Lattice study on QCD-like theory with exact center symmetry

TL;DR

This study explores the phase transition behavior of a lattice QCD-like theory with exact center symmetry, revealing a first-order transition and the interplay between center and chiral symmetries at finite temperature.

Contribution

It introduces a lattice formulation of center symmetric SU(3) gauge theory with twisted boundary conditions, providing new insights into the nonperturbative connection between center and chiral properties.

Findings

First-order center phase transition with hysteresis in Polyakov loop.

Chiral condensate decreases around the critical temperature similarly to standard QCD.

Flavor symmetry breaking due to boundary conditions manifests at high temperature.

Abstract

We investigate QCD-like theory with exact center symmetry, with emphasis on the finite-temperature phase transition concerning center and chiral symmetries. On the lattice, we formulate center symmetric $SU(3)$ gauge theory with three fundamental Wilson quarks by twisting quark boundary conditions in a compact direction ($Z_3$-QCD model). We calculate the expectation value of Polyakov loop and the chiral condensate as a function of temperature on 16^3 x 4 and 20^3 x 4 lattices along the line of constant physics realizing $m_{PS}/m_{V}=0.70$. We find out the first-order center phase transition, where the hysteresis of the magnitude of Polyakov loop exists depending on thermalization processes. We show that chiral condensate decreases around the critical temperature in a similar way to that of the standard three-flavor QCD, as it has the hysteresis in the same range as that of Polyakov loop. We also show that the flavor symmetry breaking due to the twisted boundary condition gets qualitatively manifest in the high-temperature phase. These results are consistent with the predictions based on the chiral effective model in the literature. Our approach could provide novel insights to the nonperturbative connection between the center and chiral properties.