Sphaleron Transition Rate in Presence of Dynamical Fermions

We investigate the effect of dynamical fermions on the sphaleron transition rate at finite temperature for the Abelian Higgs model in one spatial dimension. The fermion degrees of freedom are included through bosonization. Using a numerical simulation, we find that massless fermions do not change the rate within the measurement accuracy. Surprisingly, the exponential dependence of the sphaleron energy on the Yukawa coupling is not borne out by the transition rate, which shows a very weak dependence on the fermion mass.