$Z_2$ symmetry in $Z_2+$Higgs theory. In:

Abstract

Using Monte Carlo methods, we study Z2 symmetry in Z2+Higgs theory. In 3 + 1 space-time dimensions, our simulation results suggest that the Z2 symmetry is realized at large number of temporal lattice points (Nτ) in the Higgs symmetric phase. In order to see the dependence of Z2 symmetry on the number of temporal lattice points we have also studied a simple temporal one dimensional model for a given spatial site. We show that the Z2 symmetry is observed at the level of free energy at large Nτ limit. For this model, we also compute the density of states (DoS) for various Nτ values, where we show that the realization of the Z2 symmetry happens at higher Nτ. Therefore, the realization of Z2 symmetry may be due to dominance of the DoS.