Possible Restoration of $$Z_3$$ Symmetry in the Presence of Fundamental Higgs

We study the \(Z_3\) symmetry in SU(3) Higgs theory using Monte Carlo simulation methods. We focus mainly on the distribution of the Polyakov loop and related parameters to study the \(Z_3\) symmetry. We show that the \(Z_3\) symmetry is explicitly broken when Higgs condesate acquires a nonzero value. However, we also show that there is a possibility of the \(Z_3\) symmetry in the Higgs symmetric phase where Higgs condensate vanishes.