A large-$N_c$ PNJL model with explicit Z$_{N_c}$ symmetry

TL;DR

This paper develops a large-$N_c$ PNJL model with explicit Z$_{N_c}$ symmetry to better mimic Yang-Mills theories, analyzing its thermodynamics and phase structure, including deconfinement and chiral symmetry restoration.

Contribution

It introduces a Z$_{N_c}$-symmetric Polyakov-loop potential in a large-$N_c$ PNJL model and studies its phase diagram, extending previous models with explicit symmetry considerations.

Findings

Three phases identified: deconfined, confined with broken chiral symmetry, and confined with restored chiral symmetry.

The model reproduces qualitative features of the chiral transition line $T_ ext{chi}()$.

Thermodynamic behaviors match expectations from large-$N_c$ and high-temperature limits.

Abstract

A PNJL model is built, in which the Polyakov-loop potential is explicitly Z$_{N_c}$-symmetric in order to mimic a Yang-Mills theory with gauge group SU($N_c$). The physically expected large-$N_c$ and large-$T$ behaviours of the thermodynamic observables computed from the Polyakov-loop potential are used to constrain its free parameters. The effective potential is eventually U(1)-symmetric when $N_c$ is infinite. Light quark flavours are added by using a Nambu-Jona-Lasinio (NJL) model coupled to the Polyakov loop (the PNJL model), and the different phases of the resulting PNJL model are discussed in 't Hooft's large-$N_c$ limit. Three phases are found, in agreement with previous large-$N_c$ studies. When the temperature $T$ is larger than some deconfinement temperature $T_d$, the system is in a deconfined, chirally symmetric, phase for any quark chemical potential $\mu$. When $T<T_d$ however, the system is in a confined phase in which chiral symmetry is either broken or not. The critical line $T_\chi(\mu)$, signalling the restoration of chiral symmetry, has the same qualitative features than what can be obtained within a standard $N_c=3$ PNJL model.