Deconfinement and CP-breaking at $\theta=\pi$ in Yang-Mills theories and a novel phase for SU(2)

TL;DR

This paper investigates phase transitions at = in Yang-Mills theories, revealing a novel CP-broken deconfined phase for SU(2) and analyzing the conditions under which deconfinement and CP restoration occur.

Contribution

It analytically studies deconfinement and CP-breaking transitions in softly-broken =1 supersymmetric Yang-Mills theories, discovering a new phase for SU(2) with a temperature window.

Findings

Deconfinement and CP restoration occur simultaneously for most gauge groups.

SU(2) exhibits a finite temperature window with a CP-broken deconfined phase.

Implications for domain walls and junctions in the novel phase.

Abstract

We discuss the deconfinement and the CP-breaking phase transitions at $\theta=\pi$ in Yang-Mills theories. The 't Hooft anomaly matching prohibits the confined phase with CP symmetry and requires $T_{dec}(\theta=\pi) \le T_{CP}$, where $T_{dec}(\theta=\pi)$ and $T_{CP}$ denote the deconfinement and the CP-restoration temperatures, respectively, at $\theta=\pi$. We analytically study these two phase transitions in softly-broken $\mathcal{N}=1$ supersymmetric Yang-Mills theories on small $\mathbb{R}^3\times S^1$ with the periodic boundary condition for gluinos. For most gauge groups except SU(2) in this model, we find that the inequality is saturated, so deconfinement and CP restoration occur simultaneously. We demonstrate special features of the SU(2) gauge theory: There is a finite window of two temperatures, $T_{dec}(\pi)<T_{CP}$, which indicates the existence of a novel CP-broken deconfined phase. We also discuss an implication of the novel phase for domain walls and their junctions.