More about chiral symmetry restoration at finite temperature in the planar limit

TL;DR

This paper investigates the spectral properties of the Euclidean Dirac operator in the deconfined phase at finite temperature within the planar limit, revealing Gaussian matrix model behavior near the spectral edge.

Contribution

It demonstrates that eigenvalue functions near the spectral edge follow a Gaussian Hermitian matrix model, highlighting new insights into spectral fluctuations in this regime.

Findings

Eigenvalues near the spectral edge follow a Gaussian Hermitian matrix model.

Scale and shift invariant eigenvalue combinations do not match the matrix model.

Spectral gap persists around zero in the deconfined phase.

Abstract

In the planar limit, in the deconfined phase, the Euclidean Dirac operator has a spectral gap around zero. We show that functions of eigenvalues close to the spectral edge, which are independent of common rescalings and shifts gauge configuration by gauge configuration, have distributions described by a Gaussian Hermitian matrix model. However, combinations of eigenvalues that are scale and shift invariant only on the average, do not match this matrix model.