arxiv.org/pdf/2111.15584.pdf)\] \[Abstract: Using the [[0348 Ambitwistor strings|ambitwistor string]], we complete the list of [[0114 Celestial OPE|celestial OPE]] coefficients for supersymmetric theories. This uses the ambitwistor string worldsheet CFT to dynamically generate the OPE coefficients for maximally supersymmetric gauge theory, gravity and Einstein-Yang-Mills theories, including all helicity and orientation configurations. This extends previous purely bosonic results to include supersymmetry and provides explicit formulas which are, to the best of our knowledge, not in the literature. We also examine how the supersymmetric infinite dimensional soft algebras behave compared to the purely bosonic cases.\] # Campiglia, Laddha ## BMS Algebra, Double Soft Theorems, and All That \[Links: [arXiv](https://arxiv.org/abs/2106.14717), [PDF](https://arxiv.org/pdf/2106.14717.pdf)\] \[Abstract: The Lie algebra generated by supertranslation and superrotation vector fields at null infinity, known as the extended [[0064 BMS group|BMS]] (eBMS) algebra is expected to be a symmetry algebra of the quantum gravity $S$ matrix. However, the algebra of commutators of the quantized eBMS charges has been a thorny issue in the literature. On the one hand, recent developments in [[0010 Celestial holography|celestial holography]] point towards a symmetry algebra which is a closed Lie algebra with no central extension or anomaly, and on the other hand, work of Distler, Flauger and Horn has shown that when these charges are quantized at null infinity, the commutator of a supertranslation and a superrotation charge does not close into a supertranslation but gets deformed by a 2 cocycle term, which is consistent with the original proposal of Barnich and Troessaert. In this paper, we revisit this issue in light of recent developments in the classical understanding of superrotation charges. We show that, for extended BMS symmetries, a phase space at null infinity is an extension of hitherto considered phase spaces which also includes a mode associated to the spin memory and its conjugate partner. We also show that for holomorphic vector fields on the celestial plane, quantization of the eBMS charges in the new phase space leads to an algebra which closes without a 2 cocycle. The degenerate vacua are labelled by the soft news and a Schwarzian mode which corresponds to deformations of the celestial metric by superrotations. The closed eBMS quantum algebra may also lead to a convergence between two manifestations of asymptotic symmetries, one via asymptotic quantization at null infinity and the other through celestial holography.\] ## Refs - [[0060 Asymptotic symmetry]] - [[0063 Symmetry of CCFT]] # Campiglia, Nagy ## A double copy for asymptotic symmetries in the self-dual sector \[Links: [arXiv](https://arxiv.org/abs/2102.01680), [PDF](https://arxiv.org/pdf/2102.01680.pdf)\] \[Abstract: \] ## Refs - root [[0010 Celestial holography]] ## Summary - *gives* a double copy construction for symmetries in the ==self-dual sector== of YM and gravity in the ==light cone== formulation - *finds* an infinite set of double copy constructable symmetries ## Double copy of the symmetries Given in (5.57) : $\Phi \rightarrow \phi, \quad-i[,] \rightarrow \frac{1}{2}\{,\}, \quad \Lambda_{n} \rightarrow \lambda_{n}, \quad S \rightarrow \mathfrak{r} S, \quad \mathfrak{r}=\frac{\operatorname{deg}\left(\Lambda_{n}\right)+1}{\operatorname{deg}\left(\lambda_{n}\right)+1}$. This summarises the double copy of the symmetries algebras. It would be interesting to see this a the level of [[0009 Soft theorems]]. # Cano, Murcia (Apr) ## Duality-invariant extensions of Einstein-Maxwell theory \[Links: [arXiv](https://arxiv.org/abs/2104.07674), [PDF](https://arxiv.org/pdf/2104.07674.pdf)\] \[Abstract: \] ## Summary - *shows* that to six derivatives, the most general duality-preserving theory can be mapped to Maxwell theory minimally coupled to a higher-derivative gravity containing only four non-topological higher-order operators - *conjectures* this is true to all orders ## Refs - [[0006 Higher-derivative gravity]] - later paper on restricted class of solutions - [[2021#Cano, Murcia (May)]] # Cano, Murcia (May) ## Exact electromagnetic duality with nonminimal couplings \[Links: [arXiv](https://arxiv.org/abs/2105.09868), [PDF](https://arxiv.org/pdf/2105.09868.pdf)\] \[Abstract: \] ## Refs - earlier paper on perturbative expansions [[2021#Cano, Murcia (Apr)]] ## Summary - when restricted to spherically symmetric, static spacetimes, the action for EM with non-minimal coupling resums to a finite term # Cao, Pollack, Wang ## Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations \[Links: [arXiv](https://arxiv.org/abs/2103.08631), [PDF](https://arxiv.org/pdf/2103.08631.pdf)\] \[Abstract: We consider a class of holographic [[0054 Tensor network|tensor networks]] that are efficiently contractible variational ansatze, manifestly (approximate) [[0146 Quantum error correction|QEC]] codes, and can support power-law correlation functions. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility for an efficient variational ansatz, we provide guidelines for constructing networks consisting of multiple types of tensors that can support power-law correlation. We also provide an explicit construction of one such network, which approximates the holographic HaPPY pentagon code in the limit where variational parameters are taken to be small.\] ## Summary - gives a no-go theorem: with a single type of tensor, it cannot both be locally contractible and sustain power-law correlation functions (to go around it: can e.g. having multiple types of tensors) # Caron-Huot, Li ## Helicity basis for three-dimensional conformal field theory \[Links: [arXiv](https://arxiv.org/abs/2102.08160), [PDF](https://arxiv.org/pdf/2102.08160)\] \[Abstract: Three-point correlators of spinning operators admit multiple tensor structures compatible with conformal symmetry. For conserved currents in three dimensions, we point out that helicity commutes with conformal transformations and we use this to construct three-point structures which diagonalize helicity. In this helicity basis, OPE data is found to be diagonal for mean-field correlators of conserved currents and stress tensor. Furthermore, we use Lorentzian inversion formula to obtain anomalous dimensions for conserved currents at bulk tree-level order in holographic theories, which we compare with corresponding flat-space gluon scattering amplitudes.\] # Ceplak, Vegh ## Pole-skipping and Rarita-Schwinger fields \[Links: [arXiv](https://arxiv.org/abs/2101.01490), [PDF](https://arxiv.org/pdf/2101.01490.pdf)\] \[Abstract: In this note we analyse the equations of motion of a minimally coupled Rarita-Schwinger field near the horizon of an anti-de Sitter-Schwarzschild geometry. We find that at special complex values of the frequency and momentum there exist two independent regular solutions that are ingoing at the horizon. These special points in Fourier space are associated with the '[[0179 Pole skipping|pole-skipping]]' phenomenon in thermal two-point functions of operators that are holographically dual to the bulk fields. We find that the leading pole-skipping point is located at a positive imaginary frequency with the distance from the origin being equal to half of the [[0466 Lyapunov exponent|Lyapunov exponent]] for maximally [[0008 Quantum chaos|chaotic]] theories.\] ## Summary - an example of [[0179 Pole skipping|pole skipping]] for a spin-3/2 field ## Comments - fig 2 shows pole skipping at $\omega=i\pi T$ and $\omega=-3i\pi T$, but mentioned in the appendix that there are also (three) pole-skipping points at $\omega=-i\pi T$ # Chandrasekaran, Flanagan, Shehzad, Speranza ## A general framework for gravitational charges and holographic renormalisation \[Links: [arXiv](https://arxiv.org/abs/2111.11974), [PDF](https://arxiv.org/pdf/2111.11974.pdf)\] \[Abstract: \] ## Summary - general method for [[0060 Asymptotic symmetry]] and [[0209 Holographic renormalisation]] - requires variational principle for the subregion - including corners - shows that [[0360 Poisson bracket]] of charges on subregion phase space produces [[0271 Barnich-Troessaert bracket]] for open subsystems - shows that [[0209 Holographic renormalisation]] can always be done once finite action is found # Chen, Maldacena, Witten ## On the black hole/string transition \[Links: [arXiv](https://arxiv.org/abs/2109.08563), [PDF](https://arxiv.org/pdf/2109.08563.pdf)\] \[Abstract: \] ## Refs - review [[Susskind202110]][](https://arxiv.org/abs/2110.12617) - [Talk by Juan](https://www.youtube.com/watch?v=WK LWR_YSIJk&t=1s&ab_channel=InstituteforAdvancedStudy) ## Summary - connection between BHs and [[0323 Horowitz-Polchinski solution]] - connection depends on the type of string - heterotic: continuous connection - type IIB: an obstruction to continuous connection <!-- ## Comments - Gary - two papers with Joe; 2nd paper says if you start with string and increase the coupling, you start to feel the gravity; when coupling reaches a certain value, the excited string shrinks to string state; to study that, introduce a effective field theory; study a canonical ensemble near Haganorm transition (a max temperature); the field theory is to describe the winding mode - this paper starts with something Gary and Joe overlooked. The solution has non-zero entropy which is unusual (see [[0316 Thermodynamics in holography toolkit]])! but this model has $\beta$ in the Lagrangian explicitly --> # Ciambelli, Leigh, Pai ## Embeddings and Integrable Charges for Extended Corner Symmetry \[Links: [arXiv](https://arxiv.org/abs/2111.13181), [PDF](https://arxiv.org/pdf/2111.13181.pdf)\] \[Abstract: \] ## Summary - *introduces* a new notion of [[0044 Extended phase space]] (which will be called [[0393 CLP extended phase space]]) associated with the embeddings - the Noether charges are then integrable but not necessarily conserved - the charges give a presentations of corner symmetry via the [[0360 Poisson bracket]], without central extension # Cohen ## New infinities of soft charges \[Links: [arXiv](https://arxiv.org/abs/2112.09776), [PDF](https://arxiv.org/pdf/2112.09776.pdf)\] \[Abstract: \] # Colin-Ellerin, Dong, Marolf, Rangamani, Wang ## Real-time gravitational replicas: Low dimensional examples \[Links: [arXiv](https://arxiv.org/abs/2105.07002), [PDF](https://arxiv.org/pdf/2105.07002.pdf)\] \[Abstract: We continue the study of real-time replica wormholes initiated in [[2020#Colin-Ellerin, Dong, Marolf, Rangamani, Wang]]. Previously, we had discussed the general principles and had outlined a variational principle for obtaining stationary points of the real-time gravitational path integral. In the current work we present several explicit examples in low-dimensional gravitational theories where the dynamics is amenable to analytic computation. We demonstrate the computation of Rényi entropies in the cases of [[0050 JT gravity|JT gravity]] and for holographic two-dimensional CFTs (using the dual gravitational dynamics). In particular, we explain how to obtain the large central charge result for subregions comprising of disjoint intervals directly from the real-time path integral.\] ## Refs - [[0293 Renyi entropy]] - earlier work [[2020#Colin-Ellerin, Dong, Marolf, Rangamani, Wang]] ## Notations - $t_{\rm E}\to it$ - coordinates for the original boundary geometry ${v}=x+i t_{\mathrm{E}}$, $\bar{v}=x-i t_{\mathrm{E}}$ - Lorentzian lightcone coordinates $\tilde{x}^{ \pm}=x\pm t$ # Collier, Maloney ## Wormholes and Spectral Statistics in the Narain Ensemble \[Links: [arXiv](https://arxiv.org/abs/2106.12760), [PDF](https://arxiv.org/pdf/2106.12760.pdf)\] \[Abstract: We study the spectral statistics of primary operators in the recently formulated [[0154 Ensemble averaging|ensemble average]] of Narain's family of free boson conformal field theories, which provides an explicit (though exotic) example of an averaged holographic duality. In particular we study moments of the partition function by explicit computation of higher-degree Eisenstein series. This describes the analog of wormhole contributions coming from a sum of over geometries in the dual theory of "$U(1)$ gravity" in AdS$_3$. We give an exact formula for the two-point correlation function of the density of primary states. We compute the [[0062 Spectral form factor|spectral form factor]] and show that the wormhole sum reproduces precisely the late time plateau behaviour related to the discreteness of the spectrum. The spectral form factor does not exhibit a linear ramp.\] # Collier, Mazac, Wang ## Bootstrapping Boundaries and Branes \[Links: [arXiv](https://arxiv.org/abs/2112.00750), [PDF](https://arxiv.org/pdf/2112.00750)\] \[Abstract: The study of conformal boundary conditions for two-dimensional conformal field theories (CFTs) has a long history, ranging from the description of impurities in one-dimensional quantum chains to the formulation of D-branes in string theory. Nevertheless, the landscape of conformal boundaries is largely unknown, including in [[0096 Rational CFT|rational CFTs]], where the local operator data is completely determined. We initiate a systematic [[0036 Conformal bootstrap|bootstrap]] study of conformal boundaries in 2d CFTs by investigating the bootstrap equation that arises from the open-closed consistency condition of the annulus partition function with identical boundaries. We find that this deceivingly simple bootstrap equation, when combined with unitarity, leads to surprisingly strong constraints on admissible boundary states. In particular, we derive universal bounds on the tension (boundary entropy) of stable boundary conditions, which provide a rigorous diagnostic for potential D-brane decays. We also find unique solutions to the bootstrap problem of stable branes in a number of rational CFTs. Along the way, we observe a curious connection between the annulus bootstrap and the sphere packing problem, which is a natural extension of previous work on the modular bootstrap. We also derive bounds on the boundary entropy at large [[0033 Central charge|central charge]]. These potentially have implications for end-of-the-world branes in pure gravity on AdS$_3$.\] # Cotler, Jensen ## Wormholes and BH microstates in AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/2104.00601), [PDF](https://arxiv.org/pdf/2104.00601.pdf)\] \[Abstract: It has long been known that the coarse-grained approximation to the black hole density of states can be computed using classical Euclidean gravity. In this work we argue for another entry in the dictionary between Euclidean gravity and black hole physics, namely that Euclidean wormholes describe a coarse-grained approximation to the energy level statistics of black hole microstates. To do so we use the method of [[0463 Constrained instantons|constrained instantons]] to obtain an integral representation of wormhole amplitudes in Einstein gravity and in full-fledged [[0001 AdS-CFT|AdS/CFT]]. These amplitudes are non-perturbative corrections to the two-boundary problem in AdS quantum gravity. The full amplitude is likely UV sensitive, dominated by small wormholes, but we show it admits an integral transformation with a macroscopic, weakly curved saddle-point approximation. The saddle is the "double cone" geometry of Saad, Shenker, and Stanford, with fixed moduli. In the boundary description this saddle appears to dominate a smeared version of the connected two-point function of the black hole density of states, and suggests level repulsion in the microstate spectrum. Using these methods we further study Euclidean wormholes in pure Einstein gravity and in IIB supergravity on Euclidean $\mathrm{AdS}_5\times\mathbb{S}^5$. We address the perturbative stability of these backgrounds and study brane nucleation instabilities in 10d supergravity. In particular, brane nucleation instabilities of the Euclidean wormholes are lifted by the analytic continuation required to obtain the Lorentzian spectral form factor from gravity. Our results indicate a factorization paradox in AdS/CFT.\] ## Refs - jointly submitted: [[2021#Mahajan, Marolf, Santos]] ## Summary - *argues* that Euclidean wormholes describe a coarse-grained approximation to the energy level statistics of black hole microstates # Crawley, Guevara, Miller, Strominger ## Black Holes in Klein Space \[Links: [arXiv](https://arxiv.org/abs/2112.03954), [PDF](https://arxiv.org/pdf/2112.03954.pdf)\] \[Abstract: The analytic continuation of the general signature (1,3) Lorentzian Kerr-Taub-NUT black holes to signature (2,2) Kleinian black holes is studied. Their global structure is characterized by a toric Penrose diagram resembling their Lorentzian counterparts. Kleinian black holes are found to be self-dual when their mass and NUT charge are equal for any value of the Kerr rotation parameter $a$. Remarkably, it is shown that the rotation a can be eliminated by a large diffeomorphism; this result also holds in Euclidean signature. The continuation from Lorentzian to Kleinian signature is naturally induced by the analytic continuation of the S-matrix. Indeed, we show that the geometry of linearized black holes, including Kerr-Taub-NUT, is captured by (2,2) three-point scattering amplitudes of a graviton and a massive spinning particle. This stands in sharp contrast to their Lorentzian counterparts for which the latter vanishes kinematically, and enables a direct link to the S-matrix.\] # Dias, Horowitz, Santos ## Extremal black holes that are not extremal: maximal warm holes \[Links: [arXiv](https://arxiv.org/abs/2109.14633), [PDF](https://arxiv.org/pdf/2109.14633.pdf)\] \[Abstract: We study a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with nonzero Hawking temperature. The implications for Hawking evaporation are discussed.\] ## Summary - perfectly smooth solutions but nevertheless they exceed the *usual* maximal charge allowed given the mass - extremal here defined to be max charge given some mass # Dong, Hartman, Jiang ## Averaging over moduli in deformed WZW models \[Links: [arXiv](https://arxiv.org/abs/2105.12594), [PDF](https://arxiv.org/pdf/2105.12594.pdf)\] \[Abstract: [[0601 Weiss-Zumino-Witten models|WZW models]] live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have $N$ abelian conserved currents and central charge $c > N$. We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the [[0154 Ensemble averaging|ensemble-averaged]] theory has a holographic dual, generalizing recent results on [[0611 Narain CFT|Narain CFTs]]. The bulk theory, at the perturbative level, is identified as $U(1)^{2N}$ [[0089 Chern-Simons theory|Chern-Simons theory]] coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie algebra.\] ## Summary They computed an ensemble average over a class of (deformed) WZW models and found that the partition function looks like a sum over $\Gamma_{\infty} \backslash P S L(2, \mathbb{Z})$ images of something. This is then interpreted as a sum over topology in the bulk, where the bulk contains some topological matter fields. # Dong, Qi, Walter ## Holographic entanglement negativity and replica symmetry breaking \[Links: [arXiv](https://arxiv.org/abs/2101.11029), [PDF](https://arxiv.org/pdf/2101.11029.pdf)\] \[Abstract: \] ## Related - [[0210 Entanglement negativity]] - talks about issues with replica symmetry breaking - also [[0054 Tensor network]] # Donnay, Ruzziconi ## BMS Flux Algebra in Celestial Holography \[Links: [arXiv](https://arxiv.org/abs/2108.11969), [PDF](https://arxiv.org/pdf/2108.11969.pdf)\] \[Abstract: \] ## Summary - *gives* a prescription for separating the hard and soft parts of the flux, which differs from separation via the soft theorem approach by just vacuum contributions # Eberhardt ## Sum over geometries in string theory \[Links: [arXiv](https://arxiv.org/abs/2102.12355), [PDF](https://arxiv.org/pdf/2102.12355.pdf)\] \[Abstract: \] ## Refs - [[0249 Factorisation problem]] # Ecker, van der Schee, Mateos, Casalderrey-Solana ## Holographic Evolution with Dynamical Boundary Gravity \[Links: [arXiv](https://arxiv.org/abs/2109.10355), [PDF](https://arxiv.org/pdf/2109.10355)\] \[Abstract: Holography has provided valuable insights into the time evolution of strongly coupled gauge theories in a fixed spacetime. However, this framework is insufficient if this spacetime is dynamical. We present a scheme to evolve a four-dimensional, strongly interacting gauge theory coupled to four-dimensional dynamical gravity in the semiclassical regime. As in previous work, we use holography to evolve the quantum gauge theory stress tensor, whereas the four-dimensional metric evolves according to Einstein's equations coupled to the expectation value of the stress tensor. The novelty of our approach is that both the boundary and the bulk spacetimes are constructed dynamically, one time step at a time. We focus on Friedmann-Lemaître-Robertson-Walker geometries and evolve far-from-equilibrium initial states that lead to asymptotically expanding, flat or collapsing Universes\] # Emparan, Tomasevic ## Holography of time machines \[Links: [arXiv](https://arxiv.org/abs/2107.14200), [PDF](https://arxiv.org/pdf/2107.14200.pdf)\] \[Abstract: \] ## Summary - holography upholds the chronology protection ## Content - boundary has well-behaved region and region with CTC - the bulk corresponding to the well-behaved region is geodesically complete by itself - from the bulk point of view it is obvious that one cannot cross chronology horizon # Engelhardt, Penington, Shahbazi-Moghaddam (Feb) ## A World without Pythons would be so Simple \[Links: [arXiv](https://arxiv.org/abs/2102.07774), [PDF](https://arxiv.org/pdf/2102.07774.pdf)\] \[Abstract: \] ## Refs - [[0196 Python's lunch]] - [[Talk202011201102 Geoff Penington Life without pythons would be so simple]] - later paper [[2021#Engelhardt, Penington, Shahbazi-Moghaddam (May)]] ## Summary - converse of [[0196 Python's lunch]] proposal - outside the outermost QES: simple to construct # Engelhardt, Penington, Shahbazi-Moghaddam (May) ## Finding pythons in unexpected places \[Links: [arXiv](https://arxiv.org/abs/2105.09316), [PDF](https://arxiv.org/pdf/2105.09316.pdf)\] \[Abstract: \] ## Refs - [[0196 Python's lunch]] - earlier paper [[2021#Engelhardt, Penington, Shahbazi-Moghaddam (Feb)]] ## Summary - highly non-classical QES - reconstruction of interior outgoing modes is always exponentially complex - supports ==strong Python's lunch proposal== - non-minimal QES are the only sources of exponential complexity ## Strong Python's lunch proposal - nonminimal quantum extremal surfaces are the *exclusive* source of exponential complexity in the holographic dictionary - apparent violation: single sided BH formed from collapse -> no [[0212 Quantum extremal surface|QES]] by [[0082 Generalised second law]] - see [[2014#Engelhardt, Wall]] - resolution: we cannot talk about the complexity of reconstructing interior outgoing modes until we introduce a code subspace where those modes can be excited # Fallows, Ross ## Islands and mixed states in closed universes \[Links: [arXiv](https://arxiv.org/abs/2103.14364), [PDF](https://arxiv.org/pdf/2103.14364.pdf)\] \[Abstract: \] # Fan, Fotopoulos, Stieberger, Taylor, Zhu (Mar) ## Conformal Blocks from Celestial Gluon Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2103.04420), [PDF](https://arxiv.org/pdf/2103.04420.pdf)\] \[Abstract: \] ## Refs - uses expression in [[2012#Osborn]] - part II: [[2021#Fan, Fotopoulos, Stieberger, Taylor, Zhu (Aug)]] - singled valued operators ## Comments - although the 4-point involves a shadowed state, there is still OPE coming from a pair of primary gluons, which can be used to compare with results of [[0114 Celestial OPE]] from collinear expansion ## Two approaches identifying primary CCFT primary fields - $z>0,0<z<1,z<0$ describe processes with $s>0,t>0,u>0$ respectively 1. from 2d CFT point of view it is natural to assemble them into a single correlator 2. but this paper treats them separately, as correlators of distinct 2d incoming and outgoing primary fields (consistent with [[2019#Pate, Raclariu, Strominger, Yuan]]) ## Future - loops - how does subleading soft symmetries manifest in the expansion # Fan, Fotopoulos, Stieberger, Taylor, Zhu (Aug) ## Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators \[Links: [arXiv](https://arxiv.org/abs/2108.10337), [PDF](https://arxiv.org/pdf/2108.10337.pdf)\] \[Abstract: \] ## Summary - ![[FanFotopoulosStiebergerTaylorZhu202108_flowchart.png]] ## Comments - by Taylor at [[Rsc0034 Corfu Celestial workshops]] about the single-valued-ness - MHV and its conjugate are related by momentum conservation - here there is no momentum conservation - inverse Mellin transforming back may not have good physical meaning # Folkestad, Hernandez-Cuenca ## Conformal Rigidity from Focusing \[Links: [arXiv](https://arxiv.org/abs/2106.09037), [PDF](https://arxiv.org/pdf/2106.09037)\] \[Abstract: The null curvature condition (NCC) is the requirement that the Ricci curvature of a Lorentzian manifold be nonnegative along null directions, which ensures the [[0408 Raychaudhuri equation|focusing]] of null geodesic congruences. In this note, we show that the NCC together with the causal structure significantly constrains the metric. In particular, we prove that any conformal rescaling of a vacuum spacetime introduces either geodesic incompleteness or negative null curvature, provided the conformal factor is non-constant on at least one complete null geodesic. In the context of bulk reconstruction in [[0001 AdS-CFT|AdS/CFT]], our results combined with the [[0027 Bulk reconstruction using lightcone cuts|technique of light-cone cuts]] can be used in vacuum spacetimes to reconstruct the full metric in regions probed by complete null geodesics reaching the boundary. For non-vacuum spacetimes, our results constrain the conformal factor, giving an approximate reconstruction of the metric.\] # Freidel, Pranzetti, Raclariu (Nov) ## Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations \[Links: [arXiv](https://arxiv.org/abs/2111.15607), [PDF](https://arxiv.org/pdf/2111.15607.pdf)\] \[Abstract: \] ## Refs - later [[2021#Freidel, Pranzetti, Raclariu (Dec)]] # Freidel, Pranzetti, Raclariu (Dec) ## Higher spin dynamics in gravity and $w_{1 + \infty}$ celestial symmetries \[Links: [arXiv](https://arxiv.org/abs/2112.15573), [PDF](https://arxiv.org/pdf/2112.15573.pdf)\] \[Abstract: In this paper we extract from a large-$r$ expansion of the vacuum Einstein's equations a dynamical system governing the time evolution of an infinity of higher-spin charges. Upon integration, we evaluate the canonical action of these charges on the gravity phase space. The truncation of this action to quadratic order and the associated charge conservation laws yield an infinite tower of [[0009 Soft theorems|soft theorems]]. We show that the canonical action of the higher spin charges on gravitons in a [[0148 Conformal basis|conformal primary basis]], as well as conformally soft gravitons reproduces the higher spin celestial symmetries derived from the [[0030 Operator product expansion|operator product expansion]]. Finally, we give direct evidence that these charges form a canonical representation of a $w_{1+\infty}$ loop algebra on the gravitational phase space.\] # Gao, Jafferis, Kolchmeyer ## An effective matrix model for dynamical end of the world branes in Jackiw-Teitelboim gravity \[Links: [arXiv](https://arxiv.org/abs/2104.01184), [PDF](https://arxiv.org/pdf/2104.01184.pdf)\] \[Abstract: We study [[0050 JT gravity|Jackiw-Teitelboim gravity]] with dynamical end of the world branes in asymptotically nearly AdS$_2$ spacetimes. We quantize this theory in Lorentz signature, and compute the Euclidean path integral summing over topologies including dynamical branes. The latter will be seen to exactly match with a modification of the SSS matrix model. The resolution of UV divergences in the gravitational instantons involving the branes will lead us to understand the matrix model interpretation of the Wilsonian effective theory perspective on the gravitational theory. We complete this modified SSS matrix model nonperturbatively by extending the integration contour of eigenvalues into the complex plane. Furthermore, we give a new interpretation of other phases in such matrix models. We derive an effective $W(\Phi)$ dilaton gravity, which exhibits similar physics semiclassically. In the limit of a large number of flavors of branes, the effective extremal entropy $S_{0,\text{eff}}$ has the form of counting the states of these branes.\] # Garousi (Nov) ## Higher-derivative field redefinitions in the presence of boundary \[Links: [arXiv](https://arxiv.org/abs/2111.10987), [PDF](https://arxiv.org/pdf/2111.10987.pdf)\] \[Abstract: \] ## Summary - the proposal that the [[0329 String effective action]] at $\alpha^{\prime n}$ should have BC fixing up to $n$ orders in derivative constrains [[0355 Field redefinitions]] and [[0356 T-duality]] # Geng, Karch, Perez-Pardavila, Raju, Randall, Riojas, Shashi ## Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background \[Links: [arXiv](https://arxiv.org/abs/2112.09132), [PDF](https://arxiv.org/pdf/2112.09132.pdf)\] \[Abstract: We compute [[0145 Generalised area|holographic entanglement entropy]] for subregions of a [[0181 AdS-BCFT|BCFT]] thermal state living on a nongravitating black hole background. The system we consider is [[0544 Double holography|doubly holographic]] and dual to an eternal black string with an embedded Karch-Randall brane that is parameterized by its angle. Entanglement [[0213 Islands|islands]] are conventionally expected to emerge at late times to preserve unitarity at finite temperature, but recent calculations at zero temperature have shown such islands do not exist when the brane lies below a critical angle. When working at finite temperature in the context of a black string, we find that islands exist even when the brane lies below the critical angle. We note that although these islands exist when they are needed to preserve unitarity, they are restricted to a finite connected region on the brane which we call the atoll. Depending on two parameters -- the size of the subregion and the brane angle -- the entanglement entropy either remains constant in time or follows a Page curve. We discuss this rich phase structure in the context of [[0026 Bulk reconstruction|bulk reconstruction]].\] # Gesteau, Kang ## Nonperturbative gravity corrections to bulk reconstruction \[Links: [arXiv](https://arxiv.org/abs/2112.12789), [PDF](https://arxiv.org/pdf/2112.12789.pdf)\] \[Abstract: \] We introduce a new algebraic framework for understanding nonperturbative gravitational aspects of [[0026 Bulk reconstruction|bulk reconstruction]] with a finite or infinite-dimensional boundary Hilbert space. We use relative entropy equivalence between bulk and boundary with an inclusion of nonperturbative gravitational errors, which give rise to approximate recovery. We utilize the privacy/correctability correspondence to prove that the reconstruction wedge, the intersection of all entanglement wedges in pure and mixed states, manifestly satisfies bulk reconstruction. We explicitly demonstrate that local operators in the reconstruction wedge of a given boundary region can be recovered in a state-independent way for arbitrarily large code subspaces, up to nonperturbative errors in $G_N$. We further discuss state-dependent recovery beyond the reconstruction wedge and the use of the twirled [[0413 Petz map|Petz map]] as a universal recovery channel. We discuss our setup in the context of quantum [[0213 Islands|islands]] and the [[0131 Information paradox|information paradox]]. # Goto, Nozaki, Tamaoka ## Subregion Spectrum Form Factor via Pseudo Entropy \[Links: [arXiv](https://arxiv.org/abs/2109.00372), [PDF](https://arxiv.org/pdf/2109.00372)\] \[Abstract: We introduce a subsystem generalization of the [[0062 Spectral form factor|spectral form factor]] via [[0052 Pseudo-entropy|pseudo entropy]], the von-Neumann entropy for the reduced transition matrix. We consider a transition matrix between the thermofield double state and its time-evolved state in two-dimensional conformal field theories, and study the time-dependence of the pseudo entropy for a single interval. We show that the real part of the pseudo entropy behaves similarly to the spectral form factor; it starts from the thermal entropy, initially drops to the minimum, then it starts increasing, and finally approaches the vacuum entanglement entropy. We also study the theory-dependence of its behavior by considering theories on a compact space.\] # Guevara (Aug) ## Celestial OPE blocks \[Links: [arXiv](https://arxiv.org/abs/2108.12706), [PDF](https://arxiv.org/pdf/2108.12706.pdf)\] \[Abstract: Starting from the defining two-point and three-point functions of Celestial CFTs, Euclidean integral blocks are constructed for the OPE of scalar primaries. In their integral form they can alternatively be fixed using Poincare symmetry acting on both massless and massive states. Subsequently, an analytic continuation is done to define the Lorentzian version of the correlation functions and the OPE blocks as valued on the $(1, 1)$ cylinder, the universal cover of the recently studied celestial torus. The continuation is essentially the same that is used in the derivation of the [[0398 KLT relations|KLT relations]] for string amplitudes. It is shown explicitly that the continued OPE blocks encode the contributions from massive primary states as well as their shadow and [[0412 Light transform|lighttransformed]] partners of continuous spin. The corresponding pairings are also studied, thus the construction provides the fundamental relation between correlation functions and OPE coefficients in the scalar CCFT.\] ## Refs - [[0038 Celestial conformal blocks]] ## Summary - elucidates the explicit relation between three-point functions and OPE data in CCFT, focusing on the case of massless-to-massive scalar scattering - understands light-ray operators as a direct consequence of the CCFT formulation in terms of three-point functions, rather than as an a posteriori finding - clarifies the relation between the OPE data in (3, 1) and (2, 2) signatures, by means of adopting a precise prescription for analytic continuation ## Shadows and light ray operators These operators are locally independent and hence should all be considered when introducing a local OPE expansion. # Guevara (Dec) ## Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space \[Links: [arXiv](https://arxiv.org/abs/2112.05111), [PDF](https://arxiv.org/pdf/2112.05111.pdf)\] \[Abstract: We present a holographic construction of solutions to the gravitational wave equation starting from QFT scattering amplitudes. The construction amounts to a change of basis from momentum to (2,2) twistor space, together with a recently introduced analytic continuation between (2,2) and (1,3) spacetimes. We test the transform for three and four-point amplitudes in a classical limit, recovering both stationary and dynamical solutions in GR as parametrized by their tower of multipole moments, including the Kerr black hole. As a corollary, this provides a link between the Kerr-Schild classical double copy and the QFT double copy.\] # Guevara, Himwich, Pate, Strominger ## Holographic symmetry algebras for gauge theory and gravity \[Links: [arXiv](https://arxiv.org/abs/2103.03961), [PDF](https://arxiv.org/pdf/2103.03961.pdf)\] \[Abstract: All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the [[0022 Celestial sphere|celestial sphere]]. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of [[0390 Conformally soft theorems|conformally soft theorems]]. The current algebra commutators are explicitly derived from the poles in the [[0030 Operator product expansion|OPE]] coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.\] ## Refs - [[0009 Soft theorems]] - [[0328 w(1+infinity)]] ## Assumptions - only ==positive helicity== - sufficient/automatic for [[0061 Maximally helicity violating amplitudes|MHV]] - ==$\operatorname{Vir}_{L} \otimes S L(2, \mathbb{R})_{R}$-invariant== - $SL(2,\mathbb{R})_R$ means the global part of $\operatorname{Vir}_{R}$ - the full $\operatorname{Vir}_{L} \otimes \operatorname{Vir}_{R}$ is challenging - this is natural because positive helicity symmetry currents falls into finite $(2-k)$-dimensional $S L(2, \mathbb{R})_{R}$ representations - mostly for tree-level EYM ## Summary - *obtains* conformally soft current algebra for ==EYM== - *shows* that first few leading ones generate the full tower ## Tower of conformal soft current (in YM) - see Sec.2 and App.A 1. define mode expansion - $O_{k}^{a,+}(z, \bar{z})=\sum_{n} \frac{O_{k, n}^{a,+}(z)}{\bar{z}^{n+\frac{k-1}{2}}}$ 2. define soft currents - $R_{n}^{k, a}(z):=\lim _{\varepsilon \rightarrow 0} \varepsilon O_{k+\varepsilon, n}^{a,+}(z)$ - $k=1,0,-1,-2, \ldots, \quad \frac{k-1}{2} \leq n \leq \frac{1-k}{2}$ - add different $n$ together for the same $k$: - $R^{k, a}(z, \bar{z})=\sum_{n=\frac{k-1}{2}}^{\frac{1-k}{2}} \frac{R_{n}^{k, a}(z)}{\bar{z}^{n+\frac{k-1}{2}}}$ 3. find OPE between gluons - $O_{\Delta_{1}}^{a,+}\left(z_{1}, \bar{z}_{1}\right) O_{\Delta_{2}}^{b,+}\left(z_{2}, \bar{z}_{2}\right) \sim \frac{-i f^{a b}{}_c}{z_{12}} \sum_{n=0}^{\infty} B\left(\Delta_{1}-1+n, \Delta_{2}-1\right) \frac{\left(\bar{z}_{12}\right)^{n}}{n !} \bar{\partial}^{n} O_{\Delta_{1}+\Delta_{2}-1}^{c,+}\left(z_{2}, \bar{z}_{2}\right)$ 4. use definition of soft currents to get OPE between currents - $R^{k, a}\left(z_{1}, \bar{z}_{1}\right) R^{l, b}\left(z_{2}, \bar{z}_{2}\right) \sim \frac{-i f^{a b}{}_c}{z_{12}} \sum_{n=0}^{1-k}\left(\begin{array}{c}2-k-l-n \\ 1-l\end{array}\right) \frac{\left(\bar{z}_{12}\right)^{n}}{n !} \bar{\partial}^{n} R^{k+l-1, c}\left(z_{2}, \bar{z}_{2}\right)$ - $\bar{\partial}^{p} R^{k, a}\left(z_{1}, \bar{z}_{1}\right) \bar{\partial}^{q} R^{l, b}\left(z_{2}, \bar{z}_{2}\right) \sim \frac{-i f^{a b}{}_c}{z_{12}}\left(\begin{array}{c}2-k-l-p-q \\ 1-l-q\end{array}\right) \bar{\partial}^{q+p} R^{k+l-1, c}\left(z_{2}, \bar{z}_{2}\right)$ 5. use contour to get commutators - for holomorphic objects - $[A, B](z)=\oint_{z} \frac{d w}{2 \pi i} A(w) B(z)$ - **answer** $\left[R_{n}^{k, a}, R_{n^{\prime}}^{l, b}\right]=-i f^{a b}{}_c\left(\begin{array}{c}\frac{1-k}{2}-n+\frac{1-l}{2}-n^{\prime} \\ \frac{1-k}{2}-n\end{array}\right)\left(\begin{array}{c}\frac{1-k}{2}+n+\frac{1-l}{2}+n^{\prime} \\ \frac{1-k}{2}+n\end{array}\right) R_{n+n^{\prime}}^{k+l-1, c}$ 6. restrict to lowest weight for each $k$ - i.e. take $n=(k-1)/2$ for each $k$ - $\left[\widehat{R}^{k, a}, \widehat{R}^{l, b}\right]=-i f^{a b}{}_c \widehat{R}^{k+l-1, c}$ # Hajian, Ozsahin, Tekin ## First law of black hole thermodynamics and Smarr formula with a cosmological constant \[Links: [arXiv](https://arxiv.org/abs/2103.10983), [PDF](https://arxiv.org/pdf/2103.10983.pdf)\] \[Abstract: The first law of black hole thermodynamics in the presence of a cosmological constant $\Lambda$ can be generalized by introducing a term containing the variation $\delta\Lambda$. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge etc., it has been shown [Classical Quantum Gravity 35, 125012 (2018)] that the new term has the same structure: $\Lambda$ is a conserved charge associated with a gauge symmetry; and its role in the first law is quite similar to an "electric charge" rather than to the pressure. Besides, its conjugate chemical potential resembles an "electric potential" on the horizon, in contrast with the volume enclosed by horizon. In this work, first we propose and prove the generalized Smarr relation in this new paradigm. Then, we reproduce systematically the "effective volume" of a black hole which has been introduced before in the literature as the conjugate of pressure. Our construction removes the ambiguity in the definition of volume. Finally, we apply and investigate this formulation of "$\Lambda$ as a charge" on a number of solutions to different models of gravity for different spacetime dimensions. Especially, we investigate the applicability and validity of the analysis for black branes, whose enclosed volume is not well defined in principle.\] # Harlow, Ooguri ## A Euclidean perspective on completeness and weak gravity \[Links: [arXiv](https://arxiv.org/abs/2109.03838), [PDF](https://arxiv.org/pdf/2109.03838.pdf)\] \[Abstract: \] ## Summary - derives [[0177 Weak gravity conjecture]] <!-- - I gave a postdoc JC discussion on this in Fall 2021 ---> # Harlow, Shaghoulian (Essay) ## Euclidean gravity and holography \[Links: [DOI](https://www.worldscientific.com/doi/abs/10.1142/S0218271821410054)\] \[Abstract: We discuss a recent proposal that the Euclidean gravity approach to quantum gravity is correct if and only if the theory is holographic, providing several examples and general arguments to support the conjecture. This provides a natural mechanism for the low-energy gravitational effective field theory to access a host of deep ultraviolet properties, like the [[0004 Black hole entropy|Bekenstein–Hawking entropy]] of black holes, the unitarity of black hole evaporation, and the lack of exact [[0187 Global symmetries in QG|global symmetries]].\] # Harlow, Wu ## Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim Gravity \[Links: [arXiv](https://arxiv.org/abs/2108.04841), [PDF](https://arxiv.org/pdf/2108.04841.pdf)\] \[Abstract: In this paper we use the covariant Peierls bracket to compute the algebra of a sizable number of diffeomorphism-invariant observables in classical [[0050 JT gravity|Jackiw-Teitelboim gravity]] coupled to fairly arbitrary matter. We then show that many recent results, including the construction of traversable wormholes, the existence of a family of $SL(2,\mathbb{R})$ algebras acting on the matter fields, and the calculation of the scrambling time, can be recast as simple consequences of this algebra. We also use it to clarify the question of when the creation of an excitation deep in the bulk increases or decreases the boundary energy, which is of crucial importance for the "typical state" versions of the firewall paradox. Unlike the "Schwarzian" or "boundary particle" formalism, our techniques involve no unphysical degrees of freedom and naturally generalize to higher dimensions. We do a few higher-dimensional calculations to illustrate this, which indicate that the results we obtain in JT gravity are fairly robust.\] ## Refs - [Talk by Daniel](https://www.youtube.com/watch?v=A8QPsd6AbAA&list=PL2W4RYadh8Q2ZJFJGmeupLD3FnN1Tdckc&index=1&ab_channel=PratikRath) # Hernandez-Cuenca, Horowitz, Trevino, Wang ## Boundary causality violating metrics in holography \[Links: [arXiv](https://arxiv.org/abs/2103.05014), [PDF](https://arxiv.org/pdf/2103.05014.pdf), [PRL](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.081603)\] A well-behaved field theory living on a fixed background has a causality structure defined by the background metric. In [[0001 AdS-CFT|holography]], however, signals can travel through the bulk, and some bulk metrics would allow a signal to travel faster than the speed of light as seen on the boundary. These are called [[0091 Boundary causality|boundary causality]] violating metrics. Holographers usually work with a classical bulk metric, in which case they declare that boundary causality violating metrics are forbidden. However, in a full quantum gravity path integral, these metrics do contribute. The question is then: how to avoid causality violation in this context? The resolution seems to lie in the subtlety of defining the boundary conditions for the metric configurations in the path integral. ## Layout of Section 4: Resolution - timefold construction - generalised partition function - minimal timefold 1. differentiate resolution 2. extrapolate resolution - propose to contour order the path integrand 1. limit first - no issue 2. integrate first - need to fix the ambiguity - general correlation functions <!-- - (Joaquin at gravity lunch) Our examples of bdy causality violating metrics are all static and have Euclidean analogs. If we start with the Euclidean functional integral and define the Lorentzian amplitudes by analytic continuation, is there an analog of our proposal and if so, what is it? - Henry (at gravity lunch) mentioned that in the replica wormhole story, one wants the crease in the bulk timefold to pass through the quantum extremal surface. If the last operator on the boundary is in the past of the QES, then it seems the bulk timefold must extend further than the minimal timefold. - (Raphael Bousso) "more minimal" minimal timefolds by doing folding only at causal diamonds (incorporated into the new version) --> # Himwich, Pate, Singh ## Celestial Operator Product Expansions and $\rm w_{1+\infty}$ Symmetry for All Spins \[Links: [arXiv](https://arxiv.org/abs/2108.07763), [PDF](https://arxiv.org/pdf/2108.07763.pdf)\] \[Abstract: The [[0114 Celestial OPE|operator product expansion]] of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level [[0078 Collinear limit|collinear limits]], but also to obey an infinite number of additional symmetry transformations that respect the algebra of ${\rm w}_{1+\infty}$. In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of ${\rm w}_{1+\infty}$ on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons.\] ## Summary - [[0114 Celestial OPE|celestial OPE]] for massless primary operators of ==arbitrary spin== - including ==fermions and higher derivative non-minimal couplings of gluons and gravitons== - (sec.3) use only Poincare symmetry to get OPE coefficients - including coefficients of descendants - (sec.4) use [[0058 BCFW|BCFW]] to obtain [[0078 Collinear limit|collinear]] results - (sec.5) constructs the currents generating [[2021#Strominger]] - (sec.6) the OPE coefficients also satisfy the $\mathrm w_{1+\infty}$ symmetry ## Restrictions - did not consider massive - did not consider light or shadow transforms - dependence of OPE coefficients on spin is not the goal so consider them fixed - only the leading term in $1/z_{12}$ studied in both methods ## 3 OPE from symmetry - uses only Poincare symmetry to fix the tree-level OPE coefficients - not surprising because 3-point is known to be fixed by Poincare alone and they are directly related to tree-level collinear splitting functions - used only $P_{-\frac{1}{2}, \pm \frac{1}{2}}$ which do not mix $SL(2,R)$ primaries and descendants, so can restrict to the leading term in holomorphic limit ## 4 OPE from [[0058 BCFW|BCFW]] - only leading term in $1/z_{12}$ is studied and therefore requires only the first diagram in the factorisation channels - procedure - shift particles 1 and $k\ne 1,2$ - find poles in $z$ that give poles in $z_{12}$ - turns out only one such channel: ($A_3$ times $A_{n-1}$) - after inverse [[0079 Mellin transform]], $A_3$ turns into a prefactor -> get the collinear expression ## 5 $\mathrm{w}_{1+\infty}$ currents - light transform $\mathbf{L}\left[\mathcal{O}_{h, \bar{h}}\right](z, \bar{z}) \equiv \int_{\mathbb{R}} \frac{d \bar{w}}{2 \pi i} \frac{1}{(\bar{z}-\bar{w})^{2-2 \bar{h}}} \mathcal{O}_{h, \bar{h}}(z, \bar{w})$ - $\mathrm{w}^{q}(z, \bar{z}) \equiv \frac{1}{\kappa}(-1)^{2 q} \Gamma(2 q) \lim _{\varepsilon \rightarrow 0} \mathbf{L}\left[\mathcal{O}_{3-q, 1-q+\varepsilon}\right](z, \bar{z}), \quad q=1, \frac{3}{2}, 2, \frac{5}{2}, \cdots$ ## 6 $\mathrm{w}_{1+\infty}$ symmetry of OPE - only considered positive helicities and ignored EFT corrections like those in [[2016#Elvang, Jones, Naculich]] - see [[2021#Jiang (Aug)]] sec.6.4 for a discussion on this - used the action of a particular component ($n=q-1$): $\left[\widehat{\mathrm{w}}_{q-1}^{q}, \mathcal{O}_{h, \bar{h}}(z, \bar{z})\right]$ - acting on the OPE ansatz gives a constraint on the OPE coefficients; then checked that the OPE results obey this constraint - #question : why not other modes ($n\ne q-1$)? they should be determined from conformal symmetry, but should check that they agree with subleading terms explicitly computed from amplitude # Hu, Ren, Srikant, Volovich ## Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations \[Links: [arXiv](https://arxiv.org/abs/2106.16111), [PDF](https://arxiv.org/pdf/2106.16111.pdf)\] \[Abstract: Celestial and momentum space amplitudes for massless particles are related to each other by a change of basis provided by the [[0079 Mellin transform|Mellin transform]]. Therefore properties of celestial amplitudes have counterparts in momentum space amplitudes and vice versa. In this paper, we study the celestial avatar of dual superconformal symmetry of $\mathcal{N}=4$ Yang-Mills theory. We also analyze various differential equations known to be satisfied by celestial $n$-point tree-level [[0061 Maximally helicity violating amplitudes|MHV]] amplitudes and identify their momentum space origins.\] ## Refs - extends [[2020#Banerjee, Ghosh, Gonzo]] ## Summary - explains origins of some differential equations satisfied by the celestial amplitudes which are [[0058 BCFW|BCFW]] # Iliesiu, Kologlu, Turiaci ## Supersymmetric indices factorize \[Links: [arXiv](https://arxiv.org/abs/2107.09062), [PDF](https://arxiv.org/pdf/2107.09062.pdf)\] \[Abstract: The extent to which quantum mechanical features of black holes can be understood from the Euclidean gravity path integral has recently received significant attention. In this paper, we examine this question for the calculation of the [[0568 Supersymmetric index]]. For concreteness, we focus on the case of charged black holes in asymptotically flat four-dimensional $\mathcal{N}=2$ ungauged supergravity. We show that the gravity path integral with supersymmetric boundary conditions has an infinite family of Kerr-Newman classical saddles with different angular velocities. We argue that fermionic zero-mode fluctuations are present around each of these solutions making their contribution vanish, except for a single saddle that is [[0178 BPS|BPS]] and gives the expected value of the index. We then turn to non-perturbative corrections involving spacetime wormholes and show that a fermionic zero mode is present in all these geometries, making their contribution vanish once again. This mechanism works for both single- and multi-boundary path integrals. In particular, only disconnected geometries without wormholes contribute to the gravitational path integral which computes the index, and the factorization puzzle that plagues the black hole partition function is resolved for the supersymmetric index. Finally, we classify all other single-centered geometries that yield non-perturbative contributions to the gravitational index of each boundary.\] ## Extensions and followups - [[2023#Anupam, Athira, Chowdhury, Sen]]: log correction to the [[0004 Black hole entropy|black hole entropy]] match with the conventional method # Iliesiu, Mezei, Sarosi ## The volume of the black hole interior at late times \[Links: [arXiv](https://arxiv.org/abs/2107.06286), [PDF](https://arxiv.org/pdf/2107.06286); Talks: [Mezei at YITP](https://youtu.be/Ua8S3nzjqoA?feature=shared), [Iliesiu at IAS](https://youtu.be/Tw3ieMaUs_A?feature=shared)\] \[Abstract: Understanding the fate of semi-classical black hole solutions at very late times is one of the most important open questions in quantum gravity. In this paper, we provide a path integral definition of the volume of the black hole interior and study it at arbitrarily late times for black holes in various models of two-dimensional gravity. Because of a novel universal cancellation between the contributions of the semi-classical black hole spectrum and some of its non-perturbative corrections, we find that, after a linear growth at early times, the length of the interior saturates at a time, and towards a value, that is exponentially large in the entropy of the black hole. This provides a non-perturbative confirmation of the [[0204 Quantum complexity|complexity]] equals volume proposal since complexity is also expected to plateau at the same value and at the same time.\] # Ishibashi, Maeda (Apr) ## The first law of entanglement entropy in AdS black hole backgrounds \[Links: [arXiv](https://arxiv.org/abs/2104.01862), [PDF](https://arxiv.org/pdf/2104.01862.pdf)\] \[Abstract: The first law for entanglement entropy in CFT in an odd-dimensional asymptotically AdS black hole is studied by using the AdS/CFT duality. The entropy of CFT considered here is due to the entanglement between two subsystems separated by the horizon of the AdS black hole, which itself is realized as the conformal boundary of a [[0270 Black droplet|black droplet]] in even-dimensional global AdS bulk spacetime. In (2+1)-dimensional CFT, the first law is shown to be always satisfied by analyzing a class of metric perturbations of the exact solution of a 4-dimensional black droplet. In (4+1)-dimensions, the first law for CFT is shown to hold under the Neumann boundary condition at a certain bulk hypersurface anchored to the conformal boundary of the boundary AdS black hole. From the boundary view point, this Neumann condition yields there being no energy flux across the boundary of the boundary AdS black hole. Furthermore, the asymptotic geometry of a 6-dimensional small AdS black droplet is constructed as the gravity dual of our (4+1)-dimensional CFT, which exhibits a negative energy near the spatial infinity, as expected from vacuum polarization.\] ## Refs - [[0372 Holographic first law of entanglement entropy]] # Ishibashi, Maeda (Nov) ## The averaged null energy condition on holographic evaporating black holes \[Links: [arXiv](https://arxiv.org/abs/2111.05151), [PDF](https://arxiv.org/pdf/2111.05151.pdf)\] \[Abstract: \] ## Summary - uses the bulk to study the holographic stress tensor and translates to $\langle T_{\mu\nu} \rangle$ in $3d$ and $5d$ - bulk [[0477 Gao-Wald theorem]] implies conformally invariant (modified) [[0417 Averaged null energy condition]] - the horizon of an evaporating BH looks like a universe with a big crunch # Jafferis, Schneider ## Stringy ER=EPR \[Links: [arXiv](https://arxiv.org/abs/2104.07233), [PDF](https://arxiv.org/pdf/2104.07233.pdf)\] \[Abstract: \] ## Refs - [[0334 FZZ duality]] important # Jeong, Kim, Sun ## Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field \[Links: [arXiv](https://arxiv.org/abs/2104.13084), [PDF](https://arxiv.org/pdf/2104.13084.pdf)\] \[Abstract: We investigate the properties of [[0179 Pole skipping|pole-skipping]] of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and [[0325 Quasi-normal modes|quasi-normal mode]] computations. We find that the pole-skipping points are related with the [[0008 Quantum chaos|chaotic]] properties, [[0466 Lyapunov exponent|Lyapunov exponent]] ($\lambda_L$) and [[0167 Butterfly velocity|butterfly velocity]] ($v_B$), independently of the symmetry breaking patterns. We show that the diffusion constant ($D$) is bounded by $D \,\geqslant\, v_{B}^2/\lambda_{L}$, where $D$ is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit.\] # Jiang (Aug) ## Holographic chiral algebra: Supersymmetry, infinite Ward identities, and EFTs \[Links: [arXiv](https://arxiv.org/abs/2108.08799), [PDF](https://arxiv.org/pdf/2108.08799.pdf)\] \[Abstract: Celestial holography promisingly reformulates the scattering amplitude holographically in terms of celestial conformal field theory living at null infinity. Recently, an infinite-dimensional symmetry algebra was discovered in Einstein-Yang-Mills theory. The starting point in the derivation is the [[0114 Celestial OPE|celestial OPE]] of two soft currents, and the key ingredient is the summation of $\overline{SL(2,\mathbb R)}$ descendants in OPE. In this paper, we consider the supersymmetric Einstein-Yang-Mills theory and obtain the supersymmetric extension of the holographic symmetry algebra. Furthermore, we derive infinitely many [[0106 Ward identity|Ward identities]] associated with the infinite soft currents which generate the holographic symmetry algebra. This is realized by considering the OPE between a soft symmetry current and a hard operator, and then summing over its $\overline{SL(2,\mathbb R)}$ descendants. These Ward identities reproduce the known Ward identities corresponding to the leading, sub-leading, and sub-sub-leading soft graviton theorems as well as the leading and sub-leading soft gluon theorems. By performing shadow transformations, we also obtain infinitely many shadow Ward identities, including the stress tensor Ward identities for sub-leading soft graviton. Finally, we use our procedure to discuss the corrections to Ward identities in effective field theory (EFT), and reproduce the corrections to soft theorems at sub-sub-leading order for graviton and sub-leading order for photon. For this aim, we derive general formulae for the celestial OPE and its corresponding Ward identities arising from a cubic interaction of three spinning massless particles. Our formalism thus provides a unified framework for understanding the Ward identities in celestial conformal field theory, or equivalently the soft theorems in scattering amplitude.\] ## Summary - investigates OPE in supersymmetric EYM - investigates how Ward identities ([[0009 Soft theorems|soft theorems]]) are corrected by EFT corrections to the soft limits - the chiral algebra for positive helicities is *not* corrected by EFT corrections ## EFT correction to holographic chiral algebra v.s. soft theorems - the formalism only considers positive helicity *soft* particles, and it turns out that no EFT operators have the correct dimension to affect the chiral algebra derivation - on the other hand, the Ward identities are derived from soft-hard OPEs, and the hard operators are not necessarily positive-helicity; it turns out that there are EFT operators with the correct dimensions to change the results ## To do - the soft currents are corrected by EFT corrections but the constraints from these corrected relations should still be consistent with the [[0114 Celestial OPE]] calculated purely using Poincare symmetries in [[2021#Himwich, Pate, Singh]] - #todo check this # Jiang (Oct) ## Celestial OPEs and $w_{1+\infty}$ algebra from worldsheet in string theory \[Links: [arXiv](https://arxiv.org/abs/2110.04255), [PDF](https://arxiv.org/pdf/2110.04255.pdf)\] \[Abstract: [[0114 Celestial OPE|Celestial operator product expansions]] (OPEs) arise from the [[0078 Collinear limit|collinear limit]] of scattering amplitudes and play a vital role in [[0010 Celestial holography|celestial holography]]. In this paper, we derive the celestial OPEs of massless fields in string theory from the worldsheet. By studying the worldsheet OPEs of vertex operators in worldsheet CFT and further examining their behaviors in the collinear limit, we find that new vertex operators for the massless fields in string theory are generated and become dominant in the collinear limit. Mellin transforming to the conformal basis yields exactly the celestial OPEs in celestial CFT. We also derive the celestial OPEs from the collinear factorization of string amplitudes and the results derived in these two different methods are in perfect agreement with each other. Our final formulae of celestial OPEs are applicable to general dimensions, corresponding to Einstein-Yang-Mills theory supplemented by some possible higher derivative interactions. Specializing to 4D, we reproduce all the celestial OPEs for gluon and graviton in the literature. We consider various string theories, including the open and closed bosonic string, as well as the closed superstring theory with $\mathcal N=1$ and $\mathcal N=2$ worldsheet supersymmetry. In the case of $\mathcal N=2$ string, we also derive all the $\overline{SL (2,\mathbb R)}$ descendant contributions in the celestial OPE; the soft sector of such OPE just yields the [[0328 w(1+infinity)|w]]$_{1+\infty}$ algebra after rewriting in terms of chiral modes. Our stringy derivation of celestial OPEs thus initiates the first step towards the realization of celestial holography in string theory.\] # Kajuri ## Symmetry transformation of subregion bulk representations \[Links: [arXiv](https://arxiv.org/abs/2102.08937), [PDF](https://arxiv.org/pdf/2102.08937.pdf)\] \[Abstract: \] <!--- ## Comments - claims to solve an issue without using QEC, but Xi says that he misunderstood the issue - the conclusion is true but it only solves some trivial stuff - the issue still requires [[0146 Quantum error correction]] ---> # Kawabata, Nishioka, Okuyama, Watanabe (Feb) ## Probing Hawking radiation through capacity of entanglement \[Links: [arXiv](https://arxiv.org/abs/2102.02425), [PDF](https://arxiv.org/pdf/2102.02425.pdf)\] \[Abstract: \] ## Refs - [[0291 Capacity of entanglement]] - later paper [[KawabataNishiokaOkuyamaWatanabe202105]] # Kim, Lee, Nishida ## Construction of bulk solutions for towers of pole-skipping points \[Links: [arXiv](https://arxiv.org/abs/2112.11662), [PDF](https://arxiv.org/pdf/2112.11662.pdf)\] \[Abstract: \] ## Comments - very general discussion of [[0179 Pole skipping]] with higher-spin fields - proposes that integrals of propagators over horizons are generalisations of integrals of graviton propagators for shockwave geometries # Kontsevich, Segal ## Wick rotation and the positivity of energy in quantum field theory \[Links: [arXiv](https://arxiv.org/abs/2105.10161), [PDF](https://arxiv.org/pdf/2105.10161.pdf)\] \[Abstract: We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of [[0335 Complex metrics|complex-valued metrics]]. Ordinary Riemannian metrics are contained in the allowable domain, while Lorentzian metrics lie on its boundary.\] # Kravchuk, Qiao, Rychkov ## Distributions in CFT II. Minkowski Space \[Links: [arXiv](https://arxiv.org/abs/2104.02090), [PDF](https://arxiv.org/pdf/2104.02090)\] \[Abstract: CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent Euclidean OPE. It is nowadays common to assume that CFT correlators exist and have various properties also in Lorentzian signature. Some of these properties may represent extra assumptions, and it is an open question if they hold for familiar statistical-physics CFTs such as the critical 3d Ising model. Here we consider Wightman 4-point functions of scalar primaries in Lorentzian signature. We derive a minimal set of their properties solely from the Euclidean unitary CFT axioms, without using extra assumptions. We establish all [[0165 Wightman axioms|Wightman axioms]] (temperedness, spectral property, local commutativity, clustering), Lorentzian conformal invariance, and distributional convergence of the $s$-channel Lorentzian OPE. This is done constructively, by analytically continuing the 4-point functions using the $s$-channel OPE expansion in the radial cross-ratios $\rho, \bar{\rho}$. We prove a key fact that $|\rho|, |\bar{\rho}| < 1$ inside the forward tube, and set bounds on how fast $|\rho|, |\bar{\rho}|$ may tend to 1 when approaching the Minkowski space. We also provide a guide to the axiomatic QFT literature for the modern CFT audience. We review the Wightman and [[0112 Osterwalder-Schrader reconstruction theorem|Osterwalder-Schrader]] (OS) axioms for Lorentzian and Euclidean QFTs, and the celebrated OS theorem connecting them. We also review a classic result of Mack about the distributional OPE convergence. Some of the classic arguments turn out useful in our setup. Others fall short of our needs due to Lorentzian assumptions (Mack) or unverifiable Euclidean assumptions (OS theorem).\] # Kundu (Apr) ## Swampland Conditions for Higher Derivative Couplings from CFT \[Links: [arXiv](https://arxiv.org/abs/2104.11238), [PDF](https://arxiv.org/pdf/2104.11238.pdf)\] \[Abstract: There are effective field theories that cannot be embedded in any UV complete theory. We consider scalar effective field theories, with and without dynamical gravity, in $D$-dimensional anti-de Sitter (AdS) spacetime with large radius and derive precise bounds (analytically) on the coupling constants of higher derivative interactions $\phi^2\Box^k\phi^2$ by only requiring that the dual CFT obeys the standard conformal bootstrap axioms. In particular, we show that all such coupling constants, for even $k\ge 2$, must satisfy positivity, monotonicity, and log-convexity conditions in the absence of dynamical gravity. Inclusion of gravity only affects constraints involving the $\phi^2\Box^2\phi^2$ interaction which now can have a negative coupling constant. Our CFT setup is a Lorentzian four-point correlator in the Regge limit. We also utilize this setup to derive constraints on effective field theories of multiple scalars. We argue that similar analysis should impose nontrivial constraints on the graviton four-point scattering amplitude in AdS.\] # Kundu (Sep, a) ## Subleading Bounds on Chaos \[Links: [arXiv](https://arxiv.org/abs/2109.03826), [PDF](https://arxiv.org/pdf/2109.03826.pdf)\] \[Abstract: [[0008 Quantum chaos|Chaos]], in quantum systems, can be diagnosed by certain [[0482 Out-of-time-order correlator|out-of-time-order correlators (OTOCs)]] that obey the chaos bound of [[2015#Maldacena, Shenker, Stanford|Maldacena, Shenker, and Stanford (MSS)]]. We begin by deriving a dispersion relation for this class of OTOCs, implying that they must satisfy many more constraints beyond the MSS bound. Motivated by this observation, we perform a systematic analysis obtaining an infinite set of constraints on the OTOC. This infinite set includes the MSS bound as the leading constraint. In addition, it also contains subleading bounds that are highly constraining, especially when the MSS bound is saturated by the leading term. These new bounds, among other things, imply that the MSS bound cannot be exactly saturated over any duration of time, however short. Furthermore, we derive a sharp bound on the [[0466 Lyapunov exponent|Lyapunov exponent]] $\lambda_2 \le \frac{6\pi}{\beta}$ of the subleading correction to maximal chaos.\] ## Summary - subleading [[0474 Chaos bound|chaos bound]] to [[2015#Maldacena, Shenker, Stanford]] ## Intuition - since not all early-time expansions of the OTOC can be resummed into nice functions, they should be constrained in order for OTOC to be well-behaved ## Refs - saturated by extremal chaos [[Kundu202109b]] # Kusuki ## Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography \[Links: [arXiv](https://arxiv.org/abs/2112.10984), [PDF](https://arxiv.org/pdf/2112.10984)\] \[Abstract: Recently, [[0548 Boundary CFT|boundary conformal field theories]] (BCFTs) have attracted much attention in the context of quantum gravity. This is because a BCFT can be dual to gravity coupled to a heat bath CFT, known as the island model. On this background, it would be interesting to explore the duality between the boundary and the braneworld. However, this seems to be a challenging problem. The reason is because although there has been much study of rational BCFTs, there has been comparatively little study of irrational BCFTs, and irrational BCFTs are expected to be the boundary duals of the braneworlds. For this reason, we explore properties of boundary ingredients: the boundary primary spectrum, the boundary-boundary-boundary OPE coefficients and the bulk-boundary OPE coefficients. For this purpose, the conformal bootstrap is extremely useful. This is the first step in providing an understanding of BCFTs in the context of braneworld holography by using the conformal bootstrap. The techniques developed in this paper may be useful for further investigation of irrational BCFTs.\] # Lanosa, Leston, Passaglia ## Interplay between reflection positivity and crossing symmetry in the bootstrap approach to CFT \[Links: [arXiv](https://arxiv.org/abs/2112.00232), [PDF](https://arxiv.org/pdf/2112.00232)\] \[Abstract: [[0021 Crossing symmetry|Crossing symmetry]] (CS) is the main tool in the bootstrap program applied to CFT models. This consists in an equality which imposes restrictions on the CFT data of a model, i.e, the OPE coefficients and the conformal dimensions. [[0639 Reflection positivity|Reflection positivity]] (RP) has also played a role, since this condition lead to the unitary bound and reality of the [[0030 Operator product expansion|OPE]] coefficients. In this paper we show that RP can still reveal more information, showing how RP itself can capture an important part of the restrictions imposed by the full CS equality. In order to do that, we use a connection used by us in a previous work between RP and positive definiteness of a function of a single variable. This allows to write constraints on the OPE coefficients in a concise way, encoding in the conditions that certain functions of the crossratio will be positive defined and in particular completely monotonic. We will consider how the bounding of scalar conformal dimensions and OPE coefficients arise in this RP based approach. We will illustrate the conceptual and practical value of this view trough examples of general CFT models in d-dimensions.\] # Leutheusser, Liu (Oct) ## Causal connectability between quantum systems and the black hole interior in holographic duality \[Links: [arXiv](https://arxiv.org/abs/2110.05497), [PDF](https://arxiv.org/pdf/2110.05497.pdf)\] \[Abstract: \] ## Refs - talk at [[Rsc0036 Banff Gravitational Emergence in AdS-CFT]] - followup [[LeutheusserLiu202112]][](https://arxiv.org/pdf/2112.12156.pdf) - extension - [[2021#Witten (Dec, b)]]: extension to include $1/N$ corrections ## Summary - finds an emergent type III$_1$ algebra in $\mathcal{N}=4$ SYM for large $N$ # Lin, Sun, Zhang ## Deriving the PEE proposal from the Locking bit thread configuration \[Links: [arXiv](https://arxiv.org/abs/2105.09176), [PDF](https://arxiv.org/pdf/2105.09176)\] \[Abstract: In the holographic framework, we argue that the [[0292 Partial entanglement entropy|partial entanglement entropy]] (PEE) can be explicitly interpreted as the component flow flux in a locking bit thread configuration. By applying the locking theorem of [[0211 Bit thread|bit threads]], and constructing a concrete locking scheme, we obtain a set of uniquely determined component flow fluxes from this viewpoint, and successfully derive the PEE proposal and its generalized version in the multipartite cases. Moreover, from this perspective of bit threads, we also present a coherent explanation for the coincidence between the BPE (balanced partial entanglement)/EWCS ([[0319 Entanglement wedge cross-section|entanglement wedge cross section]]) duality proposed recently and the EoP ([[0258 Entanglement of purification|entanglement of purification]])/EWCS duality. We also discuss the issues implied by this coincident between the idea of the PEE and the picture of locking thread configuration.\] # Magnea ## Non-abelian infrared divergences on the celestial sphere \[Links: [arXiv](https://arxiv.org/abs/2104.10254), [PDF](https://arxiv.org/pdf/2104.10254.pdf)\] \[Abstract: We consider the [[0295 Infrared divergences in scattering amplitude|infrared factorisation]] of non-abelian multi-particle scattering amplitudes, and we study the form of the universal colour operator responsible for infrared divergences, when expressed in terms of coordinates on the '[[0022 Celestial sphere|celestial sphere]]' intersecting the future light-cone at asymptotic distances. We find that colour-dipole contributions to the infrared operator, to all orders in perturbation theory, have a remarkably simple expression in these coordinates, with scale and coupling dependence factorised from kinematics and colour. Generalising earlier suggestions in the abelian theory, we then show that the infrared operator can be computed as a correlator of vertex operators in a conformal field theory of Lie-algebra-valued free bosons on the celestial sphere. We verify by means of the [[0030 Operator product expansion|OPE]] that the theory correctly predicts the all-order structure of [[0078 Collinear limit|collinear limits]], and the tree-level factorisation of soft real radiation.\] ## Refs - generalises [[2020#Kalyanapuram]] - from QED to non-Abelian - root [[0010 Celestial holography]] ## Summary - *shows* that the infrared operator can be computed as a correlator of vertex operators in a conformal field theory of ==Lie-algebra-valued free bosons== on the celestial sphere - *verifies* by means of the [[0030 Operator product expansion|OPE]] that the theory correctly predicts the all-order structure of [[0078 Collinear limit|collinear limit]], and the tree-level factorisation of soft real radiation ## Restrictions - dipole correlations - which is enough up to 3 loops - higher loops require quadrupole etc - (but this dipole result itself is correct too all loops) ## Future - "it would be very interesting and appealing if the scale integration could be made part of the correspondence, or, in other words, if one could understand the meaning of the scale integration from the point of view of the conformal theory on the celestial sphere" - "On the celestial side, the fact that we have a local matrix theory suggests that a gauge connection on the sphere might need to be introduced, and consequently the theory is expected to become interacting" # Mago, Ren, Srikant, Volovich ## Deformed w(1+infinity) algebras in CCFT \[Links: [arXiv](https://arxiv.org/abs/2111.11356), [PDF](https://arxiv.org/pdf/2111.11356.pdf)\] \[Abstract: We compute the modification of the [[0328 w(1+infinity)|w(1+infinity) algebra]] of soft graviton, gluon and scalar currents in the [[0010 Celestial holography|Celestial CFT]] due to non-minimal couplings. We find that the [[0453 Jacobi identity or associativity of celestial OPE|Jacobi identity]] is satisfied only when the spectrum and couplings of the theory obey certain constraints. We comment on the similarities and essential differences of this algebra to [[0358 W(1+infinity)|W(1+infinity)]].\] ## Refs - follow-up [[2022#Ren, Spradlin, Srikant, Volovich]] ## Summary - *computes* modifications to [[0328 w(1+infinity)|w(1+infinity)]] algebra due to [[0338 Non-minimally coupled fields|non-minimally coupled fields]] - *finds* that Jacobi identity is only satisfied when the spectrum and couplings obtain certain constraints - *compares* with [[0358 W(1+infinity)|W(1+infinity)]] - some appendices - [[0061 Maximally helicity violating amplitudes|MHV]] and NMHV - double soft limit - alternative definition of commutators - violates Jacobi (only when there is a pole in both $z$ and $\bar z$ expansions, which does not appear in MHV) ## Setup - allow for more (non-minimal) couplings between fields of various spins, such as graviton-graviton-scalar etc - $\kappa_{-2,2,2}$: usual MHV minimal coupling - $\kappa_{0,2,2}$: scalar-graviton-graviton coupling - $\kappa_{2,2,2}$: various higher derivative terms of order $R^3$ - the ==roster of soft currents== considered is: - $H^{k, \pm 2}$ soft graviton currents - $H^{k, \pm 1,a}$ soft gluon currents - two kinds of soft scalar currents $H^{k, 0,a}$ (coloured) and $H^{k, 0}$ (uncoloured) ## Results - Jacobi identity for $s_1=s_2=s_3=+2$ requires $\kappa_{-2,2,2}=\kappa_{0,0,2}, \quad 3 \kappa_{0,2,2}^{2}=10 \kappa_{-2,2,2} \kappa_{2,2,2}$ - the Jacobi identity involving just the graviton fails to close unless an uncolored scalar soft current and an $R^3$ interaction are included with specific couplings - Jacobi identity for $s_1=s_2=1, s_3=+2$ requires $\frac{\kappa_{0,1,1}}{\kappa_{-2,2,2}}=\frac{\kappa_{1,1,2}}{\kappa_{0,2,2}}, \quad \frac{\kappa_{-1,1,1}}{\kappa_{-1,1,2}}=\frac{\kappa_{1,1,1}}{3 \kappa_{1,1,2}}$ - for $s_1=s_2=s_3=1$ requires $\kappa_{-1,1,1}=\kappa_{0,0,1}, \quad \kappa_{0,1,1}^{2}=2 \kappa_{1,1,1} \kappa_{-1,1,1}$ - must include both a coloured and an uncoloured scalar in addition to an $F^3$ interaction with fixed coupling # Mahajan, Marolf, Santos ## The double cone geometry is stable to brane nucleation \[Links: [arXiv](https://arxiv.org/abs/2104.00022), [PDF](https://arxiv.org/pdf/2104.00022.pdf)\] \[Abstract: \] ## Refs - jointly submitted: [[2021#Cotler, Jensen]] ## Summary - double cone dominates during ramp stage - other wormholes are unstable to brane nucleation - but this one is *stable* - *discusses* [[0249 Factorisation problem]] # Mahajan, Stanford, Yan ## Sphere and disk partition functions in Liouville and in matrix integrals \[Links: [arXiv](https://arxiv.org/abs/2107.01172), [PDF](https://arxiv.org/pdf/2107.01172.pdf)\] \[Abstract: We compute the sphere and disk partition functions in semiclassical [[0562 Liouville theory|Liouville]] and analogous quantities in double-scaled matrix integrals. The quantity sphere/disk$^2$ is unambiguous and we find a precise numerical match between the Liouville answer and the matrix integral answer. An application is to show that the sphere partition function in [[0050 JT gravity|JT gravity]] is infinite.\] ## Comments - an example where the sphere partition function is non-zero, unlike in string theory (see comment in [[2022#Ahmadain, Wall (a)]]) # Mai, Yang ## Stability analysis on charged black hole with non-linear complex scalar \[Links: [arXiv](https://arxiv.org/abs/2101.00026), [PDF](https://arxiv.org/pdf/2101.00026.pdf)\] \[Abstract: It has been shown recently that the charged black hole can be scalarized if Maxwell field minimally couples with a complex scalar which has nonnegative nonlinear potential. We firstly prove that such scalarization cannot be a result of continuous phase transition for general scalar potential. Furthermore, we numerically find that it is possible that the RN black hole will be scalarized by a first order phase transition spontaneously and near extremal RN black hole is not stable in micro-canonical ensemble. In addition, considering a massless scalar perturbation, we compute the quasi-normal modes of the scalarized charged black hole and the results do not only imply that the spontaneously scalarized charged black hole is favored in thermodynamics but also suggest that it is kinetically stable against scalar perturbation at linear level. Our numerical results also definitely gives negative answer to Penrose-Gibbons conjecture and two new versions of Penrose inequality in charged case are suggested.\] ## Summary - proves: at for arbitrary non-linear potential $W(|\psi|^2)$ that is positively semidefinite, spontaneous scalarisation of RN black hole cannot happen via continuous phase transition # Marolf, Santos ## AdS Euclidean wormholes \[Links: [arXiv](https://arxiv.org/abs/2101.08875), [PDF](https://arxiv.org/pdf/2101.08875)\] \[Abstract: We explore the construction and stability of asymptotically anti-de Sitter [[0278 Euclidean wormholes|Euclidean wormholes]] in a variety of models. In simple ad hoc low-energy models, it is not hard to construct two-boundary Euclidean wormholes that dominate over disconnected solutions and which are stable (lacking negative modes) in the usual sense of Euclidean quantum gravity. Indeed, the structure of such solutions turns out to strongly resemble that of the Hawking-Page phase transition for AdS-Schwarzschild black holes, in that for boundary sources above some threshold we find both a 'large' and a 'small' branch of wormhole solutions with the latter being stable and dominating over the disconnected solution for large enough sources. We are also able to construct two-boundary Euclidean wormholes in a variety of string compactifications that dominate over the disconnected solutions we find and that are stable with respect to field-theoretic perturbations. However, as in classic examples investigated by Maldacena and Maoz, the wormholes in these UV-complete settings always suffer from brane-nucleation instabilities (even when sources that one might hope would stabilize such instabilities are tuned to large values). This indicates the existence of additional disconnected solutions with lower action. We discuss the significance of such results for the [[0249 Factorisation problem|factorization problem]] of AdS/CFT.\] # Melton ## Celestial Feynman Rules for Scalars \[Links: [arXiv](https://arxiv.org/abs/2109.07462), [PDF](https://arxiv.org/pdf/2109.07462.pdf)\] \[Abstract: Off-shell celestial amplitudes with both time-like and space-like external legs are defined. The Feynman rules for scalar amplitudes, viewed as a set of recursion relations for off-shell momentum space amplitudes, are transformed to the [[0022 Celestial sphere|celestial sphere]] using the split representation. For four-point celestial amplitudes, the Feynman expansion is shown to be equivalent to a [[0020 Conformal partial wave decomposition|conformal partial wave decomposition]], providing an interpretation of conformal partial wave expansion coefficients as integrals over off-shell three-point structures. A conformal partial wave decomposition for a simple four-point $s$-channel massless scalar celestial amplitude is derived.\] # Miller (Review) ## From Noether's Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems \[Links: [arXiv](https://arxiv.org/abs/2112.05289), [PDF](https://arxiv.org/pdf/2112.05289.pdf)\] \[Abstract: Electromagnetism contains an infinite dimensional symmetry group of [[0060 Asymptotic symmetry|large gauge transformations]]. This gives rise to an infinite number of conserved quantities called "[[0009 Soft theorems|soft charges]]" via Noether's theorem. When charged particles scatter, the conservation of soft charge constrains the overall amount of radiation emitted per angle. Here we describe the physical consequences of soft charge conservation and give fresh accounts of the roles of spacelike and timelike infinity in these conservation laws. We conclude by exploring the possibility of creating a dual boundary theory of electromagnetism.\] # Mukhametzhanov ## Half-wormhole in SYK with one time point \[Links: [arXiv](https://arxiv.org/abs/2105.08207), [PDF](https://arxiv.org/pdf/2105.08207.pdf)\] \[Abstract: In this note we study the SYK model with one time point, recently considered by Saad, Shenker, Stanford, and Yao. Working in a collective field description, they derived a remarkable identity: the square of the partition function with fixed couplings is well approximated by a "wormhole" saddle plus a "pair of linked half-wormholes" saddle. It explains factorization of decoupled systems. Here, we derive an explicit formula for the half-wormhole contribution. It is expressed through a hyperpfaffian of the tensor of SYK couplings. We then develop a perturbative expansion around the half-wormhole saddle. This expansion truncates at a finite order and gives the exact answer. The last term in the perturbative expansion turns out to coincide with the wormhole contribution. In this sense the wormhole saddle in this model does not need to be added separately, but instead can be viewed as a large fluctuation around the linked half-wormholes.\] ## Summary - confirms [[2021#Saad, Shenker, Stanford, Yao]] - understands [[0249 Factorisation problem|factorisation]] ## Perturbation around half-wormhole - the series ends after finitely many terms - the last term corresponds to wormhole # Natsuume, Okamura ## Nonuniqueness of scattering amplitudes at special points \[Links: [arXiv](https://arxiv.org/abs/2108.07832), [PDF](https://arxiv.org/pdf/2108.07832.pdf)\] \[Abstract: \] ## Summary - shows that the scattering problem (in terms of potential for the scalar field) are not uniquely determined at special points in the parameter space - explains [[0179 Pole skipping]] by mapping to a quantum mechanical scattering problem # Nguyen, Salzer ## Celestial IR divergences and the effective action of supertranslation modes \[Links: [arXiv](https://arxiv.org/abs/2105.10526), [PDF](https://arxiv.org/pdf/2105.10526.pdf)\] \[Abstract: \] ## Refs - talk at [[Rsc0034 Corfu Celestial workshops]] - [[0295 Infrared divergences in scattering amplitude]] - earlier paper on effective action of superrotation modes: [[NguyenSalzer2020]] ## Boundary location - ![[NguyenSalzer2021_fig_1.png|300]] # Okuyama, Sakai ## FZZT branes in JT gravity and topological gravity \[Links: [arXiv](https://arxiv.org/abs/2108.03876), [PDF](https://arxiv.org/pdf/2108.03876)\] \[Abstract: We study [[0658 FZZT brane|Fateev-Zamolodchikov-Zamolodchikov-Teschner (FZZT) branes]] in Witten-Kontsevich topological gravity, which includes [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] as a special case. Adding FZZT branes to topological gravity corresponds to inserting determinant operators in the dual matrix integral and amounts to a certain shift of the infinitely many couplings of topological gravity. We clarify the perturbative interpretation of adding FZZT branes in the genus expansion of topological gravity in terms of a simple boundary factor and the generalized [[0617 Weil-Petersson volume|Weil-Petersson volumes]]. As a concrete illustration we study JT gravity in the presence of FZZT branes and discuss its relation to the deformations of the dilaton potential that give rise to conical defects. We then construct a non-perturbative formulation of FZZT branes and derive a closed expression for the general correlation function of multiple FZZT branes and multiple macroscopic loops. As an application we study the FZZT-macroscopic loop correlators in the Airy case. We observe numerically a void in the eigenvalue density due to the eigenvalue repulsion induced by FZZT-branes and also the oscillatory behavior of the [[0062 Spectral form factor|spectral form factor]] which is expected from the picture of eigenbranes.\] # Paquette, Williams ## Koszul duality in quantum field theory \[Links: [arXiv](https://arxiv.org/abs/https://arxiv.org/abs/2110.10257), [PDF](https://arxiv.org/pdf/https://arxiv.org/abs/2110.10257.pdf)\] \[Abstract: In this article, we introduce basic aspects of the algebraic notion of [[0510 Koszul duality|Koszul duality]] for a physics audience. We then review its appearance in the physical problem of coupling QFTs to topological line defects, and illustrate the concept with some examples drawn from twists of various simple supersymmetric theories. Though much of the content of this article is well-known to experts, the presentation and examples have not, to our knowledge, appeared in the literature before. Our aim is to provide an elementary introduction for those interested in the appearance of Koszul duality in supersymmetric gauge theories with line defects and, ultimately, its generalizations to higher-dimensional defects and [[0130 Twisted holography|twisted holography]].\] # Partouche, Toumbas, de Vaulchier ## Gauge fixing and field redefinitions of the Hartle--Hawking wavefunction path integral \[Links: [arXiv](https://arxiv.org/abs/2105.04818), [PDF](https://arxiv.org/pdf/2105.04818)\] \[Abstract: We review some recent results concerning the [[0162 No-boundary wavefunction|Hartle-Hawking wavefunction]] of the universe. We focus on pure Einstein theory of gravity in the presence of a positive cosmological constant. We carefully implement the gauge-fixing procedure for the [[0254 Minisuperspace|minisuperspace]] path integral, by identifying the single modulus and by using diffeomorphism-invariant measures for the ghosts and the scale factor. Field redefinitions of the scale factor yield different prescriptions for computing the no-boundary ground-state wavefunction. They give rise to an infinite set of ground-state wavefunctions, each satisfying a different [[0345 Wheeler-DeWitt (WdW) equation|Wheeler-DeWitt equation]], at the semi-classical level. The differences in the form of the Wheeler-DeWitt equations can be traced to ordering ambiguities in constructing the Hamiltonian upon canonical quantization. However, the inner products of the corresponding Hilbert spaces turn out to be equivalent, at least semi-classically. Thus, the model yields universal quantum predictions.\] # Pasterski, Puhm, Trevisani (May, a) ## Celestial Diamonds: Conformal Multiplets in Celestial CFT \[Links: [arXiv](https://arxiv.org/abs/2105.03516), [PDF](https://arxiv.org/pdf/2105.03516.pdf)\] \[Abstract: We examine the structure of global conformal multiplets in 2D [[0010 Celestial holography|celestial CFT]]. For a 4D bulk theory containing massless particles of spin $s=\{0,\frac{1}{2},1,\frac{3}{2},2\}$ we classify and construct all $SL(2,\mathbb{C})$ primary descendants which are organized into '[[0288 Celestial diamonds|celestial diamonds]]'. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with $SL(2,\mathbb{C})$ conformal dimension $\Delta$ and spin $J$. Radiative [[0148 Conformal basis|conformal primary wavefunctions]] have $J=\pm s$ and give rise to [[0390 Conformally soft theorems|conformally soft theorems]] for special values of $\Delta \in \frac{1}{2}\mathbb{Z}$. They are located either at the top of celestial diamonds, where they descend to trivial [[0034 Null states|null]] primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have $|J|\leq s$. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D [[0039 Shadow transform|shadow transform]] relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.\] ## Refs - a second part of this work later same month [[2021#Pasterski, Puhm, Trevisani (May, b)]] - generalised conformal primary WF explained in [[2020#Pasterski, Puhm]] ## Summary - (sec.3) classify and construct all $SL(2,\mathbb{C})$ primary descendants (n.b. not necessarily [[0034 Null states|null states]]) which are organised into [[0288 Celestial diamonds|celestial diamonds]] for spins $s=\{0,\frac{1}{2},1,\frac{3}{2},2\}$ - (sec.4) specialise to [[0010 Celestial holography|celestial CFTs]] ## Two forms of primary WF - **radiative**, $J=\pm s$: solve linearised EOM for massless spin-$s$ particles - **generalised** conformal primary WF, $|J|\le s$: allow sources and distributions; EOM not required to be satisfied # Pasterski, Puhm, Trevisani (May, b) ## Revisiting the Conformally Soft Sector with Celestial Diamonds \[Links: [arXiv](https://arxiv.org/abs/2105.09792), [PDF](https://arxiv.org/pdf/2105.09792.pdf)\] \[Abstract: [[0288 Celestial diamonds|Celestial diamonds]] encode the structure of global conformal multiplets in 2D [[0010 Celestial holography|celestial CFT]] and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to [[0390 Conformally soft theorems|conformally soft factorization theorems]], the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized currents. We then identify the top corners of the associated Goldstone diamonds with conformal [[0272 Faddeev-Kulish|Faddeev-Kulish dressings]] and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions. Finally, we combine these ingredients to speculate on 2D effective descriptions for the conformally soft sector of celestial CFT.\] ## Refs - an immediate followup to [[2021#Pasterski, Puhm, Trevisani (May, a)]] ## Example: gravity ![[PasterskiPuhmTrevisani202105b_fig1b.png]] - Goldstone diamonds: - red - (right) $h_{1,+2 ; \mu \nu}^{\mathrm{G}}=m_\mu m_\nu \varphi^1$: leading soft graviton theorem - (left) $h_{1,-2 ; \mu \nu}^{\mathrm{G}}=\bar m_\mu \bar m_\nu \varphi^1$: leading soft graviton theorem for negative helicity, but in this case it is also the shadow of the right corner (i.e. degeneracy) - top? - bottom? - dark blue - (right) $\widetilde{h}^{\mathrm{G}}_{2,+2 ; \mu \nu}=-X^2 m_\mu m_\nu \varphi^2$: shadow of the subleading soft graviton theorem for positive helicity - (left) ${h}^{\mathrm{G}}_{0,-2 ; \mu \nu}=\bar m_\mu \bar m_\nu$: subleading soft graviton theorem for negative helicity - top? - bottom? - light blue - (right) ${h}^{\mathrm{G}}_{0,2 ; \mu \nu}=m_\mu m_\nu$: subleading soft graviton theorem for positive helicity - (left) $\widetilde{h}^{\mathrm{G}}_{2,-2 ; \mu \nu}=-X^2 \bar m_\mu \bar m_\nu \varphi^2$: shadow of the subleading soft graviton theorem for negative helicity - gray - subsubleading soft graviton - memory diamonds: - canonically paired partners ## Soft charges - $Q_\zeta^{s o f t}=\int d^2 z \zeta(z, \bar{z}) \cdot \mathcal{O}^{s o f t}(z, \bar{z})$ # Pedraza, Russo, Svesko, Weller-Davies ## Lorentzian threads as 'gatelines' and holographic complexity \[Links: [arXiv](https://arxiv.org/abs/2106.12585), [PDF](https://arxiv.org/pdf/2106.12585.pdf)\] \[Abstract: \] # Pook-Kolb, Hennigar, Booth ## A Pair of Pants for the Apparent Horizon \[Links: [arXiv](https://arxiv.org/abs/2104.10265), [PDF](https://arxiv.org/pdf/2104.10265.pdf)\] \[Abstract: \] ## Refs - [[BoothHennigarPook-Kolb2021]] ## Summary - *identifies* for the first time an apparently infinite number of MOTSs present in [[0285 Brill-Lindquist initial data]] - *discusses* the role these new MOTSs play in resolving the final fate of the [[0226 Apparent horizon]]s of the two original black holes - MOTS can annihilate each other - *discusses* the stability of these surfaces ## Comments - evolution of event horizon during merger was long known (see book by Hawking and Ellis) # Porfyriadis, Remmen ## Large Diffeomorphisms and Accidental Symmetry of the Extremal Horizon \[Links: [arXiv](https://arxiv.org/abs/2112.13853), [PDF](https://arxiv.org/pdf/2112.13853.pdf)\] \[Abstract: \] ## Comments - can have matter field (massless) or no matter field - looks like JT ## Summary - doing a transformation on $h_{\mu\nu}$ where $g_{\mu\nu}=\bar{g}_{\mu\nu}+h_{\mu\nu}$ leaves the linearised Einstein equation satisfied. This of course contains the usual $SR(2)$ transformation, but it can be also some other transformation. - more like a solution generating transformation than a symmetry <!-- comment by garyhorowitz --> # Qi, Shangnan, Yang ## Holevo information and ensemble theory of gravity \[Links: [arXiv](https://arxiv.org/abs/2111.05355), [PDF](https://arxiv.org/pdf/2111.05355.pdf)\] \[Abstract: \] ## Summary - [[0268 Holevo information]] gives a notion of ==size of the ensemble== - for random tensor network with large bond dimensions, shows that [[0268 Holevo information]] is determined by the difference between the trivial entanglement wedge and the actual entanglement wedge - conjectures a formula for quantum gravity - e.g. after Page time [[0268 Holevo information]] is given by the difference between Hawking entropy and Page entropy - in [[0201 Sachdev-Ye-Kitaev model|SYK]] - thermal state: Holevo given by difference between maximal entropy and thermal entropy - TFD: determined by fermion equal-time correlation between two sides - agrees with the conjecture ## Trivial entanglement wedge - with a bath, it is just the bath - without a bath, the Holevo information seems divergent - so introduce a regularisation ## Comment on random couplings - the random parameters are not associated with different states in the bulk, but with different mappings from bulk to boundary; i.e., the random parameters in the tensors physically correspond to random parameters in the bulk-to-boundary isometry # Reeves, Rozali, Simidzija, Sully, Waddell, Wakeham ## Looking for (and not finding) a bulk brane \[Links: [arXiv](https://arxiv.org/abs/2108.10345), [PDF](https://arxiv.org/pdf/2108.10345.pdf)\] \[Abstract: \] ## Summary - when is there good dual for [[0181 AdS-BCFT]]? -> almost never! ## Refs - good dual stuff for CFT [[2009#Heemskerk, Penedones, Polchinski, Sully]] # Rosso, Turiaci ## Phase transitions for deformations of JT supergravity and matrix models \[Links: [arXiv](https://arxiv.org/abs/2111.09330), [PDF](https://arxiv.org/pdf/2111.09330.pdf)\] \[Abstract: \] ## Summary ## Comments - from [[gravitylunch]]: trying to address a paradox: some problem when deforming the JT gravity (get negative density of states) but not obvious what the gravity picture is # Saad, Shenker, Stanford, Yao ## Wormholes without averaging \[Links: [arXiv](https://arxiv.org/abs/2103.16754), [PDF](https://arxiv.org/pdf/2103.16754.pdf)\] \[Abstract: \] ![[SaadShenkerStanfordYao2021_sigma.png|300]] - $x$ integral is already gone ## Refs - explicit confirmation in [[0201 Sachdev-Ye-Kitaev model|SYK]] - [[2021#Mukhametzhanov]] ## [[0249 Factorisation problem]] ![[SaadShenkerStanfordYao2021_factor.png|400]] - see also [[2021#Mukhametzhanov]] # Saad, Shenker, Yao ## Comments on wormholes and factorization \[Links: [arXiv](https://arxiv.org/abs/2107.13130), [PDF](https://arxiv.org/pdf/2107.13130.pdf)\] \[Abstract: \] ## Refs - [[0249 Factorisation problem]] - [[0154 Ensemble averaging]] ## Summary - works with a specific member of the ensemble - dual to an alpha state - works with an effective model ## The model(s) - CGS model - only allow discs and cylinders - as approximations to JT and MM models ## Connection to D-branes - D-branes used in [[2020#Marolf, Maxfield (a)]] # Sasieta ## Ergodic equilibration of Renyi entropies and replica wormholes \[Links: [arXiv](https://arxiv.org/abs/2103.09880), [PDF](https://arxiv.org/pdf/2103.09880.pdf)\] \[Abstract: \] ## Summary - *studies* behaviour of Renyi entropies from chaotic assumptions - *computes* exact long time averages of Renyi entropies - *shows* that quantum noise around them is suppressed - *analyses* BH equilibrium in AdS/CFT ## Refs - [[0206 Replica wormholes]] # Shaghoulian ## The central dogma and cosmological horizons \[Links: [arXiv](https://arxiv.org/abs/2110.13210), [PDF](https://arxiv.org/pdf/2110.13210.pdf)\] \[Abstract: \] ## Summary - problem: dS bifurcation surface is minimax not maximin - suggestion: anchor [[0007 RT surface]] to horizon - result: no total entropy for two-sided prescription and $A/4$ when restricting to a single patch # Sharma (Jul) ## Ambidextrous light transforms for celestial amplitudes \[Links: [arXiv](https://arxiv.org/abs/2107.06250), [PDF](https://arxiv.org/pdf/2107.06250.pdf)\] \[Abstract: Low multiplicity celestial amplitudes of gluons and gravitons tend to be distributional in the celestial coordinates $z,\bar z$. We provide a new systematic remedy to this situation by studying celestial amplitudes in a basis of [[0412 Light transform|light transformed]] boost eigenstates. Motivated by a novel equivalence between light transforms and Witten's half-Fourier transforms to [[0330 Twistor theory|twistor]] space, we light transform every positive helicity state in the coordinate $z$ and every negative helicity state in $\bar z$. With examples, we show that this "ambidextrous" prescription beautifully recasts two- and three-point celestial amplitudes in terms of standard conformally covariant structures. These are used to extract examples of [[0114 Celestial OPE|celestial OPE]] for light transformed operators. We also study such amplitudes at higher multiplicity by constructing the Grassmannian representation of tree-level gluon celestial amplitudes as well as their light transforms. The formulae for n-point N$^{k-2}$MHV amplitudes take the form of Euler-type integrals over regions in Gr$(k,n)$ cut out by positive energy constraints.\] ## Summary ![[Sharma202107_4.24.png|400]] - *generalises* half-Fourier transforms to act on boost eigenstates - *proposes* ambidextrous light transforms of boost eigenstates as local operators in [[0010 Celestial holography|CCFT]] - because they get rid of delta functions and step functions ## Refs - follow-up - [[2022#Jorge-Diaz, Pasterski, Sharma]] - [[2022#Brown, Gowdy, Spence]] # Stanford, Yang, Yao ## Subleading Weingartens \[Links: [arXiv](https://arxiv.org/abs/2107.10252), [PDF](https://arxiv.org/pdf/2107.10252.pdf)\] \[Abstract: \] ## Expectation - at late enough time, the evolution $U$ should resemble a random unitary matrix drawn from Haar distribution - $\operatorname{Tr} \rho_{R}^{(a)} \rho_{R}^{(b)} \rightarrow \frac{1}{1-\left(d_{R} d_{B}\right)^{-2}}\left[\frac{1}{d_{R}}+\frac{\delta_{a b}}{d_{B}}-\frac{1}{d_{R} d_{B}^{2}}-\frac{\delta_{a b}}{d_{B} d_{R}^{2}}\right]$ - first term: dominate at early times (i.e. when $d_R$ is small compared to $d_B$) so gives the Hawking answer (i.e. before Page time) - 2nd term: replica wormhole contribution - 3rd and 4th terms are ==crucial for unitarity== - negative and non-perturbative ## RM calculation - $\int \mathrm{d} U U_{i_{1}}^{j_{1}} U_{i_{2}}^{j_{2}} \overline{U_{k_{1}}^{l_{1}} U_{k_{2}}^{l_{2}}}=\frac{1}{L^{2}-1}\left(\delta_{i_{1}}^{l_{1}} \delta_{i_{2}}^{l_{2}} \delta_{k_{1}}^{j_{1}} \delta_{k_{2}}^{j_{2}}+\delta_{i_{1}}^{l_{2}} \delta_{i_{2}}^{l_{1}} \delta_{k_{1}}^{j_{2}} \delta_{k_{2}}^{j_{1}}-\frac{1}{L} \delta_{i_{1}}^{l_{2}} \delta_{i_{2}}^{l_{1}} \delta_{k_{1}}^{j_{1}} \delta_{k_{2}}^{j_{2}}-\frac{1}{L} \delta_{i_{1}}^{l_{1}} \delta_{i_{2}}^{l_{2}} \delta_{k_{1}}^{j_{2}} \delta_{k_{2}}^{j_{1}}\right)$ - there is a pictorial way of understanding it ## Soft modes - see appendix B ## Interesting questions - large number of $Us - how to see the plateau # Strominger ## w(1+infinity) and the Celestial Sphere \[Links: [arXiv](https://arxiv.org/abs/2105.14346), [PDF](https://arxiv.org/pdf/2105.14346.pdf)\] \[Abstract: It is shown that the infinite tower of tree-level [[0009 Soft theorems|soft graviton symmetries]] in asymptotically flat 4D quantum gravity can be organized into a single chiral 2D [[0069 Kac-Moody algebra|Kac-Moody symmetry]] based on the wedge algebra of [[0328 w(1+infinity)|w(1+infinity)]]. The infinite towers of soft photon or gluon symmetries also transform irreducibly under w(1+infinity).\] ## Refs - see also [[2021#Guevara, Himwich, Pate, Strominger]] - [[0009 Soft theorems]] ## Summary - *organises* the infinity of symmetries found in [[2021#Guevara, Himwich, Pate, Strominger]] into a ==single chiral== 2D [[0069 Kac-Moody algebra|KM algebra]] based on the ==wedge algebra== of [[0328 w(1+infinity)|w(1+infinity)]] ## Comments - reorganises the currents of $S L(2, \mathbb{R})_{R}$ into $S L(2, \mathbb{R})_{\mathrm{w}}$ ## Soft graviton algebra - $\left[w_m^p, w_n^q\right]=[m(q-1)-n(p-1)] w_{m+n}^{p+q-2}$ - where $w_n^p=\frac{1}{\kappa}(p-n-1) !(p+n-1) ! H_n^{-2 p+4}$ - where $H^k(z, \bar{z})=\sum_{n=\frac{k-2}{2}}^{\frac{2-k}{2}} \frac{H_n^k(z)}{\bar{z}^{n+\frac{k-2}{2}}}$. - where $H^k=\lim _{\varepsilon \rightarrow 0} \varepsilon G_{k+\varepsilon}^{+}$ - $k=2,1,0,-1,...$ - i.e., $p,q$ are orders in soft expansions and $m,n$ are orders in antiholomorphic expansions # Suh ## Probabilistic deconstruction of a theory of gravity, Part I: flat space \[Links: [arXiv](https://arxiv.org/abs/2108.10916), [PDF](https://arxiv.org/pdf/2108.10916.pdf)\] \[Abstract: We define and analyze a stochastic process in anti-de Sitter [[0050 JT gravity|Jackiw-Teitelboim gravity]], induced by the quantum dynamics of the boundary and whose random variable takes values in AdS$_2$. With the boundary in a thermal state and for appropriate parameters, we take the asymptotic limit of the quantum process at short time scales and flat space, and show associated classical joint distributions have the Markov property. We find that Einstein's equations of the theory, sans the cosmological constant term, arise in the semi-classical limit of the quantum evolution of probability under the asymptotic process. In particular, in flat Jackiw-Teitelboim gravity, the area of compactified space solved for by Einstein's equations can be identified as a probability distribution evolving under the Markovian process.\] ## Refs - [[0050 JT gravity]] # Takeda ## Light-cone cuts and hole-ography: explicit reconstruction of bulk metrics \[Links: [arXiv](https://arxiv.org/abs/2112.11437), [PDF](https://arxiv.org/pdf/2112.11437.pdf)\] \[Abstract: In this paper, the two reconstruction methods, light-cone cuts method and hole-ography, are combined to provide complete bulk metrics of locally AdS$_3$ static spacetimes. As examples, our method is applied to the geometries of pure AdS$_3$, AdS$_3$ soliton, and [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black hole, and we see them successfully reconstructed. The light-cone cuts method is known to have difficulty in obtaining conformal factors, while the hole-ography in describing temporal components. Combining the two methods, we overcome the disadvantages and give complete metrics for a class of holographic theories such that entanglement wedge and causal wedge coincide. [[0027 Bulk reconstruction using lightcone cuts|Light-cone cuts]] are identified by entanglement entropy in our method. We expect our study to lead to the discovery of a universal relation between the two methods, by which the combination would be applied to more generic cases.\] ## Refs - [[0027 Bulk reconstruction using lightcone cuts]] - follow-up [[2022#Sugiura, Takeda]] # Taylor, Too ## Generalised proofs of the first law of entanglement entropy \[Links: [arXiv](https://arxiv.org/abs/2112.00972), [PDF](https://arxiv.org/pdf/2112.00972.pdf)\] \[Abstract: In this paper we develop generalised proofs of the [[0372 Holographic first law of entanglement entropy|holographic first law of entanglement entropy]] using [[0209 Holographic renormalisation|holographic renormalisation]]. These proofs establish the holographic first law for non-normalizable variations of the bulk metric, hence relaxing the boundary conditions imposed on variations in earlier works. Boundary and counterterm contributions to conserved charges computed via [[0019 Covariant phase space|covariant phase space]] analysis have been explored previously. Here we discuss in detail how counterterm contributions are treated in the covariant phase approach to proving the first law. Our methodology would be applicable to generalizing other holographic information analyses to wider classes of gravitational backgrounds.\] ## Summary - generalises the proof for [[0372 Holographic first law of entanglement entropy|holographic first law of entanglement entropy]] using [[0209 Holographic renormalisation|holographic renormalisation]] - hence relaxing BC on the variations # Taylor, Woodward ## Holography, cellulations and error correcting codes \[Links: [arXiv](https://arxiv.org/abs/2112.12468), [PDF](https://arxiv.org/pdf/2112.12468.pdf)\] \[Abstract: [[0146 Quantum error correction|Quantum error correction codes]] associated with the hyperbolic plane have been explored extensively in the context of the [[0073 AdS3-CFT2|AdS3/CFT2]] correspondence. In this paper we initiate a systematic study of codes associated with holographic geometries in higher dimensions, relating cellulations of the spatial sections of the geometries to stabiliser codes. We construct analogues of the HaPPY code for three-dimensional hyperbolic space (AdS4), using both absolutely maximally entangled (AME) and non-AME codes. These codes are based on uniform regular tessellations of hyperbolic space but we note that AME codes that preserve the discrete symmetry of the polytope of the tessellation do not exist above two dimensions. We also explore different constructions of stabiliser codes for hyperbolic spaces in which the logical information is associated with the boundary and discuss their potential interpretation. We explain how our codes could be applied to interesting classes of holographic dualities based on gravity-scalar theories (such as [[0050 JT gravity|JT gravity]]) through toroidal reductions of hyperbolic spaces.\] ## Summary - higher dimensional [[0146 Quantum error correction|QEC]] code ## Subtleties in higher dimensions - uniform regular tessellations still exist in $D>3$ but they are sparse - absolutely maximally entangled states are also sparse - without AME property concatenation of cells across tessellation is non-trivial <!-- ## Refs - talk at [[Rsc0045 Fundamental aspects of gravity conference London 2022]] --> # Wall (Essay) ## Violation of unitarity in gravitational subregions \[Links: [arXiv](https://arxiv.org/abs/2104.03253), [PDF](https://arxiv.org/pdf/2104.03253.pdf)\] \[Abstract: \] <!-- ## Refs - talk [KITP](https://online.kitp.ucsb.edu/online/qgravity-c20/wall/rm/jwvideo.html) ## Comments - Don's concern ![[Wall2021Essay_worry.png|500]] - some other operator attached to $e^{-\beta H/2}$ so that the result is not manifestly positive --> # Witten (Nov) ## A Note On Complex Spacetime Metrics \[Links: [arXiv](https://arxiv.org/abs/2111.06514), [PDF](https://arxiv.org/pdf/2111.06514.pdf)\] \[Abstract: For various reasons, it seems necessary to include [[0335 Complex metrics|complex saddle]] points in the "Euclidean" [[0555 Gravitational path integral|path integral]] of General Relativity. But some sort of restriction on the allowed complex saddle points is needed to avoid various unphysical examples. In this article, a speculative proposal is made concerning a possible restriction on the allowed saddle points in the gravitational path integral. The proposal is motivated by recent work of [[2021#Kontsevich, Segal|Kontsevich and Segal]] on complex metrics in quantum field theory, and earlier work of [[1995#Louko, Sorkin|Louko and Sorkin]] on topology change from a real time point of view.\] # Witten (Dec, a, Review) ## Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit? \[Links: [arXiv](https://arxiv.org/abs/2112.11614), [PDF](https://arxiv.org/pdf/2112.11614.pdf)\] \[Abstract: This article aims to explain some of the basic facts about the questions raised in the title, without the technical details that are available in the literature. We provide a gentle introduction to some rather classical results about quantum field theory in curved spacetime and about the thermodynamic limit of quantum statistical mechanics. We also briefly explain that these results have an analog in the large $N$ limit of gauge theory.\] # Witten (Dec, b) ## Gravity and the Crossed Product \[Links: [arXiv](https://arxiv.org/abs/2112.12828), [PDF](https://arxiv.org/pdf/2112.12828.pdf)\] \[Abstract: Recently [[2021#Leutheusser, Liu (Oct)]] and [[LeutheusserLiu202112]] identified an emergent algebra of Type III${}_1$ in the operator algebra of $\mathcal{N}=4$ super Yang-Mills theory for large $N$. Here we describe some $1/N$ corrections to this picture and show that the emergent Type III${}_1$ algebra becomes an algebra of Type II$_{\infty}$. The Type II$_{\infty}$ algebra is the crossed product of the Type III$_1$ algebra by its modular automorphism group. In the context of the emergent Type II$_{\infty}$ algebra, the [[0004 Black hole entropy|entropy]] of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics.\] ## Refs - extends [[2021#Leutheusser, Liu (Oct)]] and [[LeutheusserLiu202112]] ## Summary - including large $N$ corrections deforms a III${}_1$ algebra to one with a trivial centre: Type II${}_\infty$ ## Generalised free field - because the single trace operators have Gaussian correlation functions # Xie, Zhang, Silva, de Rham, Witek, Yunes ## Square Peg in a Circular Hole: Choosing the Right Ansatz for Isolated Black Holes in Generic Gravitational Theories \[Links: [arXiv](https://arxiv.org/abs/2103.03925), [PDF](https://arxiv.org/pdf/2103.03925.pdf)\] \[Abstract: The metric of a spacetime can be greatly simplified if the spacetime is [[0578 Circular spacetimes|circular]]. We prove that in generic effective theories of gravity, the spacetime of a stationary, axisymmetric and asymptotically flat solution must be circular if the solution can be obtained perturbatively from a solution in the general relativity limit. This result applies to a broad class of gravitational theories that include arbitrary scalars and vectors in their light sector, so long as their nonstandard kinetic terms and nonmininal couplings to gravity are treated perturbatively.\] ## Class of theories considered - $f(R)$ gravity, [[0140 Scalar-tensor theory|scalar tensor theory]], quadratic gravity, etc