Fluctuation corrections to bubble nucleation

TL;DR

This work delivers an exact bosonic fluctuation determinant for the electroweak bubble in a three-dimensional high-temperature setting, incorporating the $T \Phi^3$ term that renders the phase transition first order. Using a partial-wave decomposition and a fast determinant theorem, it systematically handles divergences, zero modes, and gauge artifacts to compute the 1-loop correction to the nucleation rate. The findings indicate that the 1-loop action is substantial, often exceeding the classical minimal-bubble action and generally suppressing the transition rate, with the $T \Phi^3$ contribution playing a dominant role. Comparisons with Kripfganz et al.’s heat-kernel results show good agreement for small bubbles but notable deviations for large thin-wall bubbles, highlighting the need for potential self-consistent treatment and possibly fermionic contributions in a full analysis.

Abstract

The fluctuation determinant which determines the preexponential factor of the transition rate for minimal bubbles is computed for the electroweak theory with $\sin Θ_W = 0$. As the basic action we use the three-dimensional high-temperature action including, besides temperature dependent masses, the $T Φ^3$ one-loop contribution which makes the phase transition first order. The results show that this contribution (which has then to be subtracted from the exact result) gives the dominant contribution to the one-loop effective action. The remaining correction is of the order of, but in general larger than the critical bubble action and suppresses the transition rate. The results for the Higgs field fluctuations are compared with those of an approximate heat kernel computation of Kripfganz et al., good agreement is found for small bubbles, strong deviations for large thin-wall bubbles.