Black Hole Signatures in Holographic Correlators

Joydeep Chakravarty (McGill)

Robert de Mello Koch (Huzhou U.)

Matthew Dodelson (Harvard)

Saso Grozdanov (U Edinburgh, U Ljubljana)

Sean Hartnoll (Cambridge)

Cristoforo Iossa (U. Geneva)

Robin Karlsson (Oxford)

Shota Komatsu (CERN)

Enrico Marchetto (DESY)

Mukund Rangamani (UC Davis)

Masaki Shigemori (Nagoya U.)

Topics include 

• Heavy states, holography and black holes

• Finite temperature holographic correlators

• Bouncing and bulkcone singularities

• Black hole microstates

Monday, June 15 

11:00 am Nejc Ceplak (Trinity College Dublin)

Title: Stringy Splitting of Black Hole Singularities

Abstract: The analytic structure of finite-temperature holographic correlation functions encodes information about the spacetime geometry near black hole singularities. In particular, singularities of holographic correlators in the complex time plane are related to so-called bouncing geodesics: null geodesics that pass through the black hole interior and reflect off the black hole singularity.

In this talk, I will review how signatures of bouncing geodesics are encoded in the asymptotic behaviour of holographic OPE coefficients. After discussing the Schwarzschild-AdS black hole, I will turn to two separate examples in which the classical picture is modified: Gauss-Bonnet gravity and finite-coupling corrections in strongly interacting N=4 SYM theory. I will argue that stringy corrections induce a splitting of the black hole singularity into multiple complex singularities, and that holographic correlators retain a precise imprint of this splitting.

2:00 pm Cristoforo Iossa (U. Geneva)

Title: OPE = QNM at fixed k

Abstract: We discuss the analytic structure of thermal correlators at fixed spatial momentum. These correlators admit natural short time (OPE) and large time (QNM) expansions. We show that the two expansions agree within a common domain of convergence, and can be related to each other by a Mellin transform. This allows us to map QNM data to OPE data and viceversa.

3:30 pm Enrico Marchetto (DESY)

Title: An analytic toolkit for thermal correlators

Abstract: In this talk, I will present a general analytic bootstrap framework for thermal scalar two-point functions and explain how these correlators can be decomposed in terms of generalized free field correlators. I will discuss how the distinctive features of holographic CFTs at leading order in large NNN and large coupling emerge within this framework, and I will apply the method to AdS black brane solutions. I will conclude by showing how the analytic framework translates into momentum space.

Tuesday, June 16 

11:00 am Joydeep Chakravarty (McGill)

Title: Holographic thermal correlators and the black hole interior*

Abstract: We discuss a high-energy simplification which allows us to probe local physics about a bulk point using boundary correlators. For a single-side black hole, we use it to study the Schwarzchild singularity using the thermal two-point function, and analytically prepare the interior geometry using the four-point function. For a two-sided black hole, we discuss how to use the four-point correlator to image local physics in the actual  two-sided interior.

2:00 pm Robin Karlsson (Oxford)

Title: AdS BH EFT/CFT and love numbers 

Abstract: Love numbers characterize the response of a compact object to an external perturbation and provide a means of distinguishing between different such objects. We study a black-hole effective field theory (EFT), parameterized by the Love numbers, in AdS and its holographic imprints on thermal two-point functions in the boundary theory.

3:00 pm Shota Komatsu (CERN)

Title: No Shift, Sherlock

Wednesday, June 17 

11:00 am Matthew Dodelson (Harvard)

Title: Complex scattering and the black hole interior

Abstract: We'll explore the emergence of the interior in large N matrix quantum mechanics at high temperatures. In this limit the bouncing geodesics are related to D-brane scattering. We'll first define a complex scattering matrix for any classical dynamical system, and then apply it to our problem. Our results imply that stringy interiors should have a fractal nature.

2:00 pm Robert de Mello Koch (Huzhou U.)

Title: Non-perturbative structure from invariant theory

Abstract: At finite N the ring of gauge invariant operators is not freely generated. However, the full invariant ring is a free module over a polynomial ring generated by the primary invariants. The module basis is given by finitely many secondary invariants. This motivates a physical picture in which the primary invariants are regarded as perturbative degrees of freedom while the secondary invariants are associated with distinguished non-perturbative states or sectors. This talk will show that a concrete algebraic version of this picture is already visible in simple zero-dimensional matrix integrals.

Thursday, June 18 

11:00 am Masaki Shigemori (Nagoya U.)

Title: The resolved elliptic genus and the D1-D5 system. 

Abstract: The resolved elliptic genus (REG) for the D1-D5 CFT on T^4 is a generalization of the standard supersymmetry index, the modifield elliptic genus (MEG), and contains more information about the states being counted than the MEG.  I will explain how one is naturally led to the REG by organizing BPS states of the D1-D5 CFT at its symmetric orbifold point in a way similar to the organizion of states of n spin-1/2 particles in quantum mechanics.  This talk is based on work with Marcel Hughes.

2:00 pm Sašo Grozdanov (U Edinburgh, U Ljubljana)

Title: Analytic structure of black hole correlators and signatures of curvature singularities

Abstract: I will begin by discussing the analytic structure of black hole correlation functions in momentum space, as derived from holographic thermal setups in Anti-de Sitter space. A particular focus will be the discussion of various constraints on such spectra, in particular the thermal product formula and our recently derived spectral duality relation. I will then describe our results on understanding the analytic structure in position space, where the singularities of retarded correlators can be understood in the language of the Hadamard theory of differential equations and the behavior of null geodesics. Of particular interest will be the relation between a type of null geodesic, called the bouncing geodesic, and the existence of black hole curvature singularities. Finally, I will show how all of these results can be extended to the physics of black hole perturbations in flat and de Sitter spaces by enclosing a black hole in a reflecting cavity. 

3:30 pm Mukund Rangamani (UC Davis)

Title: Thermal OPE, exact WKB, and the black hole singularity

Abstract: I will discuss analytic properties of thermal spectral functions of holographic CFTs, both at finite and asymptotic values of momenta. For a special class of scalar operators with integer dimensions in even dimensional holographic CFTs, we obtain a full transseries at large timelike momentum. This information, we argue, captures imprints of the black hole singularity in the dual field theory observables. Time permitting, I will also explain universality of these signatures. The talk is based on work with Hewei Frederic Jia.

Friday, June 19

10:00 am Ilija Buric (Trinity College Dublin)

Title: TBD

11:30 am Sean Hartnoll (Cambridge)

Title: BKL singularities and holography

Abstract: I will review the BKL scenario for spacelike singularities in general relativity and discuss possible holographic implications of this scenario. I will also discuss the possibility of a dual description of the interior based on number theoretic properties of the interior Wheeler-DeWitt wavefunctions.