Chiral symmetry at finite T, the phase of the Polyakov loop and the spectrum of the Dirac operator

Details Chiral symmetry at finite T, the phase of the Polyakov loop and the spectrum of the Dirac operator Chiral symmetry at finite T, the phase of the Polyakov loop and the spectrum of the Dirac operator

1996-01-04

arxiv.org/abs/hep-lat/9601001v1

Phys.Lett. B375 (1996) 249-254

Physics

High Energy Physics

High Energy Physics - Lattice

11 pages, REVTEX3.0, 3 EPSF figures. Packed by "uufiles" script

Scientific paper

10.1016/0370-2693(96)00262-6

A recent Monte Carlo study of {\em quenched} QCD showed that the chiral condensate is non-vanishing above $T_c$ in the phase where the average of the Polyakov loop $P$ is complex. We show how this is related to the dependence of the spectrum of the Dirac operator on the boundary conditions in Euclidean time. We use a random matrix model to calculate the density of small eigenvalues and the chiral condensate as a function of $\arg P$. 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~$T$.

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