Computation of the winding number diffusion rate due to the cosmological sphaleron

TL;DR

This paper provides an exact analytical calculation of the sphaleron-mediated transition rate in a static Einstein universe, advancing understanding of non-Abelian gauge field processes in cosmological settings.

Contribution

It presents the first exact solution for the sphaleron transition rate in 3+1 dimensions using zeta function regularization.

Findings

Derived a closed-form expression for the transition rate

Performed spectral analysis of fluctuation operators

Demonstrated the applicability of zeta function regularization

Abstract

A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe is carried out. By examining spectra of the fluctuation operators and applying the zeta function regularization scheme, a closed analytical expression for the transition rate at the one-loop level is derived. This is a unique example of an exact solution for a sphaleron model in $3+1$ spacetime dimensions.