A simple model with Z_N symmetry

TL;DR

This paper introduces a simplified model with Z_N symmetry to explore its validity in QCD with light quarks, revealing symmetry preservation below a critical temperature and its spontaneous breaking above, akin to known models.

Contribution

It constructs a flavor-dependent twisted boundary condition version of the PNJL model to analyze Z_N symmetry behavior in QCD-like theories.

Findings

Z_N symmetry is preserved below T_c and broken above T_c.

The model's dynamics resemble the original PNJL model without TBC.

The study explores the relationship between Z_N symmetry and quarkyonic phase emergence.

Abstract

We propose a simple model with the Z_N symmetry in order to answer whether the symmetry is a good concept in QCD with light quark mass. The model is constructed by imposing the flavor-dependent twisted boundary condition (TBC) on the three-flavor Polyakov-loop extended Nambu-Jona-Lasinio model. In the model, the Z_N symmetry is preserved below some temperature T_c, but spontaneously broken above T_c. Dynamics of the simple model is similar to that of the original PNJL model without the TBC, indicating that the Z_N symmetry is a good concept. We also investigate the interplay between the Z_N symmetry and the emergence of the quarkyonic phase.