A simple model with ZN symmetry

We propose a simple model with the ZN 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-Lasiniomodel. In themodel, the ZN symmetry is preserved belowsome temperature Tc, but spontaneously broken above Tc. Dynamics of the simple model is similar to that of the original PNJL model without the TBC, indicating that the ZN symmetry is a good concept. We also investigate the interplay between the ZN symmetry and the emergence of the quarkyonic phase.