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 possibilites 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.

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Two phenomenological models describing an SU (N ) quark-gluon plasma are presented. The first is obtained from high temperature expansions of the free energy of a massive gluon, while the second is derived by demanding color neutrality over a certain length scale. Each model has a single free parameter, exhibits behavior similar to lattice simulations over the range T d − 5T d , and has the correct blackbody behavior for large temperatures. The N = 2 deconfinement transition is second order in both models, while N = 3,4, and 5 are first order. Both models appear to have a smooth large-N limit. For N ≥ 4, it is shown that the trace of the Polyakov loop is insufficient to characterize the phase structure; the free energy is best described using the eigenvalues of the Polyakov loop. In both models, the confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. In the deconfined phase, the rotation of the eigenvalues in the complex plane towards 1 is responsible for the approach to the blackbody limit over the range T d − 5T d . The addition of massless quarks in SU (3) breaks Z(3) symmetry weakly and eliminates the deconfining phase transition. In contrast, a first-order phase transition persists with sufficiently heavy quarks.

We derive from a d-dimensional lattice gauge theory at finite temperature a ( d -1)-dimensional effective action in which the dynamical variables are Wilson lines and meson and baryon fields. Analysis of this model shows a first-order deconfinement transition for all values of the bare quark mass, and a second-order chiral transition at a higher temperature for zero bare quark mass. Reasonable values for the two transitions and the hadronic mass spectrum are obtained.

The addition of an adjoint Polyakov loop term to the action of a pure gauge theory at finite temperature leads to new phases of SU (N ) gauge theories. For SU (3), a new phase is found which breaks Z(3) symmetry in a novel way; for SU (4), the new phase exhibits spontaneous symmetry breaking of Z(4) to Z(2), representing a partially confined phase in which quarks are confined, but diquarks are not. The overall phase structure and thermodynamics is consistent with a theoretical model of the effective potential for the Polyakov loop based on perturbation theory.