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

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 $T>T_c$.