Finite-temperature phase transitions of third and higher order in gauge theories at large $N$

TL;DR

This paper investigates high-order phase transitions in large N gauge theories using matrix models, revealing a universal structure and suggesting possible conformal symmetry at the deconfining transition.

Contribution

It introduces a universal matrix model framework for understanding high-order phase transitions in large N gauge theories, extending the GWW transition.

Findings

Existence of continuous phase transitions of order higher than second.

The phase diagram exhibits a universal structure across parameter space.

Eigenvalue density and specific heat behavior vary significantly depending on the model.

Abstract

We study phase transitions in $SU(\infty)$ gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure. In a large region of this parameter space, there is a continuous phase transition whose order is larger than second. This is a generalization of the phase transition of Gross, Witten, and Wadia (GWW). Depending upon the detailed form of the matrix model, the eigenvalue density and the behavior of the specific heat near the transition differ drastically. We speculate that in the pure gauge theory, that although the deconfining transition is thermodynamically of first order, it can be nevertheless conformally symmetric at infinite $N$.