Thermal spectral function asymptotics and black hole singularity in holography

TL;DR

This paper analyzes the asymptotic behavior of thermal spectral functions in holographic CFTs, revealing their structure and singularities, which encode information about black hole singularities in the dual spacetime.

Contribution

It introduces a factorization of spectral functions for scalar primaries and derives a transseries expression using WKB techniques, refining understanding of black hole singularity encoding.

Findings

Spectral functions factor into polynomial and non-perturbative parts.

Derived transseries expression for the non-perturbative component.

Identified singularities in correlators related to black hole singularities.

Abstract

We investigate the analytic structure of thermal spectral function of holographic CFTs, synthesizing recent developments into a set of observations about its asymptotics. Specifically, for a class of scalar primaries with integral dimension, we demonstrate factorization of the exact spectral function into a polynomial piece, which captures the vacuum dynamics, and a non-perturbative piece, which controls its asymptotics. Using exact WKB techniques, we derive a transseries expression for the latter. We use this information to deduce the singular loci of a spatially averaged thermofield double correlator in the complex time plane. Such singularities have been argued to encode information regarding the black hole singularity in the dual spacetime. Our results give a refinement of these statements by capturing the momentum dependence.