# Abbasi, Kaminski ## Constraints on quasinormal modes and bounds for critical points from pole-skipping \[Links: [arXiv](https://arxiv.org/abs/2012.15820), [PDF](https://arxiv.org/pdf/2012.15820.pdf)\] \[Abstract: We consider a holographic thermal state and perturb it by a scalar operator whose associated real-time [[0473 Retarded Green's function|Green's function]] has only gapped poles. These gapped poles correspond to the non-hydrodynamic quasinormal modes of a massive scalar perturbation around a Schwarzschild black brane. Relations between [[0179 Pole skipping|pole-skipping]] points, critical points and quasinormal modes in general emerge when the mass of the scalar and hence the dual operator dimension is varied. First, this novel analysis reveals a relation between the location of a mode in the infinite tower of [[0325 Quasi-normal modes|quasinormal modes]] and the number of pole-skipping points constraining its dispersion relation at imaginary momenta. Second, for the first time, we consider the radii of convergence of the derivative expansions about the gapped quasinormal modes. These convergence radii turn out to be bounded from above by the set of all pole-skipping points. Furthermore, a transition between two distinct classes of critical points occurs at a particular value for the conformal dimension, implying close relations between critical points and pole-skipping points in one of those two classes. We show numerically that all of our results are also true for gapped modes of vector and tensor operators.\] # Adami, Sheikh-Jabbari, Taghiloo, Yavartanoo, Zwikel ## Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases \[Links: [arXiv](https://arxiv.org/abs/2007.12759), [PDF](https://arxiv.org/pdf/2007.12759.pdf)\] \[Abstract: We carry out in full generality and without fixing specific boundary conditions, the symmetry and charge analysis near a generic null surface for two and three dimensional (2d and 3d) gravity theories. In 2d and 3d there are respectively two and three charges which are generic functions over the codimension one null surface. The integrability of charges and their algebra depend on the state-dependence of symmetry generators which is a priori not specified. We establish the existence of infinitely many choices that render the surface charges integrable. We show that there is a choice, the "fundamental basis", where the null boundary symmetry algebra is the Heisenberg $+$ Diff($d-2$) algebra. We expect this result to be true for $d>3$ when there is no Bondi news through the null surface.\] ## Refs - [[0060 Asymptotic symmetry]] # Afkhami-Jeddi, Cohn, Hartman, Tajdini ## Free partition functions and an averaged holographic duality \[Links: [arXiv](https://arxiv.org/abs/2006.04839), [PDF](https://arxiv.org/pdf/2006.04839.pdf)\] \[Abstract: We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an [[0154 Ensemble averaging|ensemble-averaged]] free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of [[0002 3D gravity|three-dimensional gravity]] with $U(1)^c \times U(1)^c$ symmetry and a composite boundary graviton. Additionally, for small central charge $c$, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.\] # Ahn, Jahnke, Jeong, Kim, Lee, Nishida ## Classifying pole-skipping points \[Links: [arXiv](https://arxiv.org/abs/2010.16166), [PDF](https://arxiv.org/pdf/2010.16166.pdf)\] \[Abstract: We clarify general mathematical and physical properties of [[0179 Pole skipping|pole-skipping]] points. For this purpose, we analyse scalar and vector fields in hyperbolic space. This setup is chosen because it is simple enough to allow us to obtain analytical expressions for the [[0473 Retarded Green's function|Green's function]] and check everything explicitly, while it contains all the essential features of pole-skipping points. We classify pole-skipping points in three types (type-I, II, III). Type-I and Type-II are distinguished by the (limiting) behavior of the Green's function near the pole-skipping points. Type-III can arise at non-integer $i\omega$ values, which is due to a specific UV condition, contrary to the types I and II, which are related to a non-unique near-horizon boundary condition. We also clarify the relation between the pole-skipping structure of the Green's function and the near-horizon analysis. We point out that there are subtle cases where the near-horizon analysis alone may not be able to capture the existence and properties of the pole-skipping points.\] ## Summary - classifies [[0179 Pole skipping|pole skipping]] points for ==scalar and vector== fields in ==hyperbolic space== - clarifies the relation between the pole-skipping structure of the Green’s function and the near horizon analysis - discusses [[0421 Higher-spin gravity|higher spin fields]] too ## Classification - Type I and II: - non-uniqueness of ingoing solution at horizon - integer values of frequency - Type I has same number of zeros and poles; Type II has different - Green's function for type I is constant along straight lines passing through it; for type II it is quadratic or higher order - Type III: - can arise at non-integer frequencies; - due to a specific UV condition, and not to do with horizon non-uniqueness ## Type II - $\operatorname{det} \mathcal{M}^{(n)}=\alpha\left[\prod_{i=1}^{2 n}\left(k-k_{i}\right)+\left(\omega-\omega_{n}\right) f(\omega, k)\right]$: some of the $k_i$ are the same - $\left.\partial_{k} \operatorname{det} \mathcal{M}^{(n)}\right|_{*}=0$ and $\left.\partial_{k}^{2} \operatorname{det} \mathcal{M}^{(n)}\right|_{*} \neq 0$ # Akal, Kusuki, Takayanagi, Wei ## Codimension two holography for wedges \[Links: [arXiv](https://arxiv.org/abs/2007.06800), [PDF](https://arxiv.org/pdf/2007.06800.pdf)\] \[Abstract: We propose a codimension two holography between a gravitational theory on a $d+1$ dimensional wedge spacetime and a $d-1$ dimensional CFT which lives on the corner of the wedge. Formulating this as a generalization of AdS/CFT, we explain how to compute the free energy, entanglement entropy and correlation functions of the dual CFTs from gravity. In this wedge holography, the holographic entanglement entropy is computed by a double minimization procedure. Especially, for a four dimensional gravity ($d=3$), we obtain a two dimensional CFT and the holographic entanglement entropy perfectly reproduces the known result expected from the holographic conformal anomaly. We also discuss a lower dimensional example ($d=2$) and find that a universal quantity naturally arises from gravity, which is analogous to the boundary entropy. Moreover, we consider a gravity on a wedge region in Lorentzian AdS, which is expected to be dual to a CFT with a space-like boundary. We formulate this new holography and compute the holographic entanglement entropy via a Wick rotation of the AdS/BCFT construction. Via a conformal map, this wedge spacetime is mapped into a geometry where a bubble-of-nothing expands under time evolution. We reproduce the holographic entanglement entropy for this gravity dual via CFT calculations.\] ## Refs - independent work [[2020#Bousso, Wildenhain]] - later "proof" by [[Miao2020]] ## Summary - proposes [[0134 Codimension 2 holography]] ## Setup ![[AkalKusukiTakayanagiWei2020_setup.png]] - $\Sigma_{d-1}$: Dirichlet BC, effectively codim-2 - $Q1,Q2$: Neumann BC # Akers, Penington ## Leading order corrections to the quantum extremal surface prescription \[Links: [arXiv](https://arxiv.org/abs/2008.03319), [PDF](https://arxiv.org/pdf/2008.03319.pdf)\] \[Abstract: We show that a naïve application of the [[0212 Quantum extremal surface|quantum extremal surface]] (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]] (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently.\] ## Summary - naive application of QES leads to paradox at leading order - arise when there is a second QES and large incompressible bulk entropy between the two - reason: replica trick derivation of QES has wrong assumption ## Solution to the paradox - sum over all permutations for the regions interior to the two competing RT surfaces - because these are not fixed by boundary conditions ## Remarks - mixing of high and low energy - this might be the reason for RT to break down <!--- the comment that this might be the reason for RT to break down is according to Jieqiang ---> # Albayrak, Chowdhury, Kharel ## On loop celestial amplitudes for gauge theory and gravity \[Links: [arXiv](https://arxiv.org/abs/2007.09338), [PDF](https://arxiv.org/pdf/2007.09338.pdf)\] ## Refs - only one earlier paper on [[0260 Celestial loops]] although for a scalar field theory [[2017#Banerjee, Banerjee, Bhatkar, Jain]] - this paper on finite loop level amplitude. a divergent loop level amplitude is treated more recently in [[2020#Gonzalez, Puhm, Rojas]] ## Remarks - it's just doing Mellin transforms for known loop-level results, treating them in the same way as tree-level amplitudes ## Summary - loop-level ==graviton and gluon== scattering for ==(++...+) and (-+...+)== - these vanish at tree level - finite at 1-loop - explicit result for ==4 and 5 point functions== # Alday, Bae, Benjamin, Jorge-Diaz ## On the Spectrum of Pure Higher Spin Gravity \[Links: [arXiv](https://arxiv.org/abs/2009.01830), [PDF](https://arxiv.org/pdf/2009.01830)\] \[Abstract: We study the spectrum of pure massless [[0421 Higher-spin gravity|higher spin theories]] in AdS$_3$. The light spectrum is given by a tower of massless particles of spin $s=2,\cdots,N$ and their multi-particles states. Their contribution to the torus partition function organises into the vacuum character of the ${\cal W}_N$ algebra. [[0612 Modular invariance|Modular invariance]] puts constraints on the heavy spectrum of the theory, and in particular leads to negative norm states, which would be inconsistent with [[0035 Unitarity of CFT|unitarity]]. This negativity can be cured by including additional light states, below the black hole threshold but whose mass grows with the [[0033 Central charge|central charge]]. We show that these states can be interpreted as conical defects with deficit angle $2\pi(1-1/M)$. Unitarity allows the inclusion of such defects into the path integral provided $M \geq N$.\] # Altland, Sonner ## Late time physics of holographic quantum chaos \[Links: [arXiv](https://arxiv.org/abs/2008.02271), [PDF](https://arxiv.org/pdf/2008.02271.pdf)\] \[Abstract: [[0008 Quantum chaos|Quantum chaotic]] systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, [[0579 Random matrix theory|random matrix theory]]. In this paper we explain how the universal content of random matrix theory emerges as the consequence of a simple symmetry-breaking principle and its associated Goldstone modes. This allows us to write down an effective-field theory (EFT) description of quantum chaotic systems, which is able to control the level statistics up to an accuracy ${\cal O} \left(e^{-S} \right)$ with S the entropy. We explain how the EFT description emerges from explicit ensembles, using the example of a matrix model with arbitrary invariant potential, but also when and how it applies to individual quantum systems, without reference to an ensemble. Within AdS/CFT this gives a general framework to express correlations between "different universes" and we explicitly demonstrate the bulk realization of the EFT in minimal string theory where the Goldstone modes are bound states of strings stretching between bulk spectral branes. We discuss the construction of the EFT of quantum chaos also in higher dimensional field theories, as applicable for example for higher-dimensional AdS/CFT dual pairs.\] # Aminov, Grassi, Hatsuda ## Black Hole Quasinormal Modes and Seiberg-Witten Theory \[Links: [arXiv](https://arxiv.org/abs/2006.06111), [PDF](https://arxiv.org/pdf/2006.06111.pdf)\] \[Abstract: We present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld quantization conditions on [[0325 Quasi-normal modes|quasinormal mode]] frequencies in terms of the Nekrasov partition function in a particular phase of the $\Omega$-background. Our quantization conditions also enable us to find exact expressions of eigenvalues of spin-weighted spheroidal harmonics. We test the validity of our conjecture by comparing against known numerical results for Kerr black holes as well as for Schwarzschild black holes. Some extensions are also discussed.\] ## Refs - this is the original paper for [[0371 SW-QNM correspondence]] # Amstrong, Lipstein, Mei ## Color/Kinematics Duality in AdS$_4$ \[Links: [arXiv](https://arxiv.org/abs/2012.02059), [PDF](https://arxiv.org/pdf/2012.02059)\] \[Abstract: In flat space, the [[0152 Colour-kinematics duality|color/kinematics duality]] states that perturbative Yang-Mills amplitudes can be written in such a way that kinematic numerators obey the same Jacobi relations as their color factors. This remarkable duality implies [[0152 Colour-kinematics duality|BCJ relations]] for Yang-Mills amplitudes and underlies the [[0067 Double copy|double copy]] to gravitational amplitudes. In this paper, we find analogous relations for Yang-Mills [[0105 AdS amplitudes|amplitudes in AdS]]$_4$. In particular we show that the kinematic numerators of 4-point Yang-Mills amplitudes computed via Witten diagrams in momentum space enjoy a generalised gauge symmetry which can be used to enforce the kinematic Jacobi relation away from the flat space limit, and we derive deformed BCJ relations which reduce to the standard ones in the flat space limit. We illustrate these results using compact new expressions for 4-point Yang-Mills amplitudes in AdS$_4$ and their kinematic numerators in terms of spinors. We also spell out the relation to 3d conformal correlators in momentum space, and speculate on the double copy to graviton amplitudes in AdS$_4$.\] # Anegawa, Iizuka ## Notes on islands in asymptotically flat 2d dilaton BHs \[Links: [arXiv](https://arxiv.org/abs/2004.01601), [PDF](https://arxiv.org/pdf/2004.01601.pdf)\] \[Abstract: \] # Anous, Kruthoff, Mahajan ## Density matrices in quantum gravity \[Links: [arXiv](https://arxiv.org/abs/2006.17000), [PDF](https://arxiv.org/pdf/2006.17000.pdf)\] \[Abstract: \] ## Summary - inclusion of bra-ket wormholes in the gravity path integral is not a free choice - dictated by specification of a global state in the multi-universe Hilbert space ## HH versus Page - HH does not contain bra-ket wormholes ![[AnousKruthoffMahajan2020_HHvsPage.png]] # Arkani-Hamed, Pate, Raclariu, Strominger ## Celestial Amplitudes from UV to IR \[Links: [arXiv](https://arxiv.org/abs/2012.04208), [PDF](https://arxiv.org/pdf/2012.04208.pdf)\] \[Abstract: Celestial amplitudes represent 4D scattering of particles in [[0148 Conformal basis|boost]], rather than the usual energy-momentum, eigenstates and hence are sensitive to both UV and IR physics. We show that known UV and IR properties of quantum gravity translate into powerful constraints on the analytic structure of [[0010 Celestial holography|celestial]] amplitudes. For example the soft UV behavior of quantum gravity is shown to imply that the exact four-particle scattering amplitude is meromorphic in the complex boost weight plane with poles confined to even integers on the negative real axis. Would-be poles on the positive real axis from UV asymptotics are shown to be erased by a flat space analog of the AdS resolution of the [[0128 Bulk point singularity|bulk point singularity]]. The residues of the poles on the negative axis are identified with operator coefficients in the IR effective action. Far along the real positive axis, the scattering is argued to grow exponentially according to the black hole area law. Exclusive amplitudes are shown to simply factorize into conformally hard and conformally soft factors. The soft factor contains all IR divergences and is given by a celestial current algebra correlator of Goldstone bosons from spontaneously broken asymptotic symmetries. The hard factor describes the scattering of hard particles together with the boost-eigenstate clouds of soft photons or gravitons required by [[0060 Asymptotic symmetry|asymptotic symmetries]]. These provide an IR safe $\mathcal{S}$-matrix for the scattering of hard particles.\] # Armas, Jain ## Effective field theory for hydrodynamics without boosts \[Links: [arXiv](https://arxiv.org/abs/2010.15782), [PDF](https://arxiv.org/pdf/2010.15782.pdf)\] \[Abstract: We formulate the Schwinger-Keldysh effective field theory of [[0429 Hydrodynamics|hydrodynamics]] without boost symmetry. This includes a spacetime covariant formulation of classical hydrodynamics without boosts with an additional conserved particle/charge current coupled to Aristotelian background sources. We find that, up to first order in derivatives, the theory is characterised by the thermodynamic equation of state and a total of 29 independent transport coefficients, in particular, 3 hydrostatic, 9 non-hydrostatic non-dissipative, and 17 dissipative. Furthermore, we study the spectrum of linearised fluctuations around anisotropic equilibrium states with non-vanishing fluid velocity. This analysis reveals a pair of sound modes that propagate at different speeds along and opposite to the fluid flow, one charge diffusion mode, and two distinct shear modes along and perpendicular to the fluid velocity. We present these results in a new hydrodynamic frame that is linearly stable irrespective of the boost symmetry in place. This provides a unified covariant stable approach for simultaneously treating Lorentzian, Galilean, and Lifshitz fluids within an effective field theory framework and sets the stage for future studies of non-relativistic intertwined patterns of symmetry breaking.\] # Balasubramanian, Kar, Ross, Ugajin ## Spin structures and baby universes \[Links: [arXiv](https://arxiv.org/abs/2007.04333), [PDF](https://arxiv.org/pdf/2007.04333)\] \[Abstract: We extend a 2d topological model of the [[0555 Gravitational path integral|gravitational path integral]] to include sums over spin structure, corresponding to Neveu-Schwarz (NS) or Ramond (R) boundary conditions for fermions. The Euclidean path integral vanishes when the number of R boundaries is odd. This path integral corresponds to a correlator of boundary creation operators on a non-trivial baby universe Hilbert space. The [[0249 Factorisation problem|non-factorization]] necessitates a dual interpretation of the bulk path integral in terms of a product of partition functions (associated to NS boundaries) and Witten indices (associated to R boundaries), averaged over an ensemble of theories with varying Hilbert space dimension and different numbers of bosonic and fermionic states. We also consider a model with End-of-the-World (EOW) branes: the dual ensemble then includes a sum over randomly chosen fermionic and bosonic states. We propose two modifications of the bulk path integral which restore an interpretation in a single dual theory: (i) a geometric prescription where we add extra boundaries with a sum over their spin structures, and (ii) an algebraic prescription involving "spacetime [[0156 D-brane|D-branes]]". We extend our ideas to [[0050 JT gravity|Jackiw-Teitelboim gravity]], and propose a dual description of a single unitary theory with spin structure in a system with eigenbranes.\] # Banerjee, Ghosh ## MHV gluon scattering amplitudes from celestial current algebras \[Links: [arXiv](https://arxiv.org/abs/2011.00017), [PDF](https://arxiv.org/pdf/2011.00017.pdf)\] \[Abstract: We show that the [[0079 Mellin transform|Mellin transform]] of an $n$-point tree level [[0061 Maximally helicity violating amplitudes|MHV]] gluon scattering amplitude, also known as the [[0262 Celestial amplitude calculations|celestial amplitude]] in pure Yang-Mills theory, satisfies a system of $(n-2)$ linear first order partial differential equations corresponding to $(n-2)$ positive helicity gluons. Although these equations closely resemble Knizhnik-Zamolodchikov equations for $SU(N)$ current algebra there is also an additional "correction" term coming from the subleading soft gluon current algebra. These equations can be used to compute the leading term in the gluon-gluon [[0114 Celestial OPE|OPE]] on the [[0022 Celestial sphere|celestial sphere]]. Similar equations can also be written down for the momentum space tree level MHV scattering amplitudes. We also propose a way to deal with the non closure of subleading current algebra generators under commutation. This is then used to compute some subleading terms in the mixed helicity gluon OPE and our results match with those obtained from an explicit calculation using the Mellin MHV amplitude.\] ## Refs - root topic [[0010 Celestial holography]] - understanding its momentum basis origin: [[2021#Hu, Ren, Srikant, Volovich]] ## Null state - $\Psi^{a}(z, \bar{z})=\left[C_{A} L_{-1}-(\Delta+1) j_{-1}^{b} j_{0}^{b}-J_{-1}^{b} j_{0}^{b} P_{-1,-1}\right] \mathcal{O}_{\Delta,+}^{a}(z, \bar{z})=0$ (6.10) - why null state: it is a combination of descendants, but acting ascending operators on it shows that it is in fact a primary operator - derivation: ## Checking ++ OPE including subleading terms - obtained in [[2020#Ebert, Sharma, Wang]]: - $\mathcal{O}_{\Delta,+}^{a}(z, \bar{z}) \mathcal{O}_{\Delta_{1},+}^{a_{1}}\left(z_{1}, \bar{z}_{1}\right) =-i B\left(\Delta-1, \Delta_{1}-1\right)\left[\frac{f^{a a_{1} x}}{z-z_{1}}+\frac{\Delta-1}{\Delta+\Delta_{1}-2} f^{a a_{1} x} L_{-1}\right.$\left.+i\left(\frac{\Delta-1}{\Delta+\Delta_{1}-2} \delta^{a x} \delta^{a_{1} y}+\frac{\Delta_{1}-1}{\Delta+\Delta_{1}-2} \delta^{a y} \delta^{a_{1} x}\right) j_{-1}^{y}\right] \mathcal{O}_{\Delta+\Delta_{1}-1,+}^{x}\left(z_{1}, \bar{z}_{1}\right)+\cdots$ - both by symmetry and by Mellin transforming 4-point amplitude - in this paper, 3 checks 1. it is okay to not include subleading soft gluon descendants - due to null state -> the extra one is not linearly independent - for mixed helicity, there is no null state (see eqn. 9.2) 2. amplitude calculation done at 5-pt - sometimes, due to the special kinematics of three point function, some descendants decouple from the three point function. This happens, for example, in the case of gravity. So the four point function is not always a very good check. Starting from five point functions this problem is no longer there. 3. It is easy to obtain the colour-dressed $n$-point amplitude in terms of colour-ordered $(n-1)$-point amplitudes, but we want to rewrite the latter in terms of colour-ordered $(n-1)$-point amplitudes to obtain an [[0114 Celestial OPE|celestial OPE]] - when $n=4$ this is trivial (done in [[2020#Ebert, Sharma, Wang]]) - this paper does it for $n=5$ which is slightly more non-trivial (colour) (see eq. B.37) # Banerjee, Ghosh, Gonzo ## BMS Symmetry of Celestial OPE \[Links: [arXiv](https://arxiv.org/abs/2002.00975), [PDF](https://arxiv.org/pdf/2002.00975.pdf)\] \[Abstract: In this paper we study the [[0064 BMS group|BMS]] symmetry of the celestial OPE of two positive helicity gravitons in Einstein theory in four dimensions. The [[0114 Celestial OPE|celestial OPE]] is obtained by [[0079 Mellin transform|Mellin transforming]] the scattering amplitude in the (holomorphic) [[0078 Collinear limit|collinear limit]]. The collinear limit at leading order gives the singular term of the celestial OPE. We compute the first subleading correction to the OPE by analysing the four graviton scattering amplitude directly in Mellin space. The subleading term can be written as a linear combination of BMS descendants with the OPE coefficients determined by BMS algebra and the coefficient of the leading term in the OPE. This can be done by defining a suitable BMS primary state. We find that among the descendants, which appear at the first subleading order, there is one which is created by holomorphic supertranslation with simple pole on the [[0022 Celestial sphere|celestial sphere]].\] ## Remarks - emphasises the BMS symmetry of celestial CFT, which should help with understanding [[0098 BMS blocks|BMS blocks]] - explains a difference between CFT and CCFT: [[0041 CFT vs CCFT|CFT vs CCFT]] - [[0032 Virasoro algebra|Virasoro descendants]] do not appear ($L_{-n}$ for $n>1$) at the order studied in this paper ## Refs - [talk](https://youtu.be/dd7UEFTHZdY) at ICTS ## Summary - Compute the first ==*subleading*== correction to OPE - by analysing the ==4-graviton== *scattering amplitude* for the spin ==$(--++)$ case== - directly in Mellin space - Subleading terms in collinear limit give the subleading terms in celestial OPE - linear combination of *BMS descendants* - only for the ==$++\rightarrow +$== case - Also show that OPE can be obtained from BMS algebra - once one defines a suitable notion of BMS primary state ## An assumption about BMS primaries - sec. 8.0 ## Extra $u$ coordiante - uses extra $u$ coordinate as a regulator and taken to 0 as the end to obtain the celestial sphere - Overcompleteness (from Overleaf notes: section 4: a basis adapted to $\mathscr{I}$) - The only issue is that since the PSS conformal basis is complete, adding an extra label $u\in\mathbb{R}$ only makes this modified conformal basis over-complete. To see this, simply use the inverse Mellin transform to substitute for $\phi(\eta\,\omega\,q)$: - $\phi_{h,\bar h}^\eta(u,z,\bar z) = \int_0^\infty\mathrm{d}\omega\,\omega^{\mathrm{i}\lambda}\,\mathrm{e}^{-\mathrm{i}\eta\omega u}\int_{-1-\mathrm{i}\infty}^{1+\mathrm{i}\infty}\frac{\mathrm{d}\delta}{2\pi\mathrm{i}}\,\omega^{-\delta}\,\phi_{\frac{\delta+l}{2},\frac{\delta-l}{2}}^\eta(z,\bar z)$ - This expresses the modified basis as a "linear combination'' of the PSS basis. ## Central charge - central charges for the BMS algebra are not known - in this paper, not needed at first subleading order, but need it for higher ## Extensions - [[2019#Fan, Fotopoulos, Taylor]]: OPEs of a field plus some current - [[2019#Fotopoulos, Stieberger, Taylor, Zhu]]: OPEs of other operators - compare more subleading OPE coefficients obtained by symmetry (which depends on the central charges) with Mellin transformed amplitudes to get the central charge # Banerjee, Ghosh, Paul ## MHV graviton scattering amplitudes and current algebra on the celestial sphere \[Links: [arXiv](https://arxiv.org/abs/2008.04330), [PDF](https://arxiv.org/pdf/2008.04330.pdf)\] \[Abstract: The [[2014#Cachazo, Strominger|Cachazo-Strominger]] subleading soft graviton theorem for a positive helicity soft graviton is equivalent to the Ward identities for $\overline{SL(2,\mathbb C)}$ currents. This naturally gives rise to a $\overline{SL(2,\mathbb C)}$ current algebra living on the celestial sphere. The generators of the $\overline{SL(2,\mathbb C)}$ current algebra and the supertranslations, coming from a positive helicity leading soft graviton, form a closed algebra. We find that the [[0114 Celestial OPE|OPE]] of two graviton primaries in the Celestial CFT, extracted from [[0061 Maximally helicity violating amplitudes|MHV]] amplitudes, is completely determined in terms of this algebra. To be more precise, 1) The subleading terms in the OPE are determined in terms of the leading OPE coefficient if we demand that both sides of the OPE transform in the same way under this local symmetry algebra. 2) Positive helicity gravitons have [[0034 Null states|null states]] under this local algebra whose decoupling leads to differential equations for MHV amplitudes. An $n$ point MHV amplitude satisfies two systems of $(n-2)$ linear first order PDEs corresponding to $(n-2)$ positive helicity gravitons. We have checked, using Hodges' formula, that one system of differential equations is satisfied by any MHV amplitude, whereas the other system has been checked up to six graviton MHV amplitude. 3) One can determine the leading OPE coefficients from these differential equations. This points to the existence of an autonomous sector of the [[0010 Celestial holography|Celestial CFT]] which holographically computes the MHV graviton scattering amplitudes and is completely defined by this local symmetry algebra. The MHV-sector of the Celestial CFT is like a minimal model of 2-D CFT.\] ## Refs - [[0034 Null states]] - [[0114 Celestial OPE]] - [[2021#Banerjee, Ghosh, Paul]]: a followup which studies a bigger symmetry group, Virasoro ## Remarks - up to first few subleading orders (not all orders) - went to higher points (5-pt. and 6-pt.) - convention $\kappa=\sqrt{32\pi G}=2$ ## Summary - subleading soft graviton symmetry (with algebra $\overline{SL(2,\mathbb{C})}$) and supertranslation (from leading soft graviton) form a closed algebra - see [[0009 Soft theorems|soft theorems]] - find the OPE between 2 graviton primaries, extracted from [[0061 Maximally helicity violating amplitudes|MHV]] amplitudes, is completely determined by the current algebra - subleading terms determined in terms of leading - [[0034 Null states|null states]] lead to ==differential equations== for MHV amplitudes - one system of them satisfied using Hodge's formula - another checked explicitly up to 6-graviton MHV amplitude - points to existence of autonomous sector of [[0010 Celestial holography|CCFT]] ## Symmetries - supertranslations - comes from $\Delta=k=1$: leading soft graviton theorem - $S L(2, \mathbb{R})_R$-doublet: $\bar h =\pm1/2$ - generates supertranslations - in particular, $H_{\pm \frac{1}{2}, \pm \frac{1}{2}}^1$ are global translations - $\overline{SL(2,\mathbb{C})}$ current algebra - comes from $\Delta=k=0$: subleading soft graviton theorem - $S L(2, \mathbb{R})_R$-triplet: $\bar h =0,\pm1$ - $H^0_{0,0}=2\bar{L}_0$, $H^0_{0,\pm1}\propto \bar{L}_{\pm1}$ - form a closed subalgebra ## Subleading graviton-graviton OPE (11.1): $\begin{aligned} & \left.G_{\Delta_5}^{+}\left(z_5, \bar{z}_5\right) G_{\Delta_6}^{+}\left(z_6, \bar{z}_6\right)\right|_{M H V} \\ & =B\left(i \lambda_5, i \lambda_6\right)\left[-\frac{\bar{z}_{56}}{z_{56}} P_{-1,-1}+P_{-2,0}+z_{56}\left\{\left(1+i \lambda_5\right) P_{-3,0}-\frac{i \lambda_5}{i \lambda_5+i \lambda_6} J_{-2}^1 P_{-1,-1}\right\}\right. \\ & +\bar{z}_{56}\left\{\frac{2 i \lambda_5}{i \lambda_5+i \lambda_6} J_{-1}^0 P_{-1,-1}-\left(1+i \lambda_5\right) P_{-2,-1}\right\} \\ & +z_{56} \bar{z}_{56}\left\{\frac{2 i \lambda_5 i \lambda_6}{\left(i \lambda_5+i \lambda_6\right)\left(i \lambda_5+i \lambda_6+1\right)} J_{-2}^0 P_{-1,-1}-\left(1+\frac{i \lambda_5 i \lambda_6}{i \lambda_5+i \lambda_6+1}\right) P_{-3,-1}\right. \\ & \left.+\frac{i \lambda_5\left(1+i \lambda_5\right)}{2\left(i \lambda_5+i \lambda_6\right)\left(i \lambda_5+i \lambda_6+1\right)}\left(2 L_{-1} P_{-2,-1}-2 \bar{L}_{-1} P_{-3,0}+2 L_{-1} \bar{L}_{-1} P_{-2,0}-L_{-1}^2 P_{-1,-1}\right)\right\} \\ & +\cdots] G_{\Delta}^{+}\left(z_6, \bar{z}_6\right) \end{aligned}$ # Banks, Draper, Farkas ## Path Integrals for Causal Diamonds and the Covariant Entropy Principle \[Links: [arXiv](https://arxiv.org/abs/2008.03449), [PDF](https://arxiv.org/pdf/2008.03449.pdf)\] \[Abstract: We study causal diamonds in Minkowski, Schwarzschild, (anti) de Sitter, and Schwarzschild-de Sitter spacetimes using Euclidean methods. The null boundaries of causal diamonds are shown to map to isolated punctures in the Euclidean continuation of the parent manifold. Boundary terms around these punctures decrease the Euclidean action by $A_\diamond/4$, where $A_\diamond$ is the area of the holographic screen around the diamond. We identify these boundary contributions with the maximal entropy of gravitational degrees of freedom associated with the diamond.\] # Bao, Chatwin-Davies, Remmen ## Warping Wormholes with Dust: a Metric Construction of the Python's Lunch \[Links: [arXiv](https://arxiv.org/abs/2006.10762), [PDF](https://arxiv.org/pdf/2006.10762.pdf)\] \[Abstract: We show how wormholes in three spacetime dimensions can be customizably warped using pressureless matter. In particular, we exhibit a large new class of solutions in (2+1)-dimensional general relativity with energy-momentum tensor describing a negative cosmological constant and positive-energy dust. From this class of solutions, we construct wormhole geometries and study their geometric and holographic properties, including [[0007 RT surface|Ryu-Takayanagi surfaces]], [[0319 Entanglement wedge cross-section|entanglement wedge cross sections]], [[0300 Mutual information|mutual information]], and outer entropy. Finally, we construct a Python's Lunch geometry: a wormhole in asymptotically anti-de Sitter space with a local maximum in size near its middle.\] # Belin, de Boer ## Random statistics of OPE coefficients and Euclidean wormholes \[Links: [arXiv](https://arxiv.org/abs/2006.05499), [PDF](https://arxiv.org/pdf/2006.05499.pdf)\] \[Abstract: We propose an ansatz for [[0030 Operator product expansion|OPE]] coefficients in [[0008 Quantum chaos|chaotic]] conformal field theories which generalizes the [[0040 Eigenstate thermalisation hypothesis|Eigenstate Thermalization Hypothesis]] and describes any OPE coefficient involving heavy operators as a random variable with a Gaussian distribution. In two dimensions this ansatz enables us to compute higher moments of the OPE coefficients and analyse two and four-point functions of OPE coefficients, which we relate to genus-2 partition functions and their squares. We compare the results of our ansatz to solutions of Einstein gravity in AdS$_3$, including a Euclidean wormhole that connects two genus-2 surfaces. Our ansatz reproduces the non-perturbative correction of the wormhole, giving it a physical interpretation in terms of OPE statistics. We propose that calculations performed within the semi-classical low-energy gravitational theory are only sensitive to the random nature of OPE coefficients, which explains the apparent lack of [[0249 Factorisation problem|factorization]] in products of partition functions.\] ## Summary - *proposes* an ansatz for OPE coefficients in ==chaotic== CFTs - generalises [[0040 Eigenstate thermalisation hypothesis]] - describes an OPE coefficients involving heavy operators as a random variable with a Gaussian distribution - in 2d, *enables* computation of higher moments of OPE coefficients and analysis of 2 and 4 point functions of OPE coefficients - *relates* them to genus-2 partition functions and their squares - *compare* to solutions of AdS${}_3$ - including Euclidean wormhole - *reproduces* non-perturbative correction to Euclidean wormhole - *proposes* that semi-classical gravity only know about the random nature of OPE coefficients - i.e. gravity captures the part of CFT described by the OPE randomness hypothesis - explains lack of [[0249 Factorisation problem|factorisation]] ## [[0154 Ensemble averaging|Ensemble averaging]] - the discussion does not require ensemble - but if we do take an ensemble average -> then the gravity is exact (since ansatz become exact?) ## $S_{ijklmn}$ - constrained by genus-3 partition function, but not clear exactly how ## Why genus 2 - Cotler et al considers torus boundary which has no curvature so there is no saddle connecting them, but genus-2 boundary has curvature - genus-2 seems useful to expand things as OPE coefficients ## Why chaotic - holographic CFTs are maximally chaotic with a large number degrees of freedom - $Z^2$ calculated microscopically should be a perfect square, but the ansatz of OPE coefficients is an approximation - this approximation makes it not a perfect square, and the deviation is captured by gravitational wormholes ## The bulk - Wormhole connecting two genus-2 boundaries - from [[2004#Maldacena, Maoz]] ## Comments - Henry Maxfield said it's interesting and can look into it if looking for ideas ## Future - a puzzle: ansatz predicts a bulk with a torus boundary, which no solution is in AdS3 gravity 1. maybe there will be a solution with matter fields 2. maybe non-saddle configurations (certainly exist) # Belin, de Boer, Nayak, Sonner ## Charged Eigenstate Thermalization, Euclidean Wormholes and Global Symmetries in Quantum Gravity \[Links: [arXiv](https://arxiv.org/abs/2012.07875), [PDF](https://arxiv.org/pdf/2012.07875.pdf)\] \[Abstract: We generalize the [[0040 Eigenstate thermalisation hypothesis|eigenstate thermalization hypothesis]] to systems with global symmetries. We present two versions, one with microscopic charge conservation and one with exponentially suppressed violations. They agree for correlation functions of simple operators, but differ in the variance of charged one-point functions at finite temperature. We then apply these ideas to holography and to gravitational low-energy effective theories with a global symmetry. We show that Euclidean wormholes predict a non-zero variance for charged one-point functions, which is incompatible with microscopic charge conservation. This implies that global symmetries in quantum gravity must either be gauged or explicitly broken by non-perturbative effects.\] # Benjamin, Collier, Maloney ## Pure gravity and conical defects \[Links: [arXiv](https://arxiv.org/abs/2004.14428), [PDF](https://arxiv.org/pdf/2004.14428.pdf)\] \[Abstract: We revisit the spectrum of pure quantum gravity in AdS$_3$. The computation of the torus partition function will -- if computed using a [[0555 Gravitational path integral|gravitational path integral]] that includes only smooth saddle points -- lead to a density of states which is not physically sensible, as it has a negative degeneracy of states for some energies and spins. We consider a minimal cure for this non-unitarity of the pure gravity partition function, which involves the inclusion of additional states below the black hole threshold. We propose a geometric interpretation for these extra states: they are conical defects with deficit angle $2\pi(1-1/N)$, where $N$ is a positive integer. That only integer values of $N$ should be included can be seen from a modular bootstrap argument, and leads us to propose a modest extension of the set of saddle-point configurations that contribute to the gravitational path integral: one should sum over orbifolds in addition to smooth manifolds. These orbifold states are below the black hole threshold and are regarded as massive particles in AdS, but they are not perturbative states: they are too heavy to form multi-particle bound states. We compute the one-loop determinant for gravitons in these orbifold backgrounds, which confirms that the orbifold states are Virasoro primaries. We compute the gravitational partition function including the sum over these orbifolds and find a finite, modular invariant result; this finiteness involves a delicate cancellation between the infinite tower of orbifold states and an infinite number of instantons associated with $PSL(2,{\mathbb Z})$ images.\] ## Remarks - a minimal cure to negative density of states found in [[2007#Maloney, Witten]] by including conical defects - essentially adding positive contributions to the negative density of states # Berenstein, Grabovsky ## The tortoise and the hare: a causality puzzle in AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/2011.08934), [PDF](https://arxiv.org/pdf/2011.08934.pdf)\] \[Abstract: We pose and resolve a holographic puzzle regarding an apparent violation of [[0252 Causality of HEE|causality]] in AdS/CFT. If a point in the bulk of AdS moves at the speed of light, the boundary subregion that encodes it may need to move superluminally to keep up. With AdS$_3$ as our main example, we prove that the finite extent of the encoding regions prevents a paradox. We show that the length of the minimal-size encoding interval gives rise to a tortoise coordinate on AdS that measures the nonlocality of the encoding. We use this coordinate to explore circular and radial motion in the bulk before passing to the analysis of bulk null geodesics. For these null geodesics, there is always a critical encoding where the possible violation of causality is barely avoided. We show that in any other encoding, the possible violation is subcritical.\] ## Refs - [[2014#Headrick, Hubeny, Lawrence, Rangamani]] ## Summary - generalises [[2000#Gao, Wald]] in the sense that the point can stay entirely in the bulk - revolves a causality issue in ==pure AdS${}_3$== - first in several special cases - then a general proof ## Comments Using EWN, the race condition can be proven for general spacetimes satisfying [[0480 Null energy condition|NEC]]. If we relax EWN but only require boundary causality (recall EWN implies BCC), then the race condition is true for pure AdS with spherical boundary regions. # Bhattacharya, Chanda, Maulik, Northe, Roy ## Topological shadows and complexity of islands in multiboundary wormholes \[Links: [arXiv](https://arxiv.org/abs/2010.04134), [PDF](https://arxiv.org/pdf/2010.04134.pdf)\] \[Abstract: \] # Blommaert ## Dissecting the ensemble in JT gravity \[Links: [arXiv](https://arxiv.org/abs/2006.13971), [PDF](https://arxiv.org/pdf/2006.13971.pdf)\] \[Abstract: We calculate bulk and boundary correlators in [[0050 JT gravity|JT gravity]] by summing over geometries. The answers are reproduced by computing suitable ensemble averages of correlators of [[0008 Quantum chaos|chaotic quantum systems]]. We then consider bulk correlators at large spatial separations and find that semiclassical decay eventually makes way for erratic oscillations around some nonzero answer. There is no cluster decomposition because of wormholes connecting distant regions. We construct more microscopic versions of JT gravity which are dual to a single quantum system by including a set of branes in the gravitational theory the data of which describes the Hamiltonian of the dual system. We focus on the bulk description of eigenstates which involves end of the world branes and we explain how observables [[0249 Factorisation problem|factorize]] due to geometries connecting to these branes.\] ## Comments - this is something not obvious in JT but can be seen from random matrix theory # Botta-Cantcheff, Martinez, Zarate ## Renyi entropies and area operator from gravity with Hayward term \[Links: [arXiv](https://arxiv.org/abs/2005.11338), [PDF](https://arxiv.org/pdf/2005.11338.pdf)\] \[Abstract: In the context of the holographic duality, the entanglement entropy of ordinary QFT in a subregion in the boundary is given by a quarter of the area of an minimal surface embedded in the bulk spacetime. This rule has been also extended to a suitable one-parameter generalization of the von-Neuman entropy Ŝ n that is related to the Rényi entropies Sn, as given by the area of a \emph{cosmic brane} minimally coupled with gravity, with a tension related to n that vanishes as n→1, and moreover, this parameter can be analytically extended to arbitrary real values. However, the brane action plays no role in the duality and cannot be considered a part of the theory of gravity, thus it is used as an auxiliary tool to find the correct background geometry. In this work we study the construction of the gravitational (reduced) density matrix from holographic states, whose wave-functionals are described as euclidean path integrals with arbitrary conditions on the asymptotic boundaries, and argue that in general, a non-trivial Hayward term must be haven into account. So we propose that the gravity model with a coupled Nambu-Goto action is not an artificial tool to account for the Rényi entropies, but it is present in the own gravity action through a Hayward term. As a result we show that the computations using replicas simplify considerably and we recover the holographic prescriptions for the measures of entanglement entropy; in particular, derive an area law for the original Rényi entropies (Sn) related to a minimal surface in the n replicated spacetime. Moreover, we show that the gravitational modular flow contains the area operator and can explain the Jafferis-Lewkowycz-Maldacena-Suh proposal.\] ## Refs - later paper [[AriasBotta-CantcheffMartinez2021]][](https://arxiv.org/pdf/2112.10799.pdf) ## Importance - justifies(??) [[0047 Renyi at finite n for higher derivative gravity]] ## Summary - generalises [[2019#Takayanagi, Tamaoka]] to Renyi entropy - gives a path integral definition of the area operator needed for [[0024 Fixed area states]] - shows agreement with [[0048 JLMS]] ## Block structure - $\rho_{\lambda}(A)=\bigoplus_{\Gamma} \rho_{\lambda}(B)$ - $A$ is the subregion on CFT and $B$ is some codim-1 surface between $A$ and a candidate RT surface $\Gamma$ - $\mathcal{H}_{A} \otimes \mathcal{H}_{\bar{A}} \equiv \bigoplus_{\Gamma} \mathcal{H}_{B} \otimes \mathcal{H}_{\bar{B}}$ ## Problem - [[2019#Takayanagi, Tamaoka]] uses the [[Fursaev2006]] approach - Cure: [[2018#Dong, Harlow, Marolf]] says that the $n$-dependence of Renyi entropy comes from making the geometry dynamical, so for $n$-independent fixed area states it is the right answer. # Bousso, Wildenhain ## Gravity/ensemble duality \[Links: [arXiv](https://arxiv.org/abs/2006.16289), [PDF](https://arxiv.org/pdf/2006.16289.pdf)\] \[Abstract: \] # Bueno, Camps, Lopez ## HEE for perturbative HDG \[Links: [arXiv](https://arxiv.org/abs/2012.14033), [PDF](https://arxiv.org/pdf/2012.14033.pdf)\] \[Abstract: The [[0145 Generalised area|holographic entanglement entropy functional]] for [[0006 Higher-derivative gravity|higher-curvature gravities]] involves a weighted sum whose evaluation, beyond quadratic order, requires a complicated theory-dependent splitting of the Riemann tensor components. Using the splittings of general relativity one can obtain unambiguous formulas perturbatively valid for general higher-curvature gravities. Within this setup, we perform a novel rewriting of the functional which gets rid of the weighted sum. The formula is particularly neat for general cubic and quartic theories, and we use it to explicitly evaluate the corresponding functionals. In the case of Lovelock theories, we find that the anomaly term can be written in terms of the exponential of a differential operator. We also show that order-$n$ densities involving $n_R$ Riemann tensors (combined with $n-n_R$ Ricci's) give rise to terms with up to $2n_R-2$ extrinsic curvatures. In particular, densities built from arbitrary Ricci curvatures combined with zero or one Riemann tensors have no anomaly term in their functionals. Finally, we apply our results for cubic gravities to the evaluation of universal terms coming from various symmetric regions in general dimensions. In particular, we show that the universal function characteristic of corner regions in $d=3$ gets modified in its functional dependence on the opening angle with respect to the Einstein gravity result.\] ## Refs - [[0145 Generalised area]] ## Summary - *rewrites* the [[0145 Generalised area|HEE]] formula without a weighted sum - for ==[[0341 Lovelock gravity|Lovelock]]==, writes the anomaly term as the exponential of a differential operator - shows that densities constructed exclusively from Ricci curvatures do not have an anomaly term - different from [[2013#Dong]] ## Prescription - use the splitting in Einstein, but there is no justification ## Anomaly formula - $S_{\text {Anomaly }}=32 \pi \int_{\Gamma_{A}} \mathrm{~d}^{d-1} y \sqrt{h}\left[\int_{0}^{1} \mathrm{~d} u\, u \mathrm{e}^{-F(u)}\left(\frac{\partial^{2} \mathcal{L}_{E}}{\partial R_{z i z j} \partial R_{\bar{z} k \bar{z} l}} K_{z i j} K_{\bar{z} k l}\right)\right]$ - $F(u) \equiv\left[\left(1-u^{2}\right) \mathcal{K}_{A I} \hat{\partial}^{A I}+(1-u) \mathcal{K}_{B J} \hat{\partial}^{B J}\right]$ # Burko, Khanna, Sabharwal ## Scalar and gravitational hair for extreme Kerr black holes \[Links: [arXiv](https://arxiv.org/abs/2005.07294), [PDF](https://arxiv.org/pdf/2005.07294.pdf)\] \[Abstract: For scalar perturbations of an extreme Reissner-Nordstrom black hole we show numerically that the Ori pre-factor equals the [[0340 Aretakis instability|Aretakis conserved charge]]. We demonstrate a linear relation of a generalized Ori pre-factor -- a certain expression obtained from the late-time expansion or the perturbation field at finite distances -- and the Aretakis conserved charge for a family of scalar or gravitational perturbations of an extreme Kerr black hole, whose members vary only in the radial location of the center of the initial packet. We infer that it can be established that there is an Aretakis conserved charge for scalar or gravitational perturbations of extreme Kerr black holes. This conclusion, in addition to the calculation of the Aretakis charge, can be made from measurements at a finite distance: Extreme Kerr black holes have gravitational hair that can be measured at finite distances. This gravitational hair can in principle be detected by gravitational-wave detectors.\] ## Summary - [[0340 Aretakis instability|Aretakis charges]] can be measured at a finite distance # Caceres, Vasquez, Lopez ## Entanglement entropy in cubic gravitational theories \[Links: [arXiv](https://arxiv.org/abs/2009.11595), [PDF](https://arxiv.org/pdf/2009.11595.pdf)\] \[Abstract: \] ## Summary - works on the splitting problem - use two methods to calculate the [[0145 Generalised area]] in cubic gravity - minimal coupling - non-minimal # Campoleoni, Francia, Heissenberg ## On asymptotic symmetries in higher dimensions for any spin \[Links: [arXiv](https://arxiv.org/abs/2011.04420), [PDF](https://arxiv.org/pdf/2011.04420.pdf)\] \[Abstract: We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four. For spin two we provide the counterpart of the extended BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski space. We then identify higher-spin supertranslations and generalised superrotations in any dimension. These symmetries are in one-to-one correspondence with spin-$s$ partially-massless representations on the [[0022 Celestial sphere|celestial sphere]], with supertranslations corresponding in particular to the representations with maximal depth. We discuss the definition of the corresponding asymptotic charges and we exploit the supertranslational ones in order to prove the link with [[0009 Soft theorems|Weinberg's soft theorem]] in even dimensions.\] # Casali, Puhm ## Double Copy for Celestial Amplitudes \[Links: [arXiv](https://arxiv.org/abs/2007.15027), [PDF](https://arxiv.org/pdf/2007.15027.pdf)\] \[Abstract: \] ## Summary - *shows* that there is a well-defined procedure for [[0198 Celestial double copy]] - promote the numerators to differential operators acting on external wavefunctions before squaring them # Chandrasekaran, Speranza ## Anomalies in gravitational charge algebras of null boundaries and black hole entropy \[Links: [arXiv](https://arxiv.org/abs/2009.10739), [PDF](https://arxiv.org/pdf/2009.10739.pdf)\] \[Abstract: \] # Chen, Gorbenko, Maldacena ## Bra-ket wormholes in gravitationally prepared states \[Links: [arXiv](https://arxiv.org/abs/2007.16091), [PDF](https://arxiv.org/pdf/2007.16091.pdf)\] \[Abstract: \] ## Summary - case 1: Euclidean AdS preparation followed by Euclidean flat evolution - contradiction: violation of strong subadditivity - but saved by [[0216 Bra-ket wormholes]] - case 2: Lorentzian dS followed by flat evolution - explores several [[0216 Bra-ket wormholes]] ## 2.3 Subadditivity paradox # Chen, Lin ## Signatures of global symmetry violation in relative entropies and replica wormholes \[Links: [arXiv](https://arxiv.org/abs/2011.06005), [PDF](https://arxiv.org/pdf/2011.06005.pdf)\] \[Abstract: \] ## Summary - [[0187 Global symmetries in QG]] ## Rough idea - if global symmetry -> can have a lot of positive charges in the islands and negative charges in the bath -> bad - global charges can go to baby universes -> no longer conserved ## Questions - (Zhencheng's question) Why does global symmetry -> topological operator? - see [[2018#Harlow, Ooguri (Long)]] definition 2.1d - effectively topological is part of the definition # Choi, Mezei, Sarosi ## Pole skipping away from maximal chaos \[Links: [arXiv](https://arxiv.org/abs/2010.08558), [PDF](https://arxiv.org/pdf/2010.08558.pdf)\] \[Abstract: [[0179 Pole skipping|Pole skipping]] is a recently discovered subtle effect in the thermal energy density retarded two point function at a special point in the complex $(\omega,p)$ planes. We propose that pole skipping is determined by the stress tensor contribution to many-body [[0008 Quantum chaos|chaos]], and the special point is at $(\omega,p)_\text{p.s.}= i \lambda^{(T)}(1,1/u_B^{(T)})$, where $\lambda^{(T)}=2\pi/\beta$ and $u_B^{(T)}$ are the stress tensor contributions to the [[0466 Lyapunov exponent|Lyapunov exponent]] and the [[0167 Butterfly velocity|butterfly velocity]] respectively. While this proposal is consistent with previous studies conducted for maximally chaotic theories, where the stress tensor dominates chaos, it clarifies that one cannot use pole skipping to extract the Lyapunov exponent of a theory, which obeys $\lambda\leq \lambda^{(T)}$. On the other hand, in a large class of strongly coupled but non-maximally chaotic theories $u_B^{(T)}$ is the true butterfly velocity and we conjecture that $u_B\leq u_B^{(T)}$ is a universal bound. While it remains a challenge to explain pole skipping in a general framework, we provide a stringent test of our proposal in the large-$q$ limit of the [[0201 Sachdev-Ye-Kitaev model|SYK]] chain, where we determine $\lambda,\, u_B$, and the energy density two point function in closed form for all values of the coupling, interpolating between the free and maximally chaotic limits. Since such an explicit expression for a thermal correlator is one of a kind, we take the opportunity to analyze many of its properties: the coupling dependence of the diffusion constant, the dispersion relations of poles, and the convergence properties of all order hydrodynamics.\] ## Comments - [[0179 Pole skipping|pole skipping]] at non-integer frequencies ## Summary - pole-skipping does not happen at $\omega=i\lambda_L$ for ==non-maximally== chaotic theories - conjectures that $u_{B} \leq u_{B}^{(T)}$ is a universal bound, where the latter is the true butterfly velocity, for non-maximally-chaotic systems - tested this in [[0201 Sachdev-Ye-Kitaev model|SYK]] chain in a large-$q$ limit # Colin-Ellerin, Dong, Marolf, Rangamani, Wang ## Real-time gravitational replicas: Formalism and a variational principle \[Links: [arXiv](https://arxiv.org/abs/2012.00828), [PDF](https://arxiv.org/pdf/2012.00828.pdf)\] \[Abstract: This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also describe the general structure of the resulting real-time replica wormhole saddles, setting the stage for construction of explicit examples. These saddles necessarily involve [[0335 Complex metrics|complex metrics]], and thus are accessed by deforming the original real contour of integration. However, the construction of these saddles need not rely on analytic continuation, and our formulation can be used even in the presence of non-analytic boundary-sources. Furthermore, at least for replica- and CPT-symmetric saddles we show that the metrics may be taken to be real in regions spacelike separated from a so-called 'splitting surface'. This feature is an important hallmark of unitarity in a field theory dual.\] ## Refs - [[0206 Replica wormholes]] - [[0293 Renyi entropy]] - follow-up with examples: [[2021#Colin-Ellerin, Dong, Marolf, Rangamani, Wang]] ### Summary - Lorentzian [[0206 Replica wormholes|replica wormholes]] and [[0293 Renyi entropy|Renyi entropies]] ### Mentions - see [[2004#Marolf]] for closely related language on complex metrics and boundary conditions in the path integral - the idea of using Gauss-Bonnet theory was used in [[1995#Louko, Sorkin]], but there we use a generalisation to Lorentzian - [[VanRees2009]] an alternative viewpoint of seeing how the gluing of bra and ket can be done smoothly ### Gluing - done by smooth deformation to the complex metrics - -> $i\epsilon$ in the limit where the curve connecting the bra and ket becomes tight ### 5. State preparation - state $\rho_0$ is prepared at $t_0$ and evolved to time of interest, $t$ - sometimes difficult to do this for interesting states - strategy 1: start with vacuum and insert sources - strategy 2: slice open a Euclidean path integral ### Issue: causality - we do not want the past of the splitting surface to intersect the boundary domain of dependence of the entanglement region - mentions [[Wall2012]] and [[2014#Headrick, Hubeny, Lawrence, Rangamani]] # Cotler, Jensen (Jun) ## AdS$_3$ gravity and random CFT \[Links: [arXiv](https://arxiv.org/abs/2006.08648), [PDF](https://arxiv.org/pdf/2006.08648)\] \[Abstract: We compute the path integral of [[0002 3D gravity|three-dimensional gravity]] with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asymptotically Euclidean AdS$_3$ regions with torus boundary. From our results we obtain the spectral correlations between BTZ black hole microstates near threshold, as well as extract the spectral form factor at fixed momentum, which has linear growth in time with small fluctuations around it. The low-energy limit of these correlations is precisely that of a double-scaled random matrix ensemble with [[0032 Virasoro algebra|Virasoro symmetry]]. Our findings suggest that if pure three-dimensional gravity has a holographic dual, then the dual is an ensemble which generalizes [[0579 Random matrix theory|random matrix theory]].\] # Cotler, Jensen (Jul) ##  AdS$_{3}$ wormholes from a modular bootstrap \[Links: [arXiv](https://arxiv.org/abs/2007.15653), [PDF](https://arxiv.org/pdf/2007.15653.pdf)\] \[Abstract: In recent work we computed the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. Here we employ a modular bootstrap to show that the amplitude is completely fixed by consistency conditions and a few basic inputs from gravity. This bootstrap is notably for an [[0154 Ensemble averaging|ensemble]] of CFTs, rather than for a single instance. We also compare the 3d gravity result with the Narain ensemble. The former is well-approximated at low temperature by a [[0579 Random matrix theory|random matrix theory]] ansatz, and we conjecture that this behavior is generic for an ensemble of CFTs at large [[0033 Central charge|central charge]] with a [[0008 Quantum chaos|chaotic]] spectrum of heavy operators.\] # Cotler, Jensen (Oct) ## Gravitational constrained instantons \[Links: [arXiv](https://arxiv.org/abs/2010.02241), [PDF](https://arxiv.org/pdf/2010.02241.pdf)\] \[Abstract: \] ## Related topics - [[0002 3D gravity]] # Craps, Declerck, Hacker, Nguyen, Rabideau ## Slow scrambling in extremal BTZ and microstate geometries \[Links: [arXiv](https://arxiv.org/abs/2009.08518), [PDF](https://arxiv.org/pdf/2009.08518.pdf)\] \[Abstract: \] # Cvetic, Pope, Saha, Satz ## Gaussian Null Coordinates for Rotating Charged Black Holes and Conserved Charges \[Links: [arXiv](https://arxiv.org/abs/2001.04495), [PDF](https://arxiv.org/pdf/2001.04495.pdf)\] \[Abstract: \] ## Summary - studies [[0340 Aretakis instability]] and [[0456 Newman-Penrose charges]] and [[0458 Couch-Torrence inversion isometry]] # Das, Kaushal, Liu, Mandal, Trivedi ## Gauge invariant target space entanglement in D-brane holography \[Links: [arXiv](https://arxiv.org/abs/2011.13857), [PDF](https://arxiv.org/pdf/2011.13857.pdf)\] \[Abstract: \] ## Summary - a gauge invariant version of [[DasKaushalMandalTrivedi2020]] - gives a [[0202 Gravitational interpretation of RT]] # de Haro, Skenderis, Solodukhin ## Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence \[Links: [arXiv](https://arxiv.org/abs/hep-th/0002230), [PDF](https://arxiv.org/pdf/hep-th/0002230.pdf)\] \[Abstract: We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the case of pure gravity up to six dimensions and of gravity coupled to scalars. The method can also be viewed as providing a holographic reconstruction of the bulk spacetime metric and of bulk fields on this spacetime, out of conformal field theory data. Knowing which sources are turned on is sufficient in order to obtain an asymptotic expansion of the bulk metric and of bulk fields near the boundary to high enough order so that all infrared divergences of the on-shell action are obtained. To continue the holographic reconstruction of the bulk fields one needs new CFT data: the expectation value of the dual operator. In particular, in order to obtain the bulk metric one needs to know the expectation value of stress-energy tensor of the boundary theory. We provide completely explicit formulae for the holographic stress-energy tensors up to six dimensions. We show that both the gravitational and matter conformal anomalies of the boundary theory are correctly reproduced. We also obtain the conformal transformation properties of the boundary stress-energy tensors.\] ## Summary - OG for [[0209 Holographic renormalisation|holographic renormalisation]] - explicit expressions provided up to 6 boundary dims ## Conventions - footnote 6 # DeLisle, Wilson-Gerow, Stamp ## Soft theorems from boundary terms in the classical point particle currents \[Links: [arXiv](https://arxiv.org/abs/2012.13356), [PDF](https://arxiv.org/pdf/2012.13356.pdf)\] \[Abstract: \] ## Refs - [[0010 Celestial holography]] - [[0009 Soft theorems]] ## Summary - soft factorisation holds to which order - QED: subleading - gravity: subsubleading - shows that all terms factorising at tree level can be uniquely identified as boundary terms existing at classical expressions for the electric current and stress tensor **of a point particle** - not doable beyond these orders - scalar field - boundary terms factor out of all tree level amplitudes # de Rham, Tolley ## Causality in curved spacetimes: the speed of light & gravity \[Links: [arXiv](https://arxiv.org/abs/2007.01847), [PDF](https://arxiv.org/pdf/2007.01847.pdf)\] \[Abstract: Within the low-energy effective field theories of QED and gravity, the low-energy speed of light or that of gravitational waves can typically be mildly [[0115 Superluminality|superluminal]] in curved spacetimes. Related to this, small scattering time advances relative to the curved background can emerge from known effective field theory coefficients for photons or gravitons. We clarify why these results are not in contradiction with [[0118 Causality constraints for gravity|causality]], [[0120 Analyticity constraints|analyticity]] or Lorentz invariance, and highlight various subtleties that arise when dealing with superluminalities and time advances in the gravitational context. Consistent low-energy effective theories are shown to self-protect by ensuring that any time advance and superluminality calculated within the regime of validity of the effective theory is necessarily unresolvable, and cannot be argued to lead to a macroscopically larger lightcone. Such considerations are particularly relevant for putting constraints on cosmological and gravitational effective field theories and we provide explicit criteria to be satisfied so as to ensure causality.\] ## Refs - earlier paper [[2019#de Rham, Tolley]] - earlier paper [[DeRhamFrancfortZhang2020]] ## Summary - clarify why superluminality is okay, and sometimes *demanded* by [[0120 Analyticity constraints]] and [[0118 Causality constraints for gravity]] - self-protection by ensuring that any superluminality is unresolvable ## Luminality as a criteria - [[0115 Superluminality]] - in the **decouling limits**, can require all fields to be subluminal - away from decoupling limits, demanding all fields to be subluminal is **incorrect** ## The correct criteria - retarded propagator between points far away # Dibitetto, Petri, Schillo ## Nothing really matters \[Links: [arXiv](https://arxiv.org/abs/2002.01764), [PDF](https://arxiv.org/pdf/2002.01764.pdf)\] \[Abstract: \] ## Summary - [[0168 Bubble of nothing]] in $D$ dimension with $dS_d$ factor for an arbitrary $d$ - obtained by analytically continuing the singular solution we found in [[bubble_vacua]] where both spheres shrink at the same time (cf [[0231 Bulk solutions for CFTs on non-trivial geometries]]) <!-- ## Email to gary >I just looked at the paper. It is a review of two earlier papers, one of which studies the Euclidean solutions with a product of spheres like we do ([https://arxiv.org/pdf/2002.01764.pdf](https://arxiv.org/pdf/2002.01764.pdf)). The other one studies supergravity with extra fields, so not relevant to us.  > >They seem to have constructed, in our language, the special-lambda solution for the analytic branch. That seems to be the only overlap with our work. But since we figured out that these solutions are not new (because of the Hartnoll paper), I don’t think this paper has much relevance to us.  > >They did compute the action for this analytic branch, but they did not seem to use the standard counter-term method (they used the “background subtraction method” which compares two solutions with the same boundary behaviour). The question is: what solution do they compare with if the only analytic solution we find is this black hole branch. It turns out that the solution they compare with is the singular ground state solution which we can get by taking the M \to 0 limit. In the linked paper, they made a statement (around eq.3.2 and 3.3) that these singular solutions are not singular. I think that is a wrong statement (could you check whether you agree?) and therefore the whole computation seems badly motivated.  ---> # Dodelson, Ooguri ## Singularities of thermal correlators at strong coupling \[Links: [arXiv](https://arxiv.org/abs/2010.09734), [PDF](https://arxiv.org/pdf/2010.09734.pdf)\] \[Abstract: We analyze the singularities of the two-point function in a conformal field theory at finite temperature. In a free theory, the only singularity is along the boundary light cone. In the holographic limit, a new class of [[0163 Bulk cone singularity|singularities]] emerges since two boundary points can be connected by a nontrivial null geodesic in the bulk, encircling the photon sphere of the black hole. We show that these new singularities are resolved by tidal effects due to the black hole curvature, by solving the string worldsheet theory in the Penrose limit. Singularities in the asymptotically flat black hole geometry are also discussed.\] # Dong, Qi, Shangnan, Yang ## Effective entropy of quantum fields coupled with gravity \[Links: [arXiv](https://arxiv.org/abs/2007.02987), [PDF](https://arxiv.org/pdf/2007.02987.pdf)\] \[Abstract: \] # Dong, Wang ## Enhanced corrections near holographic entanglement transitions: a chaotic case study \[Links: [arXiv](https://arxiv.org/abs/2006.10051), [PDF](https://arxiv.org/pdf/2006.10051.pdf)\] \[Abstract: \] ## Refs - talk [[Talk202008170001 Xi Dong Enhanced corrections]] ## Summary - when subsystem size is half of entire system -> phase transition -> enhanced correction to entanglement entropy - this paper does it ==holographically== - need to sum over contributions from *all* bulk saddles, including ==replica non-symmetric== ones - organized in a basis of [[0024 Fixed area states]] # Donnay, Giribet, Rosso ## Quantum BMS transformations in conformally flat spacetimes and holography \[Links: [arXiv](https://arxiv.org/abs/2008.05483), [PDF](https://arxiv.org/pdf/2008.05483.pdf)\] \[Abstract: \] ## Summary - new **superdilation** symmetry - construct quantum charges # Donnay, Pasterski, Puhm ## Asymptotic Symmetries and Celestial CFT \[Links: [arXiv](https://arxiv.org/abs/2005.08990), [PDF](https://arxiv.org/pdf/2005.08990.pdf)\] \[Abstract: We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two [[0148 Conformal basis|conformal primary wavefunctions]] become pure gauge for certain integer values of the conformal dimension $\Delta$. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for [[0010 Celestial holography|celestial CFT]] is and what the [[0060 Asymptotic symmetry|asymptotic symmetry]] group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series $\Delta\in 1+i\mathbb{R}$ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a [[0039 Shadow transform|shadow transform]] are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and $\rm{Diff}(S^2)$ asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.\] ## Summary - understand conformal primaries with analytically continued conformal dimension ($\Delta=1+\mathrm{i}\lambda$) as contour integrals (on the principle series) - => so soft **Goldstone** modes fit in to this while not augmenting the basis (which is already complete) - soft gravitons of dimension 2 <-> 0 (by shadow transform) - dimension 2: generate superrotations -> [[0060 Asymptotic symmetry|asymptotic symmetry]] is Virasoro - dimension 0: generates **shadow superrotations** -> Diff($S^2$) ## Ward identity and soft theorems - superrotation Ward identity <-> subleading soft graviton - <-: shown in [[KapecLysovPasterskiStrominger2014]] - ->: this paper - shadow superrotation Ward identity <-> subleading soft graviton - <->: [[CampigliaLaddha2014]] ## Goldstone modes (of SSB AS) - $\Delta\in \mathbb{Z}$ - related to soft asymptotic charges # Eberhardt ## Partition functions of the tensionless string \[Links: [arXiv](https://arxiv.org/abs/2008.07533), [PDF](https://arxiv.org/pdf/2008.07533.pdf)\] \[Abstract: We consider string theory on $\text{AdS}_3 \times \text{S}^3 \times \mathbb{T}^4$ in the tensionless limit, with one unit of NS-NS flux. This theory is conjectured to describe the symmetric product orbifold CFT. We consider the string on different Euclidean backgrounds such as thermal $\text{AdS}_3$, the [[0086 Banados-Teitelboim-Zanelli black hole|BTZ black hole]], conical defects and wormhole geometries. In simple examples we compute the full string partition function. We find it to be independent of the precise bulk geometry, but only dependent on the geometry of the conformal boundary. For example, the string partition function on thermal $\text{AdS}_3$ and the conical defect with a torus boundary is shown to agree, thus giving evidence for the equivalence of the tensionless string on these different background geometries. We also find that thermal $\text{AdS}_3$ and the BTZ black hole are dual descriptions and the vacuum of the BTZ black hole is mapped to a single long string winding many times asymptotically around thermal $\text{AdS}_3$. Thus the system yields a concrete example of the string-black hole transition. Consequently, reproducing the boundary partition function does not require a sum over bulk geometries, but rather agrees with the string partition function on any bulk geometry with the appropriate boundary. We argue that the same mechanism can lead to a resolution of the [[0249 Factorisation problem|factorization problem]] when geometries with disconnected boundaries are considered, since the connected and disconnected geometries give the same contribution and we do not have to include them separately.\] # Ebert, Sharma, Wang ## Descendants in celestial CFT and emergent multi-collinear factorization \[Links: [arXiv](https://arxiv.org/abs/2009.07881), [PDF](https://arxiv.org/pdf/2009.07881.pdf), [JHEP](https://link.springer.com/article/10.1007/JHEP03(2021)030)\] In this paper we try to understand a proposed duality between a 4d theory and a 2d CFT, named [[0010 Celestial holography|celestial holography]]. In particular, we obtain [[0077 Multi-collinear limit|multi-collinear limits]] of the 4d physics by bootstrapping the celestial CFT. [[0077 Multi-collinear limit|Multicollinear limits]] have very specific poles and residues as a consequence of locality and unitarity. The corresponding statement on the CFT side is however unclear. The emergence of 4d physics can be studied by trying to reproduce these poles and residues from the celestial CFT, and indeed we show that [[0060 Asymptotic symmetry|asymptotic symmetries]] alone can predict the correct poles and residues assuming the dual celestial CFT exists. Descendants in the [[0114 Celestial OPE|celestial OPE]] turned out to be very important in this regard, and this paper calculates OPE coefficients of the conformal descendants to all orders and some of those of the [[0069 Kac-Moody algebra|Kac-Moody]] descendants. ## Follow-ups - [[2020#Banerjee, Ghosh]] - deals with subleading [[0107 Soft gluon symmetry|soft gluon symmetry]] and discusses [[0034 Null states|null states]] - extends (3.21) to the mixed-helicity case ## Relevant topics - [[0077 Multi-collinear limit]] - [[0010 Celestial holography]] # Emparan, Grado-White, Marolf, Tomasevic ## Multi-mouth traversable wormholes \[Links: [arXiv](https://arxiv.org/abs/2012.07821), [PDF](https://arxiv.org/pdf/2012.07821.pdf)\] \[Abstract: \] ## Comments - has multipartite entanglement entropy - as opposed to [[AlBalushiWangMarolf2020]] which is mostly bipartite (hot limit of multiboundary wormhole in the sense of [[2015#Marolf, Maxfield, Peach, Ross]]) - relation of ## Traversability and [[0264 Multi-partite entanglement]] - seems that the time scale of traveling between different asymptotic boundaries is related to having multi-partite entanglement # Engelhardt, Fischetti, Maloney ## Free energy from replica wormholes \[Links: [arXiv](https://arxiv.org/abs/2007.07444), [PDF](https://arxiv.org/pdf/2007.07444.pdf)\] \[Abstract: \] ## Refs - talk [[Talk202010010002 Alexey Milekin Free energy and replica wormholes]] ## Summary - evidence for replica symmetry breaking - discusses ensemble averaging ## Two types of free energy - annealed $F_{\mathrm{ann}} \equiv-T \ln \mathcal{P}(B)=-T \ln \overline{Z(B)}$ - no good: - quenched $\overline{F}=-T \,\overline{\ln Z(B)}$ - more appropriate ## Main takeaway - in at least some theories of gravity, there is at least one regime in which replica WH must make a large contribution to $\overline{\ln Z}$ to avoid various pathologies - this requires some non-trivial analytic continuation, which people see in spin glasses # Engelhardt, Folkestad ## Holography abhors visible trapped surfaces \[Links: [arXiv](https://arxiv.org/abs/2012.11445), [PDF](https://arxiv.org/abs/2012.11445)\] \[Abstract: We prove that consistency of the holographic dictionary implies a hallmark prediction of the [[0221 Weak cosmic censorship|weak cosmic censorship]] conjecture: that in classical gravity, trapped surfaces lie behind event horizons. In particular, the existence of a trapped surface implies the existence of an event horizon, and that furthermore this event horizon must be outside of the trapped surface. More precisely, we show that the formation of event horizons outside of a strong gravity region is a direct consequence of [[0143 Causal wedge inclusion|causal wedge inclusion]], which is required by [[0219 Entanglement wedge reconstruction|entanglement wedge reconstruction]]. We make few assumptions beyond the absence of evaporating singularities in strictly classical gravity. We comment on the implication that spacetimes with naked trapped surfaces do not admit a holographic dual, note a possible application to holographic [[0204 Quantum complexity|complexity]], and speculate on the dual CFT interpretation of a trapped surface.\] ## Refs - [[0221 Weak cosmic censorship]] - [[0226 Apparent horizon]] ## Assumptions 1. [[0219 Entanglement wedge reconstruction|EWR]] 2. there exist unitary operators on the boundary whose effect in the bulk propagates causally 3. singularities do not evaporate without violation of [[0480 Null energy condition|NEC]] (classically) - n.b. (1) and (2) together imply [[0143 Causal wedge inclusion|CWI]] # Fan, Fotopoulos, Stieberger, Taylor ## On Sugawara construction on celestial sphere \[Links: [arXiv](https://arxiv.org/abs/2005.10666), [PDF](https://arxiv.org/pdf/2005.10666.pdf)\] \[Abstract: \] ## Summary - construct Sugawara stress tensor in YM - by double soft limit of a pair of gluons - does not generate correct conformal transformations for hard states - in ==EYM==, consider alternative construction - similar to [[0067 Double copy]] construction - does generate correct conformal transformations for both soft and hard states - extension to supertranslations ## Motivation - [[0095 Sugawara construction|Sugawara construction]] on *usual* CFT can be used to build the energy-momentum tensor in the presence of [[0069 Kac-Moody algebra|Kac-Moody algebra]] - so how about [[0010 Celestial holography]] ## Sugawara construction - only captures the soft factor of the theory - confirms earlier observation by [[CheungDelaFuenteSundrum2016]] # Fiorucci, Ruzziconi ## Charge Algebra in Al(A)dS$_n$ Spacetimes \[Links: [arXiv](https://arxiv.org/abs/2011.02002), [PDF](https://arxiv.org/pdf/2011.02002.pdf)\] \[Abstract: \] ## Refs - [[0060 Asymptotic symmetry]] ## 5. Restrictive cases - with Dirichlet boundary condition fixed to that of a sphere, the AS is always the conformal group, $SO(d,2)$, except in AdS${}_3$ where it becomes the infinite group of [[0085 Asymptotic symmetry of AdS3]] # Fortin, Ma, Skiba ## 6-point conformal blocks in the snowflake channel \[Links: [arXiv](https://arxiv.org/abs/2004.02824), [PDF](https://arxiv.org/pdf/2004.02824.pdf)\] \[Abstract: We compute $d$-dimensional scalar [[0194 Higher point conformal blocks|six-point conformal blocks]] in the two possible topologies allowed by the [[0030 Operator product expansion|operator product expansion]]. Our computation is a simple application of the embedding space operator product expansion formalism developed recently. Scalar six-point conformal blocks in the comb channel have been determined not long ago, and we present here the first explicit computation of the scalar six-point conformal blocks in the remaining inequivalent topology. For obvious reason, we dub the other topology the snowflake channel. The scalar conformal blocks, with scalar external and exchange operators, are presented as a power series expansion in the conformal cross-ratios, where the coefficients of the power series are given as a double sum of the hypergeometric type. In the comb channel, the double sum is expressible as a product of two ${}_3F_2$-hypergeometric functions. In the snowflake channel, the double sum is expressible as a Kampé de Fériet function where both sums are intertwined and cannot be factorized. We check our results by verifying their consistency under symmetries and by taking several limits reducing to known results, mostly to scalar five-point conformal blocks in arbitrary spacetime dimensions.\] ## Lessons - at each number of points, there are [[0036 Conformal bootstrap|bootstrap]] equations analogous to the crossing symmetry equation for 4-point, e.g. ![[FortinMaSkiba2020_8.png|300]] - but they are not all independent - at 6 and 7 points, there are two topologies for the conformal block channels - snowflake and comb - higher points can have more topologies # Fotopoulos, Stieberger, Taylor, Zhu ## Extended Super BMS Algebra of Celestial CFT \[Links: [arXiv](https://arxiv.org/abs/2007.03785), [PDF](https://arxiv.org/pdf/2007.03785.pdf)\] \[Abstract: We study two-dimensional [[0010 Celestial holography|celestial conformal field theory]] describing four-dimensional ${\cal N}=1$ supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of [[0064 BMS group|BMS]] symmetry. We construct fermionic [[0148 Conformal basis|conformal primary wave functions]] and show how they are related via supersymmetry to their bosonic partners. We use [[0009 Soft theorems|soft]] and [[0078 Collinear limit|collinear]] theorems of supersymmetric Einstein-Yang-Mills theory to derive the [[0114 Celestial OPE|OPEs]] of the operators associated to massless particles. The bosonic and fermionic soft theorems are shown to form a sequence under supersymmetric [[0106 Ward identity|Ward identities]]. In analogy with the energy momentum tensor, the supercurrents are [[0039 Shadow transform|shadow transforms]] of soft gravitino operators and generate an infinite-dimensional supersymmetry algebra. The algebra of $\mathfrak{sbms}_4$ generators agrees with the expectations based on earlier work on the [[0060 Asymptotic symmetry|asymptotic symmetry]] group of supergravity. We also show that the supertranslation operator can be written as a product of holomorphic and anti-holomorphic supercurrents.\] ## Refs - [[0504 Double soft limits]] - follow-ups - [[2022#Banerjee, Rahnuma, Singh]]: $\mathcal{N}=8$ [[0332 Supergravity|SUGRA]] # Freidel, Geiller, Pranzetti (I-IV) ## Edge modes of gravity I-IV \[Links: I. [arXiv](https://arxiv.org/abs/2006.12527), [PDF](https://arxiv.org/pdf/2006.12527.pdf); II. [arXiv](https://arxiv.org/abs/2007.03563), [PDF](https://arxiv.org/pdf/2007.03563.pdf); III. [arXiv](https://arxiv.org/abs/2007.12635), [PDF](https://arxiv.org/pdf/2007.12635.pdf); IV. to appear; \] ## I. Corner potentials and charges - classical-quantum relation: Kirillov orbit method - employs [[0019 Covariant phase space|CPS]] - corner symmetry algebra - *independent* of boundary conditions - v.s. boundary symmetries (in a later paper): depends on BC - dependence of corner symmetry on formulations - canonical GR has just diff(S) - others have extra symmetries - symplectic potential - GR has minimal bulk potential - other have symplectic potential equal to $\theta_{\text{GR}}$ plus a corner term ## II: Corner metric and Lorentz charges ## III. Corner simplicity constraints ## IV. Corner Hilbert space # Fuchs, Schweigert ## Bulk from boundary in finite CFT by means of pivotal module categories \[Links: [arXiv](https://arxiv.org/abs/2012.10159), [PDF](https://arxiv.org/pdf/2012.10159)\] \[Abstract: We present explicit mathematical structures that allow for the reconstruction of the field content of a full local conformal field theory from its boundary fields. Our framework is the one of modular tensor categories, without requiring semisimplicity, and thus covers in particular finite rigid logarithmic conformal field theories. We assume that the boundary data are described by a pivotal module category over the modular tensor category, which ensures that the algebras of boundary fields are Frobenius algebras. Bulk fields and, more generally, defect fields inserted on defect lines, are given by internal natural transformations between the functors that label the types of defect lines. We use the theory of internal natural transformations to identify candidates for operator products of defect fields (of which there are two types, either along a single defect line, or accompanied by the fusion of two defect lines), and for bulk-boundary OPEs. We show that the so obtained OPEs pass various consistency conditions, including in particular all genus-zero constraints in Lewellen's list.\] # Gardiner, Megas ## 2d TQFT and baby universes \[Links: [arXiv](https://arxiv.org/abs/2011.06137), [PDF](https://arxiv.org/pdf/2011.06137.pdf)\] \[Abstract: In this work, we extend a 2d topological gravity model of [[2020#Marolf, Maxfield (a)|Marolf and Maxfield]] to have as its bulk action any open/closed [[0607 Topological QFT|TQFT]] obeying Atiyah's axioms. The holographic duals of these topological gravity models are ensembles of 1d topological theories with random dimension. Specifically, we find that the TQFT Hilbert space splits into sectors, between which correlators of boundary observables factorize, and that the corresponding sectors of the boundary theory have dimensions independently chosen from different Poisson distributions. As a special case, we study in detail the gravity model built from the bulk action of 2d Dijkgraaf-Witten theory, with or without end-of-the-world branes, and for arbitrary finite group $G$. The dual of this Dijkgraaf-Witten gravity model can be interpreted as a 1d topological theory whose Hilbert space is a random representation of $G$ and whose aforementioned sectors are labeled by the irreducible representations of $G$. These holographic interpretations of our gravity models require projecting out negative-norm states from the [[0051 Baby universes|baby universe]] Hilbert space, which Marolf and Maxfield achieved by the (only seemingly) ad hoc solution of adding a nonlocal boundary term to the bulk action. In order to place their solution in the completely local framework of a TQFT with defects, we couple the boundaries of the gravity model to an auxiliary 2d TQFT in a non-gravitational (i.e. fixed topology) region. In this framework, the difficulty of negative-norm states can be remedied in a local way by the introduction of a defect line between the gravitational and non-gravitational regions. The gravity model is then holographically dual to an ensemble of boundary conditions in an [[0625 Open-closed TQFT|open/closed TQFT]] without gravity.\] # Gautason, Schneiderbauer, Sybesma, Thorlacius ## Page curve for an evaporating BH \[Links: [arXiv](https://arxiv.org/abs/2004.00598), [PDF](https://arxiv.org/pdf/2004.00598.pdf)\] \[Abstract: \] ## Refs - root [[0131 Information paradox]] # Geiller, Goeller ## Dual diffeomorphisms and finite distance asymptotic symmetries in 3d gravitya \[Links: [arXiv](https://arxiv.org/abs/2012.05263), [PDF](https://arxiv.org/pdf/2012.05263.pdf)\] \[Abstract: \] # Gesteau, Kang ## Holographic baby universes: an observable story \[Links: [arXiv](https://arxiv.org/abs/2006.14620), [PDF](https://arxiv.org/pdf/2006.14620.pdf)\] \[Abstract: We formulate the [[0051 Baby universes|baby universe]] construction rigorously by giving a primordial role to the algebra of observables of quantum gravity rather than the Hilbert space. Utilizing diffeomorphism invariance, we study baby universe creation and annihilation via change in topology. We then construct the algebra of boundary observables for holographic theories and show that it enhances to contain an 'extra' Abelian tensor factor to describe the bulk in the quantum regime; via the gravitational path integral we realize this extra tensor factor, at the level of the Hilbert space, in the context of the GNS representation. We reformulate the necessary assumptions for the "baby universe hypothesis" using the GNS representation. When the baby universe hypothesis is satisfied, we demonstrate that the "miraculous cancellations" in the corresponding gravitational path integral have a natural explanation in terms of the character theory of Abelian $C^\ast$-algebras. We find the necessary and sufficient mathematical condition for the baby universe hypothesis to hold, and transcribe it into sufficient physical conditions. We find that they are incompatible with a baby universe formation that is influenced by any bulk process from the [[0001 AdS-CFT|AdS/CFT]] correspondence. We illustrate our construction by applying it to two settings, which leads to a re-interpretion of some topological models of gravity, and to draw an analogy with the topological vacua of gauge theory.\] # Ghosh, Sarkar ## Black Hole Zeroth Law in Higher Curvature Gravity \[Links: [arXiv](https://arxiv.org/abs/2009.01543), [PDF](https://arxiv.org/pdf/2009.01543.pdf)\] \[Abstract: The zeroth law of [[0127 Black hole thermodynamics|black hole mechanics]] is an assertion of constancy of the surface gravity on a stationary Killing horizon. The Hawking temperature of the black hole horizon is proportional to the surface gravity. Therefore, the constancy of the surface gravity is reminiscent of the zeroth law of ordinary thermodynamics. In this work, we provide a proof of the zeroth law in Lanczos-Lovelock theories of gravity, where the [[0554 Einstein gravity|Einstein Hilbert action]] is supplemented by [[0006 Higher-derivative gravity|higher curvature]] terms.\] # Giddings, Turiaci ## Wormhole calculus, replicas and entropies \[Links: [arXiv](https://arxiv.org/abs/2004.02900), [PDF](https://arxiv.org/pdf/2004.02900.pdf)\] \[Abstract: \] - motivation: what is the set of quantum rules? - assume - do include bra ket wormholes etc - but do not include *all* topologies - -> what would be the quantum rules if we do? # Goel, Iliesiu, Kruthoff, Yang ## Classifying boundary conditions in JT gravity: from energy-branes to $\alpha$-branes \[Links: [arXiv](https://arxiv.org/abs/2010.12592), [PDF](https://arxiv.org/pdf/2010.12592)\] \[Abstract: We classify the possible boundary conditions in [[0050 JT gravity|JT gravity]] and discuss their exact quantization. Each boundary condition that we study will reveal new features in JT gravity related to its [[0197 Matrix model|matrix integral]] interpretation, its [[0249 Factorisation problem|factorization]] properties and [[0154 Ensemble averaging|ensemble averaging]] interpretation, the definition of the theory at finite cutoff, its relation to the physics of [[0608 Quantum effects for near-extremal black holes|near-extremal black holes]] and, finally, its role as a two-dimensional model of cosmology.\] # Gonzalez, Puhm, Rojas ## Loops on the celestial sphere \[Links: [arXiv](https://arxiv.org/abs/2009.07290), [PDF](https://arxiv.org/pdf/2009.07290.pdf)\] \[Abstract: \] ## Refs - earliest work on loop-level: scalar loops [[2017#Banerjee, Banerjee, Bhatkar, Jain]] - for finite loop-level amplitudes [[2020#Albayrak, Chowdhury, Kharel]] ## Summary - infrared divergent loops in ==planar $\mathcal{N}=4$ SYM== - compute in dimensional regularisation - can be written as operator acting on the tree-level result - BDS formula becomes an **operator** acting on the tree-level conformal correlation function # Grinberg, Maldacena ## Proper time to the BH singularity from thermal one-point functions \[Links: [arXiv](https://arxiv.org/abs/2011.01004), [PDF](https://arxiv.org/pdf/2011.01004.pdf)\] \[Abstract: We argue that the proper time from the horizon to the black hole singularity can be extracted from the [[0512 Thermal one-point functions|thermal expectation values of certain operators]] outside the horizon. This works for fields which couple to [[0006 Higher-derivative gravity|higher curvature]] terms, so that they can decay into two gravitons. To extract this time, it is necessary to vary the mass of the field.\] ## Summary - proper time from the horizon to singularity can be extracted from thermal expectation values of certain operators outside the horizon - need fields that couple to higher curvature terms - -> can decay into two gravitons ## Refs - [[0512 Thermal one-point functions]] - follow-up - [[BerensteinMancilla2022]][](https://arxiv.org/pdf/2211.05144.pdf) - [[2022#David, Kumar]] # Harlow, Shaghoulian ## Global symmetry, Euclidean gravity, and BH information \[Links: [arXiv](https://arxiv.org/abs/2010.10539), [PDF](https://arxiv.org/pdf/2010.10539.pdf)\] \[Abstract: In this paper we argue for a close connection between the non-existence of global symmetries in quantum gravity and a unitary resolution of the black hole information problem. In particular we show how the essential ingredients of recent calculations of the Page curve of an evaporating black hole can be used to generalize a recent argument against global symmetries beyond the AdS/CFT correspondence to more realistic theories of quantum gravity. We also give several low-dimensional examples of quantum gravity theories which do not have a unitary resolution of the black hole information problem in the usual sense, and which therefore can and do have global symmetries. Motivated by this discussion, we conjecture that in a certain sense Euclidean quantum gravity is equivalent to holography.\] ## Refs - talk [[Talk202011161107 Daniel Harlow QG theories with global symmetry]] ## Summary - gereralises AdS/CFT argument for no [[0187 Global symmetries in QG]] to more realistic QG - gives several examples of theories with no unitary resolution of [[0131 Information paradox]] and thus can have global symmetry - conjectures an equivalence between Euclidean QG and holography ## Proposal - unitary evaporation consistent with $S=A/4G$ -> no global symmetry ## 2. Examples - worldline of relativistic particle or string worldsheet - global symmetry: Poincare symmetry of target space - no BH -> no evaporation with BH formula - canonical quantisation of [[0050 JT gravity]] - renormalisable -> well-defined quantum theory - can have BH but not compatible with entropy formula - Euclidean path integral quantisation of JT - not the same as canonical quantisation for gravitational systems - equivalent to average over quantum systems - 2+1 pure gravity - Euclidean path integral: unclear - see [[0002 3D gravity]] - canonical - no unitary BH evaporation: - no local dof to evaporate into - the number of microstates is not compatible with the Bekenstein-Hawking formula since the quantization of the moduli space at fixed genus leads to a continuous spectrum and the sum over spatial genus is also divergent ## 3. Two approaches in JT 1. view the renormalisable bulk theory as a complete theory of QG - to have unitary evaporation: need BH entropy formula to be wrong -> this theory can have an arbitrary number of excitations near horizon -> a.k.a. remnants - allowed to have global symmetries: and it does because the matter CFT can 2. view it as a low-energy effective theory - can have holography and QES to get correct Page curve - in this case we do not know the UV theory -> the UV theory may not have global symmetry ## 4. Argument - three assumptions 1. couple reservoir $R$ and quantum gravity system $S$ s.t. an initial state of pure state BH and vacuum in $R$ has unitary evolution described by semiclassical gravity 2. for at least one initial state of the black hole, island formula works 3. coupling between $R$ and $S$ preserves global symmetry - at late enough times, there will be islands contained in the entanglement wedge of $R$, but not in the entanglement wedge of any of $S$ or any of $R_i$, the subregions of $R$ -> an operator charged under global symmetry in the island would not be recovered from the union of the subregions ## 5. Euclidean gravity and holography - **Conjecture**: The *Euclidean* path integral in a gravitational EFT with a quantum UV completion correctly computes von Neumann entropies <=> UV completion is holographic, in which case the entropies are those of the holographic theory - Hawking says thermal entropy is zero because thermal circle is proportional to $\beta$ ($S(\beta)=\left(1-\beta \partial_{\beta}\right) \log Z=0$) -> fixed by including another topology where thermal circle shrinks to zero (through bulk) -> this is holographic: the true d.o.f.s are on the boundary so okay to have different topology in bulk - i.e. Euclidean path integral (with different Euclidean topologies) is different from canonical quantisation in the bulk, but it is okay: this equivalence only need to be true at the boundary - high-low temperature duality - on boundary, the duality relates geometries where thermal circle contracts and ones where it does not - in AdS3, this reduces to modular invariance of the boundary theory - so the bulk picture is: by allowing different topologies in Euclidean gravity, we restore this high-low temperature duality in the bulk so that low energy EFT knows about high energy # Hartman, Shaghoulian, Strominger ## Islands in asymptotically flat 2D gravity \[Links: [arXiv](https://arxiv.org/abs/2004.13857), [PDF](https://arxiv.org/pdf/2004.13857.pdf)\] \[Abstract: \] ## Refs - root [[0131 Information paradox]] ## The model - CGHS + RST (dilaton) - assumes conformal matter so that [[AlmheiriMahajanMaldacenaZhao2019]] method (QES as higher dim HRT) can be used - matter - $4 \mathrm{e}^{-2 \phi}\left[\nabla_{\mu} \nabla_{\nu} \phi-g_{\mu \nu}\left(\square \phi-(\nabla \phi)^{2}+1\right)\right]=T_{\mu \nu}$ # Hartnoll, Horowitz, Kruthoff, Santos ## Gravitational duals to the grand canonical ensemble abhor Cauchy horizons \[Links: [arXiv](https://arxiv.org/abs/2006.10056), [PDF](https://arxiv.org/pdf/2006.10056.pdf)\] \[Abstract: \] ## Summary - the grand canonical ensemble -> dual to RN BH -> can have Cauchy horizons - CFT deformation by a neutral scalar operator -> generically destroys it - the scalar field triggers a rapid collapse of the ER bridge at the would-be Cauchy horizon - also comments on dilatonic BHs ## Introduction - CFT -> AdS Schwarzschild - deform CFT with a **relevant** operator -> scalar field with negative mass squared - [[FrenkelHartnollKruthoffShi2020]] - the Schwarzschild singularity generalises to a one-parameter family of Kasner like singularities - this paper: what does turning on relevant deformation mean for charged black holes - result: removes the Cauchy horizon - **irrelevant deformations**: $m^2>0$. Cauchy horizons allowed but only possible at a discrete set of $m^2$ at each temperature - irrelevant ones destroy the asymptotic AdS region -> need cut-off or allowed to flow to some UV fixed point where it is relevant -> but we only need knowledge of inside horizon ## Holographic v.s. usual - usual: generic initial conditions - here: CFT is fined tuned if relevant deformation is set to zero - holographic version is **weaker**: a source present at all time helps with not letting perturbation fall off fast enough ## Potential connections - [[0154 Ensemble averaging]] - can the probe in [[2019#Saad]] etc probe the interior as well? # Hashimoto ## Building bulk from Wilson loops \[Links: [arXiv](https://arxiv.org/abs/2008.10883), [PDF](https://arxiv.org/pdf/2008.10883.pdf)\] \[Abstract: \] ## Summary - formula for bulk metric using expectation values of Wilson loops ## Refs - much earlier work on holographic Wilson loop reviewed in [[Rsc0010 Hong Liu Lectures on holography]] - [[Talk202010050001 Koji Hashimoto Building bulk from Wilson loops]] - [Hashimoto talk pdf](http://www-gauge.scphys.kyoto-u.ac.jp/seminar/presen/slides2021/Hashimoto210421.pdf) # Hayden, Penington ## Black hole microstates vs. the additivity conjectures \[Links: [arXiv](https://arxiv.org/abs/2012.07861), [PDF](https://arxiv.org/pdf/2012.07861.pdf)\] \[Abstract: We argue that one of the following statements must be true: (a) extensive violations of quantum information theory's [[0549 Additivity conjectures|additivity conjectures]] exist or (b) there exists a set of 'disentangled' black hole microstates that can account for the entire Bekenstein-Hawking entropy, up to at most a subleading $O(1)$ correction. Possibility (a) would be a significant result in quantum communication theory, demonstrating that entanglement can enhance the ability to transmit information much more than has currently been established. Option (b) would provide new insight into the microphysics of black holes. In particular, the disentangled microstates would have to have nontrivial structure at or outside the black hole horizon, assuming the validity of the [[0212 Quantum extremal surface|quantum extremal surface]] prescription for calculating [[0301 Entanglement entropy|entanglement entropy]] in [[0001 AdS-CFT|AdS/CFT]].\] # Headrick ## Entanglement Renyi entropies in holographic theories \[Links: [arXiv](https://arxiv.org/abs/1006.0047), [PDF](https://arxiv.org/pdf/1006.0047.pdf)\] \[Abstract: Ryu and Takayanagi conjectured a formula for the [[0301 Entanglement entropy|entanglement (von Neumann) entropy]] of an arbitrary spatial region in an arbitrary holographic field theory. The von Neumann entropy is a special case of a more general class of entropies called [[0293 Renyi entropy|Renyi entropies]]. Using Euclidean gravity, Fursaev computed the entanglement Renyi entropies (EREs) of an arbitrary spatial region in an arbitrary holographic field theory, and thereby derived the [[0007 RT surface|RT formula]]. We point out, however, that his EREs are incorrect, since his putative saddle points do not in fact solve the Einstein equation. We remedy this situation in the case of two-dimensional CFTs, considering regions consisting of one or two intervals. For a single interval, the EREs are known for a general CFT; we reproduce them using gravity. For two intervals, the RT formula predicts a phase transition in the entanglement entropy as a function of their separation, and that the [[0300 Mutual information|mutual information]] between the intervals vanishes for separations larger than the phase transition point. By computing EREs using gravity and CFT techniques, we find evidence supporting both predictions. We also find evidence that large-$N$ symmetric-product theories have the same EREs as holographic ones.\] ## Summary - first holographic [[0293 Renyi entropy|Renyi]] calculation # Hernandez-Cuenca, Horowitz ## Bulk reconstruction of metrics with a compact space asymptotically \[Links: [arXiv](https://arxiv.org/abs/2003.08409), [PDF](https://arxiv.org/pdf/2003.08409)\] \[Abstract: Holographic duality implies that the geometric properties of the gravitational bulk theory should be encoded in the dual field theory. These naturally include the metric on dimensions that become compact near the conformal boundary, as is the case for any asymptotically locally $\text{AdS}_n\times\mathbb{S}^k$ spacetime. Almost all previous work on [[0026 Bulk reconstruction|metric reconstruction]] ignores these dimensions and would thus at most apply to dimensionally-reduced metrics. In this work, we generalize the approach to bulk [[0027 Bulk reconstruction using lightcone cuts|reconstruction using light-cone cuts]] and propose a prescription to obtain the full higher-dimensional metric of generic spacetimes up to an overall conformal factor. We first extend the definition of light-cone cuts to include information about the asymptotic compact dimensions, and show that the full conformal metric can be recovered from these extended cuts. We then give a prescription for obtaining these extended cuts from the dual field theory. The location of the usual cuts can still be obtained from bulk-point singularities of correlators, and the new information in the extended cut can be extracted by using appropriate combinations of operators dual to [[0169 Kaluza-Klein|Kaluza-Klein]] modes of the higher-dimensional bulk fields.\] # Hijano, Neuenfeld ## Soft photon theorems from CFT Ward identities in the flat limit of AdS/CFT \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: \] ## Summary - extend earlier paper [[2019#Hijano]] - construct flat space S-matrix from CFT operators in the flat limit - obtains both electric and magnetic soft theorems in flat space - changing quantisation scheme (standard v.s. alternative) in AdS corresponds to the S-transformation of $SL(2,\mathbb{Z})$ electric-magnetic duality in the bulk ## Possible extensions - from U(1) to non-Abelian # Himwich, Narayanan, Pate, Paul, Strominger ## The soft $\mathcal{S}$-matrix in gravity \[Links: [arXiv](https://arxiv.org/abs/2005.13433), [PDF](https://arxiv.org/pdf/2005.13433.pdf)\] \[Abstract: The gravitational $\mathcal{S}$-matrix defined with an infrared (IR) cutoff factorizes into hard and soft factors. The soft factor is universal and contains all the IR and [[0078 Collinear limit|collinear]] divergences. Here we show, in a momentum space basis, that the intricate expression for the soft factor is fully reproduced by two boundary currents, which live on the [[0022 Celestial sphere|celestial sphere]]. The first of these is the supertranslation current, which generates spacetime supertranslations. The second is its symplectic partner, the Goldstone current for spontaneously broken supertranslations. The current algebra has an off-diagonal level structure involving the gravitational cusp anomalous dimension and the logarithm of the IR cutoff. It is further shown that the [[0287 Memory effect|gravitational memory effect]] is contained as an IR safe observable within the soft $\mathcal{S}$-matrix.\] ## Summary - The (universal) soft factor is reproduced by two boundary currents: - supertranslation current - Goldstone current for SSB supertranslations - decomposition of *states* into supertranslation-charged and neutral components <=> factorisation of $S$-matrix into IR-divergent and IR-finite parts ## Refs - extension of [[NandePateStrominger2017]]: from just QED to now gravity - to understand this in GR directly rather than using amplitudes: [[2021#Nguyen, Salzer]] # Hod (Essay) ## A proof of the strong cosmic censorship conjecture \[Links: [arXiv](https://arxiv.org/abs/2012.01449), [PDF](https://arxiv.org/pdf/2012.01449.pdf)\] \[Abstract: \] ## Refs - [[0208 Strong cosmic censorship]] # Hollowood, Kumar ## Islands and Page curves for evaporating BHs in JT gravity \[Links: [arXiv](https://arxiv.org/abs/2004.14944), [PDF](https://arxiv.org/pdf/2004.14944.pdf)\] \[Abstract: \] # Horowitz, Wang ## Consequences of analytic boundary conditions in AdS \[Links: [arXiv](https://arxiv.org/abs/2002.10609), [PDF](https://arxiv.org/pdf/2002.10609.pdf), [JHEP](https://link.springer.com/article/10.1007%2FJHEP04%282020%29045)\] \[Abstract: We investigate the effects of an analytic boundary metric for smooth asymptotically anti-de Sitter gravitational solutions. The boundary dynamics is then completely determined by the initial data due to [[0475 Corner conditions|corner conditions]] that all smooth solutions must obey. We perturb a number of familiar static solutions and explore the boundary dynamics that results. We find evidence for a nonlinear asymptotic instability of the planar black hole in four and six dimensions. In four dimensions we find indications of at least exponential growth, while in six dimensions, it appears that a singularity may form in finite time on the boundary. This instability extends to pure AdS (at least in the Poincare patch). For the class of perturbations we consider, there is no sign of this instability in five dimensions.\] ## Significance - the singularities found to form in finite asymptotic time imply the termination of time for any putative CFT - the presence (and generic-ness) of these instabilities may be argued to be evidence against using analytic boundary conditions or requiring bulk solutions to be smooth ## Related - [[2019#Horowitz, Wang]] - [[0475 Corner conditions]] - [[0339 Stability of GR solutions]] - [[0310 Initial data in AdS]] - [[0490 The 3+1 decomposition]] # Hsin, Iliesiu, Yang ## A violation of global symmetries from replica wormholes and the fate of black hole remnants \[Links: [arXiv](https://arxiv.org/abs/2011.09444), [PDF](https://arxiv.org/pdf/2011.09444.pdf)\] \[Abstract: \] ## Summary - states with different global symmetry charges are non-orthogonal - consistent with central dogma: as seen from outside, BH is like a quantum system with entropy $S_{BH}$ - global symmetry naturally emerges from [[0154 Ensemble averaging]] averaging - i.e. each member does not have the symmetry ## Review of previous arguments - form BH with different values of charges, Hawking radiation -> lost - remnant would violate entropy bounds - using EW reconstruction - [[2018#Harlow, Ooguri (Short)]] [[2020#Harlow, Shaghoulian]] - splitable: some kind of Noether theorem: use charges to generate symmetries # Iacobacci, Muck ## Conformal Primary Basis for Dirac Spinors \[Links: [arXiv](https://arxiv.org/abs/2009.02938), [PDF](https://arxiv.org/pdf/2009.02938.pdf)\] \[Abstract: We study solutions to the Dirac equation in Minkowski space $\mathbb{R}^{1,d+1}$ that transform as $d$-dimensional conformal primary spinors under the Lorentz group $SO(1,d+1)$. Such solutions are parameterized by a point in $\mathbb{R}^d$ and a conformal dimension $\Delta$. The set of wavefunctions that belong to the principal continuous series, $\Delta =\frac{d}2 + i\nu$, with $\nu\geq 0$ and $\nu \in \mathbb{R}$ in the [[0256 Massive particles in CCFT|massive]] and massless cases, respectively, form a complete basis of delta-function normalizable solutions of the Dirac equation. In the massless case, the [[0148 Conformal basis|conformal primary wavefunctions]] are related to the wavefunctions in momentum space by a [[0079 Mellin transform|Mellin transform]].\] # Iliesiu, Turiaci ## The statistical mechanics of near-extremal BHs \[Links: [arXiv](https://arxiv.org/abs/2003.02860), [PDF](https://arxiv.org/pdf/2003.02860.pdf)\] \[Abstract: An important open question in black hole thermodynamics is about the existence of a "mass gap" between an extremal black hole and the lightest near-extremal state within a sector of fixed charge. In this paper, we reliably compute the partition function of Reissner-Nordström near-extremal black holes at temperature scales comparable to the conjectured gap. We find that the density of states at fixed charge does not exhibit a gap; rather, at the expected gap energy scale, we see a continuum of states. We compute the partition function in the canonical and grand canonical ensembles, keeping track of all the fields appearing through a dimensional reduction on $S^2$ in the near-horizon region. Our calculation shows that the relevant degrees of freedom at low temperatures are those of 2d [[0050 JT gravity|Jackiw-Teitelboim gravity]] coupled to the electromagnetic $U(1)$ gauge field and to an $SO(3)$ gauge field generated by the dimensional reduction.\] ## Summary - *computes* the partition function of RN near-extremal BHs at temperature scales comparable to the mass gap - *finds* **no gap** in the density of states - by *including* quantum fluctuations - *using* dimensional reduction (to [[0050 JT gravity|JT gravity]]) ## Mass gap - above extremality, $\delta E=E-M_0=T^2/M_\text{gap}$, so at small $T<M_\text{gap}$, one might say there is not enough energy to emit even a single quantum of average energy $T$ (because $\delta E/T<1$) - either semiclassical physics breaks down - or there is a literal gap between extremal BH and the lightest near-extremal BH in the spectrum of BHs - a good answer if we have [[0359 Supersymmetry|SUSY]] but unclear whether it truly exists for non-SUSY BHs like RN ## Resolutions - Hawking radiation - now $E-M_{0} \sim \frac{3}{2} T>T$ so we do have enough energy for Hawking quanta - mass gap? - no mass gap ## Refs - AdS${}_3$ - [[2019#Ghosh, Maxfield, Turiaci]] # Jafferis, Lamprou ## Inside the Hologram: Reconstructing the bulk observer's experience \[Links: [arXiv](https://arxiv.org/abs/2009.04476), [PDF](https://arxiv.org/pdf/2009.04476.pdf)\] \[Abstract: \] ## Observer - observer is a BH entangled to a reference system as a TFD - can use conformal generators to shift the BH towards the boundary - observer has an atmosphere around it and in the atmosphere one can use [[0016 HKLL]] to reconstruct an operator in it # Jain ## Effective field theory for non-relativistic hydrodynamics \[Links: [arXiv](https://arxiv.org/abs/2008.03994), [PDF](https://arxiv.org/pdf/2008.03994.pdf)\] \[Abstract: We write down a Schwinger-Keldysh effective field theory for non-relativistic (Galilean) [[0429 Hydrodynamics]]. We use the null background construction to covariantly couple Galilean field theories to a set of background sources. In this language, Galilean hydrodynamics gets recast as relativistic hydrodynamics formulated on a one-dimension higher spacetime admitting a null Killing vector. This allows us to import the existing field-theoretic techniques for relativistic hydrodynamics into the Galilean setting, with minor modifications to include the additional background vector field. We use this formulation to work out an interacting field theory describing stochastic fluctuations of energy, momentum, and density modes around thermal equilibrium. We also present a translation of our results to the more conventional Newton-Cartan language and discuss how the same can be derived via a non-relativistic limit of the effective field theory for relativistic hydrodynamics.\] # Kalyanapuram ## Soft Gravity by Squaring Soft QED on the Celestial Sphere \[Links: [arXiv](https://arxiv.org/abs/2011.11412), [PDF](https://arxiv.org/pdf/2011.11412.pdf)\] \[Abstract: We recast the soft S-matrices on the [[0022 Celestial sphere|celestial sphere]] as correlation functions of certain 2-dimensional models of topological defects. In pointing out the [[0067 Double copy|double copy]] structure between the soft photon and soft graviton cases, we arrive at a putative classical double copy between the corresponding topological models and a rederivation of gauge invariance and the equivalence principle as Ward identities of the 2-dimensional theories.\] # Kastikainen ## Conical defects and holography in topological AdS gravity \[Links: [arXiv](https://arxiv.org/abs/2006.02803), [PDF](https://arxiv.org/pdf/2006.02803.pdf)\] \[Abstract: \] ## Summary - studies [[0387 Higher codimension defects]] - evaluates the delta function contribution from [[0341 Lovelock gravity|Lovelock scalars]] using two methods ## Localised action - for a codimension-$2p$ defect, the integral over Lovelock scalar $\mathcal{R}_{(m)}$ contributes $D_{(m, p)}(\alpha)= \begin{cases}C_{(m, p)} U_{(p)}(\alpha) \int_{A} \sqrt{h} \widehat{\mathcal{R}}_{(m-p)}, & p \leq m \\ 0, & p>m\end{cases}$ <!-- ## Correspondence > Dear Diandian, > > This is a good question which I did not really think about when I was working on this. I’m fairly certain that in Einstein gravity the contribution is zero. For general Lovelock scalars, the situation is less trivial. However, a quick way to check this is to consider the derivation done in Appendix B of my paper and try to apply it to codimension-(2p+1) defects. The idea of that derivation is to surround the defect with a codimension-1 surface and compute the limit of the (generalized) Gibbons-Hawking surface term when the boundary is shrank to the defect. > >The difference is that there are now 2p angular coordinates around the defect in contrast to 2p-1 for codimension-2p defects. Hence it looks like the contribution would vanish even for Lovelock scalars. This is, because of how the indices get distributed among the different factors in the (generalized) Gibbons-Hawking term and, because the intrinsic Riemann tensor of the codimension-1 surface does not have cross components along angles and intrinsic coordinates of the defect. > >I’m happy to discuss this more if you are interested. > >Best, >Jani >Dear Jani, > Thank you very much for your answers! I need to think about the calculation a bit more, but your comment about them vanishing in odd cases seems very interesting.  > I have a very vague feeling that in odd dimensions there may be some kind of anomaly in the sense of having log terms in an expansion around the defects, analogous to the Fefferman-Graham scenario (not when the defect reaches the boundary but near the defect itself). I wonder if this may change the conclusion that the contribution is zero. Do you have any thoughts on this? > I may get back to you later once I think more about this but thank you again for the reply! > Best, Diandian >Dear Diandian, > In the calculations of my paper it is assumed that the metric of the codimension-2p defect is fixed to take a particular form. For defects with p>1, the metric has non-trivial curvature also away from the defect so that it is probably not a solution of Einstein’s equations. For codimension-2 defects this is not a problem, because such a defect can be introduced by a discrete quotient which only modifies the curvature at fixed points of the quotient (at the defect where it becomes infinite). Hence codimension-2 defects are relevant for Einstein gravity. Similar result also holds for Lovelock gravity theories with only one Lovelock scalar in the action and codimension-2p defects: equations of motions in these theories are blind to the additional curvature away from the codimension-2p defect so one can find them as solutions (which I do in my paper for special Lovelock theories). > The defect metrics I considered did not have a logarithmic term by choice. So what you are saying (analogously to the FG expansion) is that a logarithmic term should appear if one imposes the defect metric to be on-shell (in Einstein gravity) away from the defect. The codimension-2 defect metric is always on-shell outside of the defect without logarithms since it can be obtained as a quotient of an on-shell metric. Imposing a codimension-3 defect to be on-shell for sure requires a change in the metric, but I don’t know if it requires a logarithmic term or not. It should not be too difficult to check what kind of modification does the trick or if any? Whether the defect contribution to the Ricci scalar would be a Dirac delta function in this case is not clear and is an interesting question. > Thanks, sounds good! > Best, Jani ---> # Khodabakhshi, Shirzad, Shojai, Mann ## Black hole entropy and boundary conditions \[Links: [arXiv](https://arxiv.org/abs/2005.11697), [PDF](https://arxiv.org/pdf/2005.11697.pdf)\] \[Abstract: \] ## Summary - investigates [[0004 Black hole entropy]] formula in both Wald and Euclidean methods with different BCs, focusing on ==$f(R)$== as the example ## Degeneracy - Need degenerate Lagrangian to make variation principle well-defined - Need Ostrogradsky approach to decrease the order of derivatives ## Wald method - they showed that the boundary term does not contribute to the Noether charge although they do contribute to symplectic potential (this seems very obvious and hence not very significant) ## Euclidean method - the BC independence is more easily seen in quotient space, where the sole contribution is from the tip of the cone and nothing from the asymptotic boundary as along as there is a good variational principle - but here they were working in the covering space so there is apparent dependence on BC but the answer cannot depend on it by the above argument # Kim, Lee, Nishida ## Holographic scalar and vector exchange in OTOCs and pole-skipping phenomena \[Links: [arXiv](https://arxiv.org/abs/2011.13716), [PDF](https://arxiv.org/pdf/2011.13716.pdf)\] \[Abstract: We study scalar and vector exchange terms in [[0482 Out-of-time-order correlator|OTOC]] holographically. By applying a computational method in graviton exchange, we analyse exponential behaviours in scalar and vector exchange terms at late times. We show that their exponential behaviours in simple holographic models are related to [[0179 Pole skipping|pole-skipping]] points obtained from the near-horizon equations of motion of scalar and vector fields. Our results are generalisations of the relation between the graviton exchange effect in [[0482 Out-of-time-order correlator|OTOCs]] and the [[0179 Pole skipping|pole-skipping]] phenomena of the dual operator, to scalar and vector fields.\] ## Summary - studies the relation between [[0482 Out-of-time-order correlator|OTOC]] and the exponential behaviour at late times ==for scalar and vector fields==, which generalises the [[0482 Out-of-time-order correlator|OTOC]] for graviton exchange ## Chaotic pole vs others - chaotic pole corresponds to chaos, which is related to graviton exchange - lower poles corresponds to other "exchange terms" in [[0482 Out-of-time-order correlator|OTOC]] - checked for scalar and vector fields # Kiritsis, Nitti, Preau ## Holographic QFTs on S2×S2, spontaneous symmetry breaking and Efimov saddle points \[Links: [arXiv](https://arxiv.org/abs/2005.09054), [PDF](https://arxiv.org/pdf/2005.09054.pdf)\] \[Abstract: \] ## Refs - [[0231 Bulk solutions for CFTs on non-trivial geometries]] # Koren (Thesis) ## The Hierarchy Problem: From the Fundamentals to the Frontiers \[Links: [arXiv](https://arxiv.org/abs/2009.11870), [PDF](https://arxiv.org/pdf/2009.11870.pdf), [Inspire](https://inspirehep.net/literature/1869328)\] \[Abstract: \] ## 1. [[0080 Effective field theory]] ### 1.1 EFT basis - three ingredients for constructing effective description - list of important degrees of freedom. e.g. $\phi_i$ - symmetries - constrain the dynamics - a notion of power counting - organizes the effects in terms of importance - usually $E/\lambda$ where $E$ is an energy and $\lambda$ is a cut-off scale above which we expect new physics - **engineering dimension** - action $S=\int \mathrm{d}^{d} x\left(-\frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi-\frac{1}{2} m^{2} \phi^{2}-\frac{1}{4 !} \lambda \phi^{4}-\frac{1}{6 !} \tau \phi^{6}+\ldots\right)$ - scale $x^{\mu} \rightarrow s x^{\prime \mu}$: interested in long-distance limit $s\gg 1$ - then (after restoring kinetic term by rescaling field) $S=\int \mathrm{d}^{d} x^{\prime}\left(-\frac{1}{2} \partial_{\mu^{\prime}} \phi^{\prime} \partial^{\mu^{\prime}} \phi^{\prime}-\frac{1}{2} m^{2} s^{2} \phi^{\prime 2}-\frac{1}{4 !} \lambda s^{4-d} \phi^{\prime 4}-\frac{1}{6 !} \tau s^{6-2 d} \phi^{\prime 6}+\ldots\right)$ - $\Delta_{\phi^{2}}=2$ relevant, $\Delta_{\phi^{6}}=-2$ irrelevant - connection to cut-off - let $\tau \rightarrow \bar{\tau} \Lambda^{6-2 d}$ etc so that $\tau$ is dimensionless - then in $d=4$, $\frac{1}{6 !} \frac{\tau}{\Lambda^{-2}} \phi^{\prime 6} = \frac{1}{6 !} \bar{\tau} \phi^{\prime 6}$: As energy scale goes down, $\bar{\tau}$ is smaller so that the coupling is less important ($\bar{\tau} = \tau \Lambda^2$ smaller) - bottom-up approach - write down all Lagrangian compatible with symmetry and measure them coefficients - top-down approach - already have a theory - integrate out - need the low-energy degrees of freedom correctly reproduce the effects of the integrated-out degrees of freedom - need to use path integrals to do so - path integral $Z=\int \mathcal{D} \phi \mathcal{D} \Phi e^{i S(\phi, \Phi)}$ - integrate out heavy fields $Z=\int \mathcal{D} \phi e^{i S_{\mathrm{eff}}(\phi)}$ - why has information been lost: - we really need the partition function as a functional of the sources Z[J_\phi], and we take functional derivatives with respect to these sources as a step to calculating correlation functions or scattering amplitudes. In integrating out our heavy $\Phi$, we no longer have a source we can put in our Lagrangian to turn on that $\Phi$, as it no longer appears in the action - GUT - single gauge coupling - breaks down to SM at $M_\text{GUT}$ via Higgs mechanism # Kravchuk, Qiao, Rychkov ## Distributions in CFT I. Cross-ratio space \[Links: [arXiv](https://arxiv.org/abs/2001.08778), [PDF](https://arxiv.org/pdf/2001.08778.pdf)\] \[Abstract: \] ## Summary of the series - I (this paper) - show that the [[0031 Conformal block]] expansion converges in the sense of distributions - II - show CFT Wightman function in Lorentzian space are tempered distributions -> thus establish [[0165 Wightman axioms]] - III - analytic continuation to Lorentzian cylinder ## Refs - an overview in [[Rsc0014 Rychkov TASI2019 Lorentzian CFT]] ## Assumptions - only need the modern Euclidean [[0036 Conformal bootstrap]] axioms - specifically, only need reality of OPE and and the convergence properties of [[0031 Conformal block]] expansion ## Time ordering - only **Wightman function**s are considered, but all causal relations among the 4 points are allowed - other ordering (e.g. retarded or time ordered) can be obtained by inserting some functions like $\Theta$ but these make the functions more singular and requires more careful treatment ## Special kinematic configurations - in Euclidean space, all 4-point functions can be obtained from doing OPE - see [[0031 Conformal block#Convergence in Euclidean]] - but in Lorentzian, there exist kinematic configurations when no channel converges - see Appendix A - this paper proposes a different way to solve this problem that works for all kinematic configurations # Laddha, Prabhu, Raju, Shrivastava ## The Holographic Nature of Null Infinity \[Links: [arXiv](https://arxiv.org/abs/2002.02448), [PDF](https://arxiv.org/pdf/2002.02448.pdf)\] \[Abstract: \] # Langhoff, Nomura ## Ensemble from Coarse Graining: Reconstructing the Interior of an Evaporating Black Hole \[Links: [arXiv](https://arxiv.org/abs/2008.04202), [PDF](https://arxiv.org/pdf/2008.04202.pdf)\] \[Abstract: \] # Law, Zlotnikov (Apr) ## Massive Spinning Bosons on the Celestial Sphere \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: A natural extension of the [[2017#Pasterski, Shao, Strominger (Jan)|Pasterski-Shao-Strominger]] (PSS) prescription is described, enabling the map of Minkowski space amplitudes with massive spinning external legs to the [[0022 Celestial sphere|celestial sphere]] to be performed. An integral representation for the [[0148 Conformal basis|conformal primary wave function]] (CPW) of massive spinning bosons on the celestial sphere is derived explicitly for spin-one and -two. By analogy with the spin-zero case, the spinning bulk-to-boundary propagator on Euclidean AdS is employed to extend the massive CPW integral representation to arbitrary integer spin, and to describe the appropriate inverse transform of massive spinning CPWs back to the plane wave basis in Minkowski space. Subsequently, a massive spin-$s$ momentum operator representation on the celestial sphere is determined, and used in conjunction with known Lorentz generators to derive Poincaré symmetry constraints on generic massive spinning two-, three- and four-point celestial amplitude structures. Finally, as a consistency check, three-point Minkowski space amplitudes of two massless scalars and a spin-one or -two massive boson are explicitly mapped to the celestial sphere, and the resulting three-point function coefficients are confirmed to be in exact agreement with the results obtained from Poincaré symmetry constraints.\] # Law, Zlotnikov (Aug) ## Relativistic partial waves for celestial amplitudes \[Links: [arXiv](https://arxiv.org/abs/2008.02331), [PDF](https://arxiv.org/pdf/2008.02331.pdf)\] \[Abstract: \] ## Refs - root [[0010 Celestial holography]] ## Summary - relativistic partial wave expansion for 4-pt celestial amplitudes of massless external particles - examples: scalars, gluons, gravitons, open superstring gluons - connection with relativistic partial waves in the *bulk* ## Relativistic partial wave - basis of partial waves $\left\langle\Phi_{m_{1}, s_{1}}^{\vec{J}, \Delta}, \Phi_{m_{2}, s_{2}}^{\vec{J}, \Delta}\right\rangle_{i j}=\delta\left(m_{1}-m_{2}\right) \delta_{s_{1}, s_{2}}$ - **expansion** $\tilde{f}_{\vec{J}, \Delta}(x)=\sum_{s \geq \max \left(\left|J_{a b}\right|\right)} \int_{0}^{\infty} d m \Phi_{m, s}^{\vec{J}, \Delta}(x)\left\langle\tilde{f}_{\vec{J}, \Delta^{\prime}}\left(x^{\prime}\right), \Phi_{m, s}^{\vec{J}, \Delta^{\prime}}\left(x^{\prime}\right)\right\rangle_{i j}$ - each term as gluing of two 3-pt functions $\Phi_{b u l k, s-c h .}^{\vec{J}, m, s}=2 m^{4} \sum_{b=-s}^{s} \int_{0}^{\infty} \frac{d y}{y^{3}} \int d z d \bar{z} \delta^{(4)}\left(\sum_{i=1}^{2} \epsilon_{i} p_{i}+p\right) A_{b}\left(p_{1}, p_{2}, p\right) \delta^{(4)}\left(\sum_{j=3}^{4} \epsilon_{j} p_{j}-p\right) A_{b}^{*}\left(p_{3}, p_{4},-p\right)$ - in terms of 3-pt function on the celestial sphere $R_{\Delta_{i}, J_{i}} \delta(i \bar{z}-i z) \Phi_{m, s}^{\vec{J}, \Delta}(x)=\sum_{J=-\mathrm{s}}^{s} \int_{1-i \infty}^{1+i \infty} \frac{d \Delta}{2 \pi i} \int d w d \bar{w} V_{J}^{\Delta}(w, \bar{w}) {A_{3}}^{\Delta_{1}, \Delta_2,\Delta}_{J_1,J_2,J}\left({A_{3}}_{J_{3}, J_{4}, J}^{\Delta_{3}, \Delta_{4}, \Delta}\right)^{*}$ ## Gluon example - $\tilde{f}_{g l u}^{--++}(x)=\sum_{s \geq 0} \int_{0}^{\infty} d m \Phi_{m, s}^{\vec{J}, \Delta}(x)\left\langle\tilde{f}_{g l u}^{--++}, \Phi_{m, s}^{\vec{J}, \Delta^{\prime}}\right\rangle_{12}$ for $1<x$ # Lentz ## Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory \[Links: [arXiv](https://arxiv.org/abs/2006.07125), [PDF](https://arxiv.org/pdf/2006.07125.pdf)\] \[Abstract: Solitons in space--time capable of transporting time-like observers at superluminal speeds have long been tied to violations of the weak, strong, and dominant energy conditions of general relativity. The negative-energy sources required for these solitons must be created through energy-intensive uncertainty principle processes as no such classical source is known in particle physics. This paper overcomes this barrier by constructing a class of soliton solutions that are capable of superluminal motion and sourced by purely positive energy densities. The solitons are also shown to be capable of being sourced from the stress-energy of a conducting plasma and classical electromagnetic fields. This is the first example of hyper-fast solitons resulting from known and familiar sources, reopening the discussion of superluminal mechanisms rooted in conventional physics.\] # Liu ## Scrambling and decoding the charged quantum information \[Links: [arXiv](https://arxiv.org/abs/2003.11425), [PDF](https://arxiv.org/pdf/2003.11425.pdf)\] \[Abstract: \] ## Refs - hint on [[0177 Weak gravity conjecture]] from requiring decoupling condition in Hayden-Preskill experiment - [[0326 Charged BH in holography]] # Liu, Raju ## Quantum Chaos in Topologically Massive Gravity \[Links: [arXiv](https://arxiv.org/abs/2005.08508), [PDF](https://arxiv.org/pdf/2005.08508.pdf)\] \[Abstract: \] ## Summary - [[0179 Pole skipping|pole skipping]] for [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] in TMG ## Lyapunov exponent - saturated in comoving frames, but violated in Schwarzschild coordinates; this was understood as an artefact of improper boundary conditions along the $\phi$ circle, pointed out in [[2019#Mezei, Sarosi]] # Maloney, Witten ## Averaging Over Narain Moduli Space \[Links: [arXiv](https://arxiv.org/abs/2006.04855), [PDF](https://arxiv.org/\frac{pdf}{2006.04855.pdf), [Talk at Chicago](https://youtu.be/JMRVAaVNpxk?feature=shared)\] \[Abstract: Recent developments involving [[0050 JT gravity|JT gravity]] in two dimensions indicate that under some conditions, a gravitational path integral is dual to an [[0154 Ensemble averaging|average over an ensemble]] of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT's to [[0554 Einstein gravity|Einstein gravity]] in three dimensions. But this is difficult. For a simpler problem, here we average over Narain's family of two-dimensional CFT's obtained by toroidal compactification. These theories are believed to be the most general ones with their [[0033 Central charge|central charges]] and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like $U(1)^{2D}$ [[0089 Chern-Simons theory|Chern-Simons theory]] than like Einstein gravity.\] # Margalef-Bentabol, Villasenor ## Geometric formulation of the CPS methods with boundaries \[Links: [arXiv](https://arxiv.org/abs/2008.01842), [PDF](https://arxiv.org/pdf/2008.01842.pdf)\] \[Abstract: \] ## Summary - **relative bicomplex framework** = extended version of **relative framework** + **variational bicomplex framework** - natural to deal with boundary contributions, including corners - prove that relative theory with boundary = non-relative theory with no boundary - completely characterise the arbitrariness ## Comments - rephrased [[2019#Harlow, Wu]] in a mathematical language but nothing new - does not resolve the issue of ambiguity in the symplectic structure # Marolf, Maxfield (a) ## Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information \[Links: [arXiv](https://arxiv.org/abs/2002.08950), [PDF](https://arxiv.org/pdf/2002.08950.pdf)\] \[Abstract: \] ## Refs - [[0051 Baby universes]] - [[0640 Topological models of gravity]] - [[0070 Reflection positivity of gravitational path integral]] ## Construction (Sec. 2.2 & 2.3) - Hilbert space states - $\left|Z\left[J_{1}\right] \cdots Z\left[J_{m}\right]\right\rangle \in \mathcal{H}_{\mathrm{BU}}$ - specify boundary conditions for $m$ boundaries - operator - $\widehat{Z[J}]\left|Z\left[J_{1}\right] \cdots Z\left[J_{m}\right]\right\rangle=\left|Z[J] Z\left[J_{1}\right] \cdots Z\left[J_{m}\right]\right\rangle$ - inserting a boundary and boundary conditions - commutator - $\left[\widehat{Z[J]}, \widehat{Z[J^{\prime}]}\right]=0$ - because they are just boundary conditions - $\alpha$ space - due to commutators vanishing can simultaneously diagonalise - $\widehat{Z[J}]|\alpha\rangle=Z_{\alpha}[J]|\alpha\rangle \quad \forall J$ - general amplitude - $\left\langle Z\left[J_{1}\right] \cdots Z\left[J_{n}\right]\right\rangle=\sum\left\langle\mathrm{HH}| \alpha_{0}\right\rangle\left\langle\alpha_{0}\left|Z\left[J_{1}\right]\right| \alpha_{1}\right\rangle \cdots\left\langle\alpha_{n-1}\left|Z\left[J_{n}\right]\right| \alpha_{n}\right\rangle\left\langle\alpha_{n} |\mathrm{HH}\right\rangle$ - $=\mathfrak{Z} \sum_{\alpha} p_{\alpha} Z_{\alpha}\left[J_{1}\right] \cdots Z_{\alpha}\left[J_{n}\right]$ ## More construction (Sec. 2.4) - allow slicing that defines the states to cut open AdS boundaries - then there can be pieces of the boundary $\mathcal{M}_i$ left unpaired as part of the definition of a state - boundary conditions $\psi_i$ - the boundaries of $\mathcal{M}_i$ are called $\Sigma_i$ (possibly disconnected) - different $\mathcal{M}_i$ can be paired to make a whole AdS boundary with boundary condition $Z\left[\tilde{J}^{*}, J\right]=(\psi[\tilde{J}], \psi[J])$ - important: $\psis do not commute. e.g. $\left\langle\psi\left[J_{2}\right] \psi\left[J_{1}\right] \mid \psi\left[J_{1}\right] \psi\left[J_{2}\right]\right\rangle=\left\langle Z\left[J_{2}^{*}, J_{1}\right] Z\left[J_{1}^{*}, J_{2}\right]\right\rangle \neq\left\langle Z\left[J_{2}^{*}, J_{2}\right] Z\left[J_{1}^{*}, J_{1}\right]\right\rangle$ because the different pairings of $\mathcal{M}_i$ give different pairings ## Interpretation of amplitude - compatible with [[0154 Ensemble averaging]] - each $\alpha$ is a theory in the ensemble - by looking at the expression for amplitude above ## Null states ## Entropy bound - obtain entropy by Legendre transform of $Z$ (usual way of obtaining entropy from partition function) - $S_{\alpha}(E):=\inf _{\beta}\left\{\beta E+\log Z_{\alpha}(\beta)\right\}$ ## D-branes - introduce spacetime D-branes # Marolf, Maxfield (b) ## Observations of Hawking radiation: the Page curve and baby universes \[Links: [arXiv](https://arxiv.org/abs/2010.06602), [PDF](https://arxiv.org/pdf/2010.06602.pdf)\] \[Abstract: \] ## Refs - [[0051 Baby universes]] ## Summary - emphasises operationally defined entropy in dealing with [[0131 Information paradox]] - experiments of asymptotic observers are consistent with unitarity, although they'd need more than one system to test whether a density matrix is mixed -> replicas - at the cost of superselection sectors - Polchinski and Strominger picture can be thought of as late time extrapolation of replica wormholes ## Chap 1-5: Reviews - use in-in formalism to calculate inner products etc - Hawking entropy is a result of tracing over the interior parts of the Cauchy surface - the result is pure if the interior part of Cauchy surface is included in the computation - defining the **density matrix** - density matrix of a region = linear functional that maps operators on that region to their expectation values - i.e. unique $\rho$ such that $\mathcal{O}\mapsto \operatorname{Tr}(\rho\mathcal{O})$ - to recover it, let $\mathcal{O}=|j\rangle\langle i|$ # Maxfield, Turiaci ## The path integral of 3D pure gravity near extremality; or, JT gravity with defects as a matrix integral \[Links: [arXiv](https://arxiv.org/abs/2006.11317), [PDF](https://arxiv.org/\frac{pdf}{2006.11317.pdf); Talks: [Strings2020](https://www.youtube.com/watch?v=hKOdqX2CWok&ab_channel=Strings2020)\] \[Abstract: We propose that a class of new topologies, for which there is no classical solution, should be included in the path integral of [[0002 3D gravity|three-dimensional pure gravity]], and that their inclusion solves pathological negativities in the spectrum, replacing them with a nonperturbative shift of the [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] extremality bound. We argue that a two-dimensional calculation using a dimensionally reduced theory captures the leading effects in the near extremal limit. To make this argument, we study a closely related two-dimensional theory of [[0050 JT gravity|Jackiw-Teitelboim gravity]] with dynamical defects. We show that this theory is equivalent to a matrix integral.\] ## Summary - 3d gravity has negative density of states when BTZ is near extremal -> fixed if including topologies for which there is no classical solution - dimensionally reduce 3d gravity to 2d - -> captures the leading effects near extremality - & show that JT is equivalent to a matrix integral ## 3d path integral - [[2007#Maloney, Witten]]: construct partition function of 3d pure gravity from sum over saddle points - -> problem: negative density of states near extremal BTZ - ![[MaxfieldTuriaci2020_3fillings.png]] - first two are okay - 3rd filling gives negative density of states - in the 2d description, it has a conical singularity - -> should include defects in JT gravity ## 2d theory - see [[0050 JT gravity]] - now add defects: ![[MaxfieldTuriaci2020_includeDefects.png|300]] - important: defect can be reproduced as an imaginary geodesic distance - ![[MaxfieldTuriaci2020_defectAsImaginaryLoop.png|400]] ## The catch - coming back to 3d, results in 2d with extra defects can cure the negative DOS - defects become KK instantons # May, van Raamsdonk ## Interpolating between multi-boundary wormholes and single-boundary geometries in holography \[Links: [arXiv](https://arxiv.org/abs/2011.14258), [PDF](https://arxiv.org/pdf/2011.14258.pdf)\] \[Abstract: \] ## Refs - [[0083 Traversable wormhole]] # Milekhin ## Quantum error correction and large $N$ \[Links: [arXiv](https://arxiv.org/abs/2008.12869), [PDF](https://arxiv.org/pdf/2008.12869.pdf)\] \[Abstract: In recent years [[0146 Quantum error correction|quantum error correction]] (QEC) has become an important part of [[0001 AdS-CFT|AdS/CFT]]. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by studying the error correcting properties of the fermionic sector of various large $N$ theories. Specifically we examine $SU(N)$ matrix quantum mechanics and 3-rank tensor $O(N)^3$ theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error correcting code. Our considerations are based purely on large $N$ analysis and do not appeal to a particular form of Hamiltonian or holography.\] # Nakata, Takayanagi, Taki, Tamaoka, Wei ## Holographic Pseudo Entropy \[Links: [arXiv](https://arxiv.org/abs/2005.13801), [PDF](https://arxiv.org/pdf/2005.13801)\] \[Abstract: We introduce a quantity, called [[0052 Pseudo-entropy|pseudo entropy]], as a generalization of [[0301 Entanglement entropy|entanglement entropy]] via post-selection. In the AdS/CFT correspondence, this quantity is dual to areas of minimal area surfaces in time-dependent Euclidean spaces which are asymptotically AdS. We study its basic properties and classifications in qubit systems. In specific examples, we provide a quantum information theoretic meaning of this new quantity as an averaged number of Bell pairs when the post-selection is performed. We also present properties of the pseudo entropy for random states. We then calculate the pseudo entropy in the presence of local operator excitations for both the two dimensional free massless scalar CFT and two dimensional holographic CFTs. We find a general property in CFTs that the pseudo entropy is highly reduced when the local operators get closer to the boundary of the subsystem. We also compute the holographic pseudo entropy for a Janus solution, dual to an exactly marginal perturbation of a two dimensional CFT and find its agreement with a perturbative calculation in the dual CFT. We show the linearity property holds for holographic states, where the holographic pseudo entropy coincides with a weak value of the area operator. Finally, we propose a mixed state generalization of pseudo entropy and give its gravity dual.\] # Narayanan ## Massive Celestial Fermions \[Links: [arXiv](https://arxiv.org/abs/2009.03883), [PDF](https://arxiv.org/pdf/2009.03883.pdf)\] \[Abstract: In an effort to further the study of amplitudes in the [[0010 Celestial holography|celestial CFT]] (CCFT), we construct [[0148 Conformal basis|conformal primary wavefunctions]] for massive fermions. Upon explicitly calculating the wavefunctions for Dirac fermions, we deduce the corresponding transformation of momentum space amplitudes to celestial amplitudes. The shadow wavefunctions are shown to have opposite spin and conformal dimension $2-\Delta$. The Dirac conformal primary wavefunctions are delta function normalizable with respect to the Dirac inner product provided they lie on the principal series with conformal dimension $\Delta = 1+i\lambda$ for $\lambda\in\mathbb{R}$. It is shown that there are two choices of a complete basis: single spin $J=\frac{1}{2}$ or $J=-\frac{1}{2}$ and $\lambda\in\mathbb{R}$ or multiple spin $J=\pm\frac{1}{2}$ and $\lambda\in\mathbb{R}_{+\cup 0}$. The massless limit of the Dirac conformal primary wavefunctions is shown to agree with previous literature. The momentum generators on the celestial sphere are derived and, along with the Lorentz generators, form a representation of the Poincare algebra. Finally, we show that the massive spin-1 conformal primary wavefunctions can be constructed from the Dirac conformal primary wavefunctions using the standard Clebsch-Gordan coefficients. We use this procedure to write the massive spin-$\frac{3}{2}$, Rarita-Schwinger, conformal primary wavefunctions. This provides a prescription for constructing all massive fermionic and bosonic conformal primary wavefunctions starting from spin-$\frac{1}{2}$.\] # Natsuume, Okamura ## Pole-skipping and zero temperature \[Links: [arXiv](https://arxiv.org/abs/2011.10093), [PDF](https://arxiv.org/pdf/2011.10093.pdf)\] \[Abstract: \] ## Summary - studies [[0179 Pole skipping|pole skipping]] of ==scalar== [[0473 Retarded Green's function]] in ==rotating BTZ== in the non-extremal and extremal limit - pole-skipping does *not* occur in general in the extremal limit, but does occur in a special case ## Subtlety of extremality 1. cannot take $T\to 0$ naively from non-extremal result. 2. poles in Green's function are replaced by branch cuts ## Results at extremality There are two temperatures: left and right. In the extremal limit $T_L \to 0$, and the left contributes to $(\omega-k)^\nu$ which is power law to the Green's function, but the right still has poles etc (still finite temperature). But if $\nu=1$, the power law becomes a simple zero, and pole-skipping happens due to this zero and a pole from the right contribution. # Okuyama, Sakai ## Multi-boundary correlators in JT gravity \[Links: [arXiv](https://arxiv.org/abs/2004.07555), [PDF](https://arxiv.org/pdf/2004.07555)\] \[Abstract: We continue the systematic study of the thermal partition function of [[0050 JT gravity|Jackiw-Teitelboim (JT) gravity]] started in [[2019#Okuyama, Sakai]]. We generalize our analysis to the case of multi-boundary correlators with the help of the boundary creation operator. We clarify how the Korteweg-de Vries constraints arise in the presence of multiple boundaries, deriving differential equations obeyed by the correlators. The differential equations allow us to compute the genus expansion of the correlators up to any order without ambiguity. We also formulate a systematic method of calculating the WKB expansion of the Baker-Akhiezer function and the 't Hooft expansion of the multi-boundary correlators. This new formalism is much more efficient than our previous method based on the topological recursion. We further investigate the low temperature expansion of the two-boundary correlator. We formulate a method of computing it up to any order and also find a universal form of the two-boundary correlator in terms of the error function. Using this result we are able to write down the analytic form of the spectral form factor in JT gravity and show how the ramp and plateau behavior comes about. We also study the [[0162 No-boundary wavefunction|Hartle-Hawking state]] in the free boson/fermion representation of the tau-function and discuss how it should be related to the multi-boundary correlators.\] # Pasterski, Puhm ## Shifting Spin on the Celestial Sphere \[Links: [arXiv](https://arxiv.org/abs/2012.15694), [PDF](https://arxiv.org/pdf/2012.15694.pdf)\] \[Abstract: We explore [[0148 Conformal basis|conformal primary wavefunctions]] for all half integer spins up to the graviton. Half steps are related by supersymmetry, integer steps by the classical double copy. The main results are as follows: we 1) introduce a convenient spin frame and null tetrad to organize all radiative modes of varying spin; 2) identify the massless spin-3/2 conformal primary wavefunction as well as the conformally soft Goldstone mode corresponding to large supersymmetry transformations; 3) indicate how to express a conformal primary of arbitrary spin in terms of differential operators acting on a scalar primary; 4) demonstrate that conformal primary metrics satisfy the double copy in a variety of forms -- operator, Weyl, and Kerr-Schild -- and are exact, albeit complex, solutions to the fully non-linear Einstein equations of Petrov type N; 5) propose a novel generalization of conformal primary wavefunctions; and 6) show that this generalization includes a large class of physically interesting metrics corresponding to ultra-boosted black holes, [[0117 Shockwave|shockwaves]] and more.\] # Pasterski, Verlinde ## HPS meets AMPS: How Soft Hair Dissolves the Firewall \[Links: [arXiv](https://arxiv.org/abs/2012.03850), [PDF](https://arxiv.org/pdf/2012.03850.pdf)\] \[Abstract: \] # Pollack, Rozali, Sully, Wakeham ## Eigenstate Thermalization and Disorder Averaging in Gravity \[Links: [arXiv](https://arxiv.org/abs/2002.02971), [PDF](https://arxiv.org/pdf/2002.02971.pdf)\] \[Abstract: Naively, a resolution of the [[0131 Information paradox|black hole information paradox]] appears to involve microscopic details of a theory of quantum gravity. However, recent work has argued that a unitary Page curve can be recovered by including novel replica instantons in the [[0555 Gravitational path integral|gravitational path integral]]. Moreover, replica instantons seem to rely on disorder averaging the microscopic theory, without a definite connection to a single, underlying unitary quantum system. In this letter, we show that disorder averaging and replica instantons emerge naturally from a gravitational effective theory built out of typical microscopic states. We relate replica instantons to a moment expansion of the simple operators appearing in the [[0040 Eigenstate thermalisation hypothesis|Eigenstate Thermalization Hypothesis]], describe Feynman rules for computing the moments, and find an elegant microcanonical description of replica instantons in terms of wormholes and Euclidean black holes.\] # Qiao ## Classification of convergent OPE channels for Lorentzian CFT 4-point functions \[Links: [arXiv](https://arxiv.org/abs/2005.09105), [PDF](https://arxiv.org/pdf/2005.09105.pdf)\] \[Abstract: \] ## Refs - independent work [[CorcoranStaudacher2020]] - a different classification - OPE convergence [[PappadopuloRychkovEspinRattazzi2012]] ## The idea - the only non-trivial piece to analytically continue is $g(u,v)$ which is studied by using radial coordinates $\rho,\bar\rho$ and a good series expansion ## Lorentzian configurations - either both $z$ and $\bar z$ real, or $z^*=\bar z$ - -> can separate these configurations into $S, U, T, E_{st}, E_{tu}, E_{su}, E_{stu}$ ## An important ordering - no matter what Lorentzian time each point becomes, the Euclidean starting point has the ordering $\epsilon_1>\epsilon_2>...$ ## Coordinates - $x_{i j}^{2}:=\sum_{\mu=0}^{d-1}\left(x_{i}^{\mu}-x_{j}^{\mu}\right)^{2}=\left(\tau_{i}-\tau_{j}\right)^{2}+\left(\mathbf{x}_{i}-\mathbf{x}_{j}\right)^{2}$ - $u=\frac{x_{12}^{2} x_{34}^{2}}{x_{13}^{2} x_{24}^{2}}, \quad v=\frac{x_{14}^{2} x_{23}^{2}}{x_{13}^{2} x_{24}^{2}}$ - $u=z \bar{z}, \quad v=(1-z)(1-\bar{z})$ - $z(u, v)=\frac{1}{2}\left(1+u-v+i \sqrt{4 u-(1+u-v)^{2}}\right)$ $\bar{z}(u, v)=\frac{1}{2}\left(1+u-v-i \sqrt{4 u-(1+u-v)^{2}}\right)$ - radial coordinates $\rho,\bar\rho$ - in [[HogervorstRychkov2013]] ## Assumptions of the Euclidean CFT - conformal invariance - reflection positivity - convergence of OPE in Euclidean ## Analytic properties # Rutter, van Rees ## Applications of alpha space \[Links: [arXiv](https://arxiv.org/abs/2003.07964), [PDF](https://arxiv.org/pdf/2003.07964.pdf)\] \[Abstract: \] ## Summary - *extends* alpha space from 1 to 2 dimensions - *finds* [[0031 Conformal block]] expansion of known functions - *recovers* several lightcone bootstrap results - *establishes* a connection between alpha space and Lorentzian inversion formula ## Refs - alpha space introduced in [[HogervorstVanRees2017]] - useful in [[2021#Atanasov, Melton, Raclariu, Strominger]] for constructing conformal blocks ## Alpha space transform - 1D - $\hat{f}(\alpha)=\int_{0}^{1} \frac{d z}{z^{2}} f(z) \Psi_{\alpha}(z)$ - $\Psi_{\alpha}(z)=\frac{1}{2}\left(Q(\alpha) k_{\alpha+1 / 2}(z)+Q(-\alpha) k_{-\alpha+1 / 2}(z)\right)={ }_{2} F_{1}\left(\frac{1}{2}+\alpha, \frac{1}{2}-\alpha, 1, \frac{z-1}{z}\right)$ - $Q(\alpha)=\frac{2 \Gamma(-2 \alpha)}{\Gamma\left(\frac{1}{2}-\alpha\right)^{2}}$ - $k_{h}(z)=z^{h} \,{}_2F_{1}(h, h, 2 h, z)$ - 2D - $\hat{f}(\alpha, \bar{\alpha})=\int_{0}^{1} \frac{d z}{z^{2}} \int_{0}^{1} \frac{d \bar{z}}{\bar{z}^{2}} \Psi_{\alpha}(z) \Psi_{\bar{\alpha}}(\bar{z}) f(z, \bar{z})$ - inverse: - $f(z, \bar{z})=\int[d \alpha] \int[d \bar{\alpha}] \frac{4 \Psi_{\alpha}(z) \Psi_{\bar{\alpha}}(\bar{z})}{Q(\pm \alpha) Q(\pm \bar{\alpha})} \hat{f}(\alpha, \bar{\alpha})$ # Stanford ## More quantum noise from wormholes \[Links: [arXiv](https://arxiv.org/abs/2008.08570), [PDF](https://arxiv.org/pdf/2008.08570.pdf)\] \[Abstract: \] ## Summary - studies wormholes in ==dilaton gravity with matter== - closely related to wormholes that give Page curve - noise needed to make BH evaporation unitary to solve [[0131 Information paradox]] - semiclasssical gravity gives us this noise by computing an [[0154 Ensemble averaging]] average # Takayanagi, Uetoko ## Chern-Simons Gravity Dual of BCFT \[Links: [arXiv](https://arxiv.org/abs/2011.02513), [PDF](https://arxiv.org/pdf/2011.02513.pdf)\] \[Abstract: In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called [[0548 Boundary CFT|boundary conformal field theory]] (BCFT). We determine the correct boundary action on the end of the world brane in the [[0089 Chern-Simons theory|Chern-Simons gauge theory]]. This reproduces known results of the [[0181 AdS-BCFT|AdS/BCFT]] for the Einstein gravity. We also give a prescription of calculating [[0007 RT surface|holographic entanglement entropy]] by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.\] # Traube ## Cardy Algebras, Sewing Constraints and String-Nets \[Links: [arXiv](https://arxiv.org/abs/2009.11895), [PDF](https://arxiv.org/pdf/2009.11895)\] \[Abstract: In [SY21] it was shown how string-net spaces for the Cardy bulk algebra in the Drinfeld center $\mathsf{Z}(\mathsf{C})$ of a modular tensor category $\mathsf{C}$ give rise to a consistent set of correlators. We extend their results to include open-closed world sheets and allow for more general field algebras, which come in the form of ($\mathsf{C}|\mathsf{Z}(\mathsf{C})$)-Cardy algebras. To be more precise, we show that a set of fundamental string-nets with input data from a ($\mathsf{C}|\mathsf{Z}(\mathsf{C})$)-Cardy algebra gives rise to a solution of the sewing constraints formulated in [[2013#Kong, Li, Runkel]] and that any set of fundamental string-nets solving the sewing constraints determine a ($\mathsf{C}|\mathsf{Z}(\mathsf{C})$)-Cardy algebra up to isomorphism. Hence we give an alternative proof of the results in [[2013#Kong, Li, Runkel]] in terms of string-nets.\] # Tsiares ## Universal Dynamics in Non-Orientable CFT$_2$ \[Links: [arXiv](https://arxiv.org/abs/2011.09250), [PDF](https://arxiv.org/pdf/2011.09250.pdf)\] \[Abstract: [[0003 2D CFT|Two-dimensional conformal field theories]] (CFTs) defined on [[0620 Non-orientable CFT|non-orientable]] Riemann surfaces obey consistency Cardy conditions analogous to those in the orientable case. We revisit those conditions for irrational theories with central charge $c>1$ in the context of two-point functions of primaries on the Real Projective plane $\mathbb{RP}^2$ and the partition function on the Klein bottle $\mathbb{K}^2$. Using the irrational versions of the Virasoro [[0573 Crossing kernel|fusion]] and [[0612 Modular invariance|fusion]] kernels we derive universal expressions for the non-orientable CFT data at large conformal dimension, assuming a gap in the spectrum of scalar primaries. In particular, we derive asymptotic formulas at finite [[0033 Central charge|central charge]] for the averaged Light-Light-Heavy product $C_{LLH}\times\Gamma_{H}$ of OPE coefficients with the $\mathbb{RP}^2$ one-point function normalizations, as well as for the parity-weighted density of heavy scalar primaries (or equivalently the density of heavy $\Gamma_H^2$). We discuss the gravitational interpretation of the results.\] # Tsujimura, Nambu ## Null wave front as RT surface \[Links: [arXiv](https://arxiv.org/abs/2003.13374), [PDF](https://arxiv.org/pdf/2003.13374.pdf)\] \[Abstract: The [[0007 RT surface|Ryu-Takayanagi formula]] provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu-Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we propose that null rays emitted from the AdS boundary can be regarded as such a flow. In particular, we show that in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu-Takayanagi surfaces. In addition, based on the viewpoint of flow, we propose a wave optical formula to calculate the holographic entanglement entropy.\] ## Summary - in spherical static spacetimes, wave front's become extremal surfaces - propose a wave optical formula or calculating the entanglement entropy ## Extremal surfaces 1. write down metric 2. parameterise the RT surface $r(\theta)$ (or $r(x)$ for planar) 3. extremise the SEE functional - n.b this is just like butterfly velocity calculation ## Null rays 1. parameterise the rays by $(t,r,\theta)$ 2. find $r=r_{\text{NG}}(\theta,b)$ and $t_{\text{NG}}(\theta,b)$, where $b$ labels the different directions 3. to find wavefront, eliminate $b$ and find $r_{\text{WF}}(\theta,t)$ # Turiaci, Usatyuk, Weng ## Dilaton-gravity, deformations of the minimal string, and matrix models \[Links: [arXiv](https://arxiv.org/abs/2011.06038), [PDF](https://arxiv.org/pdf/2011.06038.pdf)\] \[Abstract: A large class of two-dimensional dilaton-gravity theories in asymptotically AdS$_2$ spacetimes are holographically dual to a [[0197 Matrix model|matrix integral]], interpreted as an [[0154 Ensemble averaging|ensemble average]] over Hamiltonians. Viewing these theories as [[0050 JT gravity|Jackiw-Teitelboim gravity]] with a gas of defects, we extend this duality to a broader class of dilaton potentials compared to previous work by including conical defects with small deficit angles. In order to do this we show that these theories are equal to the large $p$ limit of a natural deformation of the $(2,p)$ minimal string theory.\] # Wang, Wu, Yang, Ying ## Derive Lovelock Gravity from String Theory in Cosmological Background \[Links: [arXiv](https://arxiv.org/abs/2012.13312), [PDF](https://arxiv.org/pdf/2012.13312.pdf)\] \[Abstract: It was proved more than three decades ago, that the first order $\alpha^\prime$ correction of [[0329 String effective action|string effective theory]] could be written as the [[0425 Gauss-Bonnet gravity|Gauss-Bonnet]] term, which is the quadratic term of [[0341 Lovelock gravity|Lovelock gravity]]. In cosmological background, with an appropriate [[0355 Field redefinitions|field redefinition]] , we reorganize the infinite $\alpha^\prime$ corrections of string effective action into a finite term expression for any specific dimension. This finite term expression matches Lovelock gravity exactly and thus fix the couplings of Lovelock gravity by the coefficients of [[0329 String effective action|string effective action]]. This result thus provides a strong support to string theory.\] ## Refs - [[0006 Higher-derivative gravity]] - maybe not very non-trivial because of the very restricted class of metrics; a less restricted class of metrics in [[HohmZwiebach2019]] # White, Cao, Swingle ## Conformal field theories are magical \[Links: [arXiv](https://arxiv.org/abs/2007.01303), [PDF](https://arxiv.org/pdf/2007.01303.pdf)\] \[Abstract: "[[0538 Magic|Magic]]" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the $\mathbb Z_3$ Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the $q = 3$ ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a [[0539 MERA|MERA]] representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of [[0001 AdS-CFT|AdS-CFT]].\] # Witten (June, b) ## Matrix Models and Deformations of JT Gravity \[Links: [arXiv](https://arxiv.org/abs/2006.13414), [PDF](https://arxiv.org/pdf/.pdf2006.13414)\] \[Abstract: Recently, it has been found that [[0050 JT gravity|JT gravity]], which is a two-dimensional theory with bulk action $-\frac{1}{2}\int {\mathrm d}^2x \sqrt g\phi(R+2)$, is [[0471 String-matrix duality|dual]] to a [[0197 Matrix model|matrix model]], that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action $-\frac{1}{2}\int {\mathrm d}^2x \sqrt g(\phi R+W(\phi))$ is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if $W(0)=0$, and otherwise a rather complicated answer.\] # Wondrak, Kaminski, Bleicher ## Shear transport far from equilibrium via holography \[Links: [arXiv](https://arxiv.org/abs/2002.11730), [PDF](https://arxiv.org/pdf/2002.11730.pdf)\] \[Abstract: In heavy-ion collisions, the quark-gluon plasma is produced far from equilibrium. This regime is currently inaccessible by quantum chromodynamics (QCD) computations. We calculate shear transport and entropy far from equilibrium in a holographic model, defining a time-dependent ratio of [[0430 Holographic shear viscosity|shear viscosity]] to entropy density, $\eta/s$. Large deviations of up to 60% from its near-equilibrium value, $1/4\pi$, are found for realistic situations at the Large Hadron Collider. We predict the far-from-equilibrium time-dependence of $\eta/s$ to substantially affect the evolution of the QCD plasma and to impact the extraction of QCD properties from flow coefficients in heavy-ion collision data.\] # Zhao ## Collision in the interior of wormhole \[Links: [arXiv](https://arxiv.org/abs/2011.06016), [PDF](https://arxiv.org/pdf/2011.06016.pdf)\] \[Abstract: The Schwarzschild wormhole has been interpreted as an entangled state. If Alice and Bob fall into each of the black hole, they can meet in the interior. We interpret this meeting in terms of the quantum circuit that prepares the entangled state. Alice and Bob create growing perturbations in the circuit, and we argue that the overlap of these perturbations represents their meeting. We compare the gravity picture with circuit analysis, and identify the post-collision region as the region storing the gates that are not affected by any of the perturbations.\] <!-- ## Refs - talk at [[Rsc0036 Banff Gravitational Emergence in AdS-CFT]] and at UCSB -->