Large-NcPolyakov–Nambu–Jona-Lasinio model with explicitZNcsymmetry

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 $\mathrm{SU}({N}_{c})$. The physically expected large-${N}_{c}$ and large-$T$ behaviors 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 studies resorting to effective approaches of QCD. 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 $\ensuremath{\mu}$. When $T<{T}_{d}$ however, the system is in a confined phase in which chiral symmetry is either broken or not. The critical line ${T}_{\ensuremath{\chi}}(\ensuremath{\mu})$, signalling the restoration of chiral symmetry, has the same qualitative features than what can be obtained within a standard ${N}_{c}=3$ PNJL model.