Thermal N = 4 SYM theory as a 2D Coulomb gas

TL;DR

This paper models N=4 supersymmetric Yang-Mills theory at finite temperature as a two-dimensional Coulomb gas of eigenvalues, revealing different eigenvalue distributions in confined and deconfined phases.

Contribution

It introduces a novel Coulomb gas representation of the theory's eigenvalues, providing new insights into phase transitions at finite temperature.

Findings

Eigenvalues condense on a strip in the confined phase

Eigenvalues form an ellipsoidal droplet in the deconfined phase

The Coulomb gas description captures phase transition behavior

Abstract

We consider N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group at large N and at finite temperature on a spatial S^3. We show that, at finite weak 't Hooft coupling, the theory is naturally described as a two dimensional Coulomb gas of complex eigenvalues of the Polyakov-Maldacena loop, valued on the cylinder. In the low temperature confined phase the eigenvalues condense onto a strip encircling the cylinder, while the high temperature deconfined phase is characterised by an ellipsoidal droplet of eigenvalues.