Analytic thermal bootstrap meets holography

TL;DR

This paper develops a method to compute thermal holographic correlators by combining their analytic structure with the KMS condition and OPE coefficients, providing explicit calculations and interpretations in black brane and black hole backgrounds.

Contribution

It introduces a novel approach to compute thermal correlators using analytic structure and OPE data, connecting to Witten diagrams and extending to black hole backgrounds.

Findings

Holographic two-point functions split into principal, regularized, and arcs contributions.

Principal contributions match numerical solutions for specific conformal dimensions.

Expansion in generalized free field correlators has a natural Witten diagram interpretation.

Abstract

We compute thermal holographic correlators by combining their analytic structure with the Kubo-Martin-Schwinger (KMS) condition and multi-stress tensor OPE coefficients determined from the dual AdS description. We focus on two-point functions of identical scalar operators with integer conformal dimensions at zero spatial separation. In the black brane background, we show explicitly that holographic two-point functions split into three contributions: a principal one, computed exactly, plus regularized and arcs contributions, both approximated through the use of OPE coefficients asymptotics. For $\Delta_\phi=3$, we show that the principal contribution agree with good approximation with the numerical solution of the bulk wave equation. Moreover, we demonstrate that the expansion in generalized free field correlators proposed in [Barrat,6/2025] admits a natural interpretation in terms of Witten diagrams. Finally, we initiate the study of thermal correlators in the spherically symmetric black hole background, computing their principal contributions.