Dynamical Restoration of Z_N Symmetry in SU(N)+Higgs Theories

TL;DR

This paper investigates how Z_N symmetry in SU(N)+Higgs theories is explicitly broken in the Higgs phase but effectively restored in the symmetric phase, affecting phase transition characteristics and topological defect solutions.

Contribution

It demonstrates the effective restoration of Z_N symmetry in the Higgs symmetric phase and explores its implications for phase transitions and topological defects.

Findings

Z_N symmetry is broken in the Higgs phase

Z_N symmetry is effectively restored in the Higgs symmetric phase

Restoration influences the nature of the confinement-deconfinement transition

Abstract

We study the Z_N symmetry in SU(N)+Higgs theories with the Higgs field in the fundamental representation. The distributions of the Polyakov loop show that the Z_N symmetry is explicitly broken in the Higgs phase. On the other hand, inside the Higgs symmetric phase the Polyakov loop distributions and other physical observables exhibit the Z_N symmetry. This effective restoration of the Z_N symmetry changes the nature of the confinement-deconfinenement transition. We argue that the Z_N symmetry will lead to time independent topological defect solutions in the Higgs symmetric deconfined phase which will play important role at high temperatures.