Free Fermions and Thermal AdS/CFT

TL;DR

This paper provides an exact solution to finite temperature U(N) gauge theories on S^3 using a unitary matrix model, revealing a phase transition akin to the Hawking-Page transition, described via free fermions and phase space methods.

Contribution

It offers an exact, representation-based solution for finite N gauge theories and connects the large N phase transition to free fermion descriptions similar to BPS geometries.

Findings

Exact solution for finite N gauge theories on S^3.

Large N phase transition resembles Douglas-Kazakov transition.

Thermal AdS, black holes, and phase transitions described by free fermions.

Abstract

The dynamics of finite temperature U(N) gauge theories on $S^3$ can be described, at weak coupling, by an effective unitary matrix model. Here we present an exact solution to these models, for any value of $N$, in terms of a sum over representations. Taking the large $N$ limit of this solution provides a new perspective on the deconfinement transition which is supposed to be dual to the Hawking-Page transition. The large $N$ phase transition manifests itself here in a manner similar to the Douglas-Kazakov phase transition in 2d Yang-Mills theory. We carry out a complete analysis of the saddle representation in the simplest case involving only the order parameter ${\rm Tr}U$. We find that the saddle points corresponding to thermal $AdS$, the small black hole and the large black hole can all be described in terms of free fermions. They all admit a simple phase space description {\it a la} the BPS geometries of Lin, Lunin and Maldacena.