Correlation functions in finite temperature CFT and black hole singularities

TL;DR

This paper calculates finite-temperature correlation functions in a 4D conformal field theory using AdS/CFT, revealing an exponentiation property and linking graviton emission corrections to black hole singularity structure.

Contribution

It provides a new formula for thermal two-point functions in AdS/CFT, including first-order graviton corrections related to black hole singularities.

Findings

Derived a formula matching the expected OPE structure.

Identified an exponentiation property in the correlation functions.

Computed the first correction due to graviton emission, connecting to black hole singularity.

Abstract

We compute thermal 2-point correlation functions in the black brane $AdS_5$ background dual to 4d CFT's at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.