Thermal holographic correlators and KMS condition

TL;DR

This paper investigates how thermal two-point functions in holographic conformal field theories satisfy the KMS condition by analyzing stress-tensor and double-trace contributions, providing explicit calculations and methods to impose periodicity in Euclidean time.

Contribution

It demonstrates how to impose the KMS condition to determine the double-trace part of thermal correlators from the stress-tensor sector in holographic CFTs.

Findings

KMS condition fixes double-trace contributions in correlators

Explicit calculations in asymptotic approximation match resummation methods

Stress-tensor sector computed exactly near the AdS boundary

Abstract

Thermal two-point functions in holographic CFTs receive contributions from two parts. One part comes from the identity, the stress tensor and multi-stress tensors and constitutes the stress-tensor sector. The other part consists of contributions from double-trace operators. The sum of these two parts must satisfy the KMS condition -- it has to be periodic in Euclidean time. The stress-tensor sector can be computed by analyzing the bulk equations of motions near the AdS boundary and is not periodic by itself. We show that starting from the expression for the stress-tensor sector one can impose the KMS condition to fix the double-trace part, and hence the whole correlator. We perform explicit calculations in the asymptotic approximation, where the stress-tensor sector can be computed exactly. One can either sum over the thermal images of the stress-tensor sector and subtract the singularities or solve for the KMS condition directly and perform the Borel resummation of the resulting double-trace data -- the results are the same.