Possible higher order phase transition in large-$N$ gauge theory at finite temperature

TL;DR

This paper investigates the phase transitions in large-$N$ gauge theories at finite temperature, revealing potential higher-order transitions and emphasizing the role of confining potentials, with implications for lattice simulations.

Contribution

It proposes a universal matrix model framework showing that large-$N$ gauge theories can exhibit higher-order phase transitions beyond the known third order.

Findings

Identification of a universal structure in the phase transition behavior.

Different confining potentials lead to distinct eigenvalue density and free energy behaviors.

Potential for lattice simulations to test the order of phase transitions.

Abstract

We analyze the phase structure of $SU(\infty)$ gauge theory at finite 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 temperature, a background field for the Polyakov loop, and a quartic coupling, it exhibits a universal structure: in the large portion of the parameter space, there is a continuous phase transition analogous to the third-order phase transition of Gross, Witten and Wadia, but the order of phase transition can be higher than third. We show that different confining potentials give rise to drastically different behavior of the eigenvalue density and the free energy. Therefore lattice simulations at large $N$ could probe the order of phase transition and test our results.