Updates on the density of states method in finite temperature symplectic gauge theories

TL;DR

This paper discusses the application of the density of states method, specifically the LLR technique, to analyze the finite temperature deconfinement phase transition in an $Sp(4)$ gauge theory, with implications for dark sector phenomenology.

Contribution

It provides an updated analysis of the phase transition in $Sp(4)$ gauge theory using the LLR density of states method, including insights into the thermodynamic limit.

Findings

First analysis of the transition in the thermodynamic limit

Demonstrates the effectiveness of the LLR method for this problem

Provides a roadmap for future research in this area

Abstract

First-order phase transitions in the early universe have rich phenomenological implications, such as the production of a potentially detectable signal of stochastic relic background gravitational waves. The hypothesis that new, strongly coupled dynamics, hiding in a new dark sector, could be detected in this way, via the telltale signs of its confinement/deconfinement phase transition, provides a fascinating opportunity for interdisciplinary synergy between lattice field theory and astro-particle physics. But its viability relies on completing the challenging task of providing accurate theoretical predictions for the parameters characterising the strongly coupled theory. Density of states methods, and in particular the linear logarithmic relaxation (LLR) method, can be used to address the intrinsic numerical difficulties that arise due the meta-stable dynamics in the vicinity of the critical point. For example, it allows one to obtain accurate determinations of thermodynamic observables that are otherwise inaccessible, such as the free energy. In this contribution, we present an update on results of the analysis of the finite temperature deconfinement phase transition in a pure gauge theory with a symplectic gauge group, $Sp(4)$, by using the LLR method. We present a first analysis of the properties of the transition in the thermodynamic limit, and provide a road map for future work, including a brief preliminary discussion that will inform future publications.