Thermal Correlators and Black Holes: From Infinity to Singularity

Abstract

This thesis investigates the relationship between thermal correlation functions in conformal field theories (CFTs) and the geometry of black holes within the AdS/CFT correspondence. Using a common technique -- a near-boundary expansion -- we examine two main themes.

First, we study deep geometric features of black holes from the CFT perspective. We demonstrate that information about the black hole singularity is encoded in the stress-tensor sector of the boundary correlator. More precisely, by resumming the contributions from the stress tensor and its composites, we discover branch-point singularities in the complex time plane. These singularities precisely correspond to the bulk geodesics that traverse the black hole interior, reflect off the singularity, and return to the boundary of the maximally extended spacetime. Furthermore, we explain the role of double-trace operators in the restoration of analyticity and KMS condition, and establish a map between individual bulk geodesics and OPE sectors of the thermal boundary correlator.

Second, we explore the universality of thermal stress-tensor correlators in CFTs with pure gravity duals. Through detailed holographic calculations in Einstein and Gauss-Bonnet gravity, we analyse the structure of two-point functions near the lightcone and identify a robust universal behaviour -- in this regime, the correlators are described by three universal functions. The bulk Lagrangian only affects the arguments of these functions through corrections to the cubic stress-tensor couplings and the thermal stress-tensor one-point function. We explain how this behaviour is connected to causality constraints, such as the averaged null energy condition (ANEC). In particular, we demonstrate that saturation of the ANEC leads to the correlator becoming independent of temperature.

Together, these results highlight the power of the near-boundary method as an effective tool for extracting physical data in holographic CFTs. Our results also suggest that thermal correlators -- especially their stress-tensor sector -- serve as sensitive probes of geometry beyond the black hole horizon and offer valuable insights into causality constraints and universal features of holographic theories.