Aspects of thermal one-point functions and response functions in AdS Black holes

TL;DR

This paper analytically computes scalar one-point functions in AdS black holes, clarifies their pole structure, and extends techniques to spatially varying sources and large mass black holes, enhancing understanding of holographic response functions.

Contribution

It introduces a method for analytic calculation of scalar one-point functions in AdS black holes, including spatially modulated sources and large mass corrections, with detailed pole structure analysis.

Findings

Analytic expressions for one-point functions in various AdS black hole backgrounds.

Clarification of the pole structure related to operator mixing.

Extension of techniques to spatially varying sources and large mass limits.

Abstract

We revisit the problem of analytically computing the one point functions for scalar fields in planar AdS black holes of arbitrary dimension, which are sourced by the Weyl squared tensor. We analyze the problem in terms of power series expansions around the boundary using the method of Frobenius. We clarify the pole structure of the final answer in terms of operator mixing, as argued previously by Grinberg and Maldacena. We generalize the techniques to also obtain analytic results for slowly modulated spatially varying sources to first non-trivial order in the wave vector for arbitrary dimension. We also study the first order corrections to the one point function of the global AdS black hole at large mass, where we perturb in terms that correspond to the curvature of the horizon.