More on quantum kinks in gauge theories on $R^2 \otimes S^1$

TL;DR

This paper investigates quantum kink solutions in gauge theories on a space-time with two spatial dimensions and a circle, analyzing their profiles and stability through effective actions and one-loop calculations.

Contribution

It provides explicit kink profiles in scalar QED and examines the impact of derivative corrections on vacuum stability in $SU(2)$ Yang-Mills theory.

Findings

Existence of soliton solutions in scalar QED.

Derivative corrections can destabilize the vacuum in $SU(2)$ Yang-Mills.

Effective actions including derivative terms are computed at zero and finite temperature.

Abstract

Quantum kinks in gauge theories on $R^2\otimes S^1$ space-time are studied. To obtain the, explicit profile of the kinks, we calculated effective actions including derivative corrections for vacuum gauge fields on $S^1$ at zero, and finite temperature up to one-loop level. It is found that there are soliton solutions in scalar QED. We also find that the derivative correction tends to make the vacuum unstable in $SU(2)$ Yang-Mills theory.