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

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

2011-07-23

arxiv.org/abs/1107.4672v2

Physical Review D 85, 016009 (2012)

Physics

High Energy Physics

High Energy Physics - Phenomenology

To appear in Phys Rev D

Scientific paper

10.1103/PhysRevD.85.016009

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

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