Holographic Euclidean thermal correlator

TL;DR

This paper calculates exact Euclidean thermal correlators for stress tensor and $U(1)$ current in a holographic setup using black hole backgrounds, solving boundary value problems via Heun equations.

Contribution

It introduces a method to compute holographic thermal correlators by relating Einstein and Maxwell equations to Heun equations, providing exact solutions.

Findings

Exact two-point correlators for $U(1)$ current and stress tensor obtained.

Boundary value problems partly solved using Heun equation connection relations.

Provides a new approach for holographic thermal correlator calculations.

Abstract

In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and $U(1)$ current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein's gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact two-point thermal correlators for $U(1)$ current and stress tensor in the scalar and shear channels.