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

## TL;DR

This paper investigates how the phase of the Polyakov loop influences chiral symmetry breaking in quenched QCD at finite temperature, revealing a dependence of the Dirac spectrum on boundary conditions and phase, with implications for chiral restoration.

## Contribution

It introduces a random matrix model to connect the Polyakov loop phase with the Dirac spectrum and chiral condensate, showing phase-dependent chiral symmetry restoration temperatures.

## Key findings

- Chiral condensate remains non-zero above T_c in certain Polyakov loop phases.
- Chiral symmetry is restored at higher T in the phase with =2/3.
- In the =
phase of SU(2), the condensate stays non-zero for all T.

## Abstract

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~$T$.