Thermal correlation functions in CFT and factorization

TL;DR

This paper investigates thermal correlation functions in conformal field theories using holography, revealing universal formulas, corrections at strong coupling, and a factorization property of 3-point functions in certain regimes.

Contribution

It provides a universal holographic formula for free energy, incorporates ' corrections, and uncovers a factorization property of 3-point functions at finite temperature.

Findings

Universal formula for holographic free energy in terms of the c-anomaly.

Leading ' corrections reproduce strong coupling effects.

Factorization property of 3-point functions when _i= _j+ _k.

Abstract

We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in $d$ dimensions in terms of the $c$-anomaly coefficient. By including $\alpha'$ corrections to the black brane background, one can reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula, which reduces to the expected expressions in different limits. When the dimensions satisfy $\Delta_i= \Delta_j+ \Delta_k$, the thermal 3-point function satisfies a factorization property. We argue that in $d>2$ factorization is a reflection of the semiclassical regime.