Thermal Correlators and Black Holes: From Infinity to Singularity

TL;DR

This thesis investigates how thermal correlation functions in conformal field theories encode information about black hole interiors, singularities, and causality through holographic duality, revealing universal behaviors and the role of stress-tensor operators.

Contribution

It uncovers the connection between boundary stress-tensor correlators and bulk black hole singularities, and identifies universal features of thermal correlators in holographic CFTs with gravity duals.

Findings

Stress-tensor correlators encode black hole singularity information.

Universal near-lightcone behavior of thermal correlators in holographic CFTs.

Saturation of the averaged null energy condition leads to temperature-independent correlators.

Abstract

This thesis explores thermal correlation functions in conformal field theories (CFTs) and their connection to black hole geometry within the AdS/CFT correspondence, using a near-boundary expansion as the main tool. Two themes are examined. First, we show that the stress-tensor sector of boundary correlators encodes information about black hole singularities. By resumming contributions from the stress-tensor and its composites, we uncover branch-point singularities in complex time, corresponding to bulk geodesics that cross the horizon, reflect off the singularity, and return to the boundary. We further clarify the role of double-trace operators in restoring analyticity and the KMS condition, and establish a map between bulk geodesics and OPE sectors of the thermal correlator. Second, we study thermal stress-tensor correlators in CFTs with pure gravity duals. Through holographic calculations in Einstein and Gauss-Bonnet gravity, we identify a robust universal behaviour - near the lightcone 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 relate this behaviour to causality constraints such as the averaged null energy condition (ANEC), showing that ANEC saturation makes the correlator temperature-independent. Overall, our results demonstrate that thermal correlators - especially their stress-tensor sector - serve as sensitive probes of black hole interiors, causality, and universality in holographic CFTs.