Chiral symmetry restoration and [formula omitted]N symmetry

Abstract

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.