On the gauge dependence of vacuum transitions at finite temperature

TL;DR

This paper investigates the gauge dependence in calculating vacuum transition rates at finite temperature, highlighting that while physical observables should be gauge-independent, practical perturbative methods introduce small gauge dependencies.

Contribution

It demonstrates that gauge dependence in perturbative calculations of vacuum transitions is minimal when using gauges compatible with the perturbative expansion, using the Abelian Higgs model as an example.

Findings

Gauge dependence is small in consistent gauges.

Explicit perturbative calculations introduce some gauge dependence.

Effective potential analysis in the Abelian Higgs model illustrates the issue.

Abstract

In principle, observables as for example the sphaleron rate or the tunneling rate in a first-order phase transition are gauge-independent. However, in practice a gauge dependence is introduced in explicit perturbative calculations due to the breakdown of the gradient expansion of the effective action in the symmetric phase. We exemplify the situation using the effective potential of the Abelian Higgs model in the general renormalizable gauge. Still, we find that the quantitative dependence on the gauge choice is small for gauges that are consistent with the perturbative expansion.