CHIRAL-SYMMETRY AT FINITE-T, THE PHASE OF THE POLYAKOV LOOP AND THE SPECTRUM OF THE DIRAC OPERATOR

A recent Monte Carlo study of quenched QCD showed that the chiral cond ensate is non-vanishing above T-c in the phase where the average of th e Polyakov loop P is complex. We show how this is related to the depen dence of the spectrum of the Dirac operator on the boundary conditions in Euclidear. time. We use a random matrix model to calculate the den sity of small eigenvalues and the chiral condensate as a function of a rg P. The chiral symmetry is restored in the arg P = 2 pi/3 phase at a higher T than in the arg P = 0 phase. In the phase arg P = pi of the SU(2) gauge theory the chiral condensate stays nonzero for all T.