On the gauge dependence of vacuum transitions at finite temperature

Understand

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.