Exact thermal correlators of holographic $CFT$s

TL;DR

This paper derives exact thermal correlators in holographic conformal field theories with chemical potential and angular momentum by solving quasi-normal mode equations and employing the AGT correspondence to connect solutions.

Contribution

It introduces a novel method to compute exact retarded Green's functions in thermal CFTs with chemical potential and rotation using Heun equations and Liouville CFT techniques.

Findings

Exact retarded Green's functions obtained for charged and rotating black holes.

Connection formulae derived using AGT correspondence and Liouville CFT.

Method provides a new way to analyze thermal correlators in holography.

Abstract

We compute the exact retarded Green's functions in thermal $CFT$s with chemical potential and angular momenta using holography respectively. We consider the field equations satisfied by the quasi-normal modes in both charged and rotating black holes in $AdS$ spacetime and mapped them to the Heun equations by appropriate changes of variables. The AGT correspondence allows us to find the connection formulae among the solutions of the Heun equations near different singularities by using the crossing relations of the five-point correlators in the Liouville $CFT$. The connection formulae associated with the boundary conditions imposed on the bulk field equations yield the exact thermal correlators in the boundary $CFT$.