On Gauge Symmetry Breaking via Euclidean Time Component of Gauge Fields

TL;DR

This paper investigates gauge symmetry breaking mechanisms at finite temperature in theories with extra dimensions, finding that symmetry can only be broken via the extra dimension's zero mode, not the Euclidean time direction.

Contribution

It provides a detailed one-loop analysis of gauge symmetry breaking via zero modes in theories with extra dimensions and finite temperature, clarifying the roles of different order parameters.

Findings

Gauge symmetry breaks only through the extra dimension zero mode.

No nontrivial vacuum configuration for the Euclidean time zero mode.

Effective potential analysis confirms the symmetry breaking pattern.

Abstract

We study gauge theories with/without an extra dimension at finite temperature, in which there are two kinds of order parameters of gauge symmetry breaking. The one is the zero mode of the gauge field for the Euclidean time direction and the other is that for the direction of the extra dimension. We evaluate the effective potential for the zero modes in one-loop approximation and investigate the vacuum configuration in detail. Our analyses show that gauge symmetry can be broken only through the zero mode for the direction of the extra dimension and no nontrivial vacuum configuration of the zero mode for the Euclidean time direction is found.