No $Z_N$ - bubbles in hot Yang-Mills theory

TL;DR

This paper demonstrates that in high-temperature pure Yang-Mills theory, the expected $Z_N$-phase transitions with domain walls do not occur in Minkowski space, indicating no spontaneous $Z_N$-symmetry breaking.

Contribution

It provides a theoretical proof that $Z_N$-phases and domain walls are absent in the physical Minkowski space for hot Yang-Mills theory.

Findings

No $Z_N$-phases in Minkowski space

Absence of spontaneous $Z_N$-symmetry breaking

Implication for phase structure of Yang-Mills theory

Abstract

Pure Yang-Mills theory at high temperature is considered. We show that no distinct $Z_N$- phases separated by domain walls do exist in the physical Minkowski space. That means the absense of the spontaneous breaking of $Z_N$- symmetry in the physical meaning of this word.