Lattice study of the critical bubble in $\mathrm{SU(8)}$ deconfinement transition

TL;DR

This study investigates the critical bubble in a 4D SU(8) pure gauge model to better understand first order phase transitions relevant for gravitational wave signals, using advanced lattice Monte Carlo methods.

Contribution

First direct resolution of the critical bubble in a pure Yang-Mills model, providing data for nucleation rates and insights into order parameter effectiveness.

Findings

Determined the critical bubble probability in SU(8) gauge theory.

Compared bubble nucleation results with thin wall calculations.

Highlighted the importance of order parameter choice in lattice simulations.

Abstract

Strongly coupled theories are of phenomenological interest, for example as dark matter candidates. Theories that can undergo first order thermal phase transitions are particularly appealing as potential sources of a stochastic gravitational wave background. Determining the expected gravitational wave signal from a first order phase transition requires accurate information on the bubble nucleation rate, but thus far for strongly coupled models these have relied on semiclassical methods. As a first step towards determining the nucleation rate, in this paper we study the confinement-deconfinement phase transition in a 4D SU(8) pure gauge model, using multicanonical Monte Carlo. Resolving the critical bubble for the first time in a pure Yang-Mills model, we determine the critical bubble probability and compare it to results from thin wall calculations. We also compare the effectiveness of different lattice pseudo-order parameters at resolving the condensation transition between the metastable phase and critical bubble branch, and point out the choice of order parameter is crucial to accurately resolve the critical configurations.