Chiral symmetry restoration and Z(N) symmetry

We demonstrate that chiral symmetry restoration in quenched finite temperature QCD depends crucially on the Z(3) phase of the Polyakov loop P. This dependence is a general consequence of the coupling of the chiral order parameter to the Polyakov loop, We construct a model for chiral symmetry breaking and restoration which includes the effect of a nontrivial Polyakov loop by calculating the effective potential for the chiral condensate of a Nambu-Jona-Lasinio model in a uniform temperature dependent A(0) gauge field background. Above the deconfinement temperature there are three possible phases corresponding to the Z(3) symmetric phases of the Polyakov loop in the pure gauge theory, In the phase in which tr(c)(P) is real and positive the first-order deconfining transition induces chiral symmetry restoration in agreement with simulation results. in the two phases where Re [tr(c)(P)] < 0 the sign of the leading finite temperature correction to the effective potential is reversed from the normal phase, and chiral symmetry is not restored at the deconfinement transition; this agrees with the recent simulation studies of Chandrasekharan and Christ, In the case of SU(N) a rich set of possibilities emerges. The generality of the mechanism makes it likely to occur in full QCD as well; this will increase the lifetimes of metastable Z(3) phases.