Quark–gluon thermodynamics with the ${Z}_{N_c}$ symmetry

Abstract

We investigate quark–gluon thermodynamics with the symmetry. The flavor-dependent twist boundary condition (TBC) is imposed on Nc degenerate flavor quarks in the SU(Nc) gauge theory. This model is useful to understand the mechanism of color confinement. Thermodynamics of this quark–gluon system is studied by imposing the TBC on the Polyakov-loop extended Nambu–Jona–Lasinio (PNJL) model. The TBC model is applied to two- and three-color cases. The symmetry is preserved below some temperature Tc, but spontaneously broken above Tc. The color confinement below Tc preserves the flavor symmetry. Above Tc, the flavor symmetry is broken, but the breaking is suppressed by the entanglement between the Polyakov loop and the chiral condensate. Particularly at low temperature, dynamics of the TBC model is similar to that of the PNJL model with the standard fermion boundary condition, indicating that the symmetry is a good approximate concept in the latter model even if the current quark mass is small. The present prediction can be tested in future by lattice QCD, since the quark–gluon dynamics with a flavor-dependent imaginary chemical potential has no sign problem.