Topology and $\theta$ dependence in finite temperature $G_2$ lattice gauge theory

TL;DR

This paper investigates the topological features and $ heta$ dependence of $G_2$ lattice gauge theory at finite temperature, revealing a transition in topological behavior at deconfinement similar to $SU(N)$ theories.

Contribution

It provides the first detailed Monte Carlo analysis of topological properties and $ heta$ dependence in $G_2$ gauge theory across the deconfinement transition.

Findings

Topological quantities change abruptly at deconfinement

Instanton gas behavior emerges above $T_c$

Topological features resemble those in $SU(N)$ gauge theories

Abstract

In this work we study the topological properties of the $G_2$ lattice gauge theory by means of Monte Carlo simulations. We focus on the behaviour of topological quantities across the deconfinement transition and investigate observables related to the $\theta$ dependence of the free energy. As in $SU(N)$ gauge theories, an abrupt change happens at deconfinement and an instanton gas behaviour rapidly sets in for $T>T_c$.