Confinement-deconfinement transition in $SU(3)$-Higgs theory

TL;DR

This study investigates how lattice cutoff effects influence the confinement-deconfinement transition and $Z_3$ symmetry in $SU(3)$-Higgs theory, revealing dependence on lattice parameters and potential symmetry restoration in the continuum limit.

Contribution

It provides new insights into the lattice cutoff effects on phase transition nature and $Z_3$ symmetry in $SU(3)$-Higgs theory, especially regarding the continuum limit behavior.

Findings

Transition is first order for $N_\tau \ge 3$

$Z_3$ symmetry breaking decreases with increasing $N_\tau$

$Z_3$ symmetry may be restored in the continuum limit

Abstract

We study lattice cutoff effects on the confinement-deconfinement transition and the $Z_3$ symmetry in $SU(3)$-Higgs theory in $3+1$ dimensions. The Higgs in this study is a complex triplet with vanishing bare mass and quartic coupling. The lattice cutoff is regulated by varying the number of temporal lattice sites, $N_\tau$. Our results show that the nature of the confinement-deconfinement transition depends on $N_\tau$. For $N_\tau=2$ the transition is found to be the end point of a first-order transition and is first order for $N_\tau \ge 3$. The distributions of the Polyakov loop and other observables, sensitive to the $Z_3$ symmetry, show that the strength of $Z_3$ explicit breaking decreases with $N_\tau$. Up to $T\simeq 2T_c$, the free energy difference between $Z_3$ states decreases with $N_\tau$, suggesting the realization of $Z_3$ symmetry in the continuum limit.