Zero interface tension at the deconfining phase transition for a matrix model of a $SU(\infty)$ gauge theory

TL;DR

This paper uses a matrix model to study the deconfining phase transition in large N SU(N) gauge theories, revealing that interface tensions vanish at the critical temperature, with potential non-monotonic behavior at small N.

Contribution

It demonstrates that both the order-disorder and order-order interface tensions vanish at the deconfining transition in the matrix model, providing estimates of their behavior near the critical temperature and large N.

Findings

Interface tensions vanish at the critical temperature.

Possible non-monotonic behavior of tensions at small N.

Quantitative estimates of tension vanishing near T_d.

Abstract

Using a matrix model, we model the deconfining phase transition at nonzero temperature for a SU(N) gauge theory at large $N$. At infinite $N$ the matrix model exhibits a Gross-Witten-Wadia transition. We show that as a consequence, both the order-disorder and the order-order interface tensions vanish identically at the critical temperature $T_d$. We estimate how these quantities vanish in the matrix model as $T \rightarrow T_d$ and as $N \rightarrow \infty$. The numerical solution of the matrix model suggests possible non-monotonic behavior in $N$ for relatively small values of $N \sim 5$.