Phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $\theta$-angle

TL;DR

This paper investigates the phase structure of $q$-deformed Yang-Mills theory on a sphere at non-zero $ heta$-angle, revealing multiple phase transitions through exact finite-$N$ partition function analysis.

Contribution

It provides the first numerical evidence for a series of phase transitions in $q$-deformed Yang-Mills theory at non-zero $ heta$-angle, confirming prior conjectures.

Findings

Multiple phase transitions at non-zero $ heta$-angle

Numerical evaluation of exact partition function

Confirmation of previous theoretical conjectures

Abstract

We study the phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $\theta$-angle using the exact partition function at finite $N$. By evaluating the exact partition function numerically, we find evidence for the existence of a series of phase transitions at non-zero $\theta$-angle as conjectured in [hep-th/0509004].