Dirac Eigenvalue Spectrum at Finite Temperature Using Domain Wall Fermions

TL;DR

This paper investigates the Dirac eigenvalue spectrum at finite temperature in QCD using domain wall fermions, exploring implications for chiral symmetry restoration and $U(1)_A$ symmetry at temperatures near the phase transition.

Contribution

It provides a detailed analysis of the temperature dependence of the Dirac eigenvalue spectrum with domain wall fermions, employing normalization methods for direct evaluation of the Banks-Casher relation.

Findings

Eigenvalue spectrum varies with temperature near the phase transition.

Results suggest partial restoration of $U(1)_A$ symmetry at high temperatures.

Methodology enables precise connection between eigenvalues and chiral symmetry.

Abstract

We present a study of the Dirac eigenvalue spectrum near the region of the QCD phase transition. This study makes use of a sequence of ensembles with temperatures from 150 MeV to 200 MeV generated with $2 + 1$ flavors of dynamical domain wall fermions (DWF) and the dislocation sup- pressing determinant ratio (DSDR) action on a $16^3\times 8$ lattice with an extent of 32 or 48 in the fifth dimension. All the simulations lie on a line of constant physics with 200 MeV pions. The DWF Dirac operator is normalized using the methods of Giusti and Luscher combined with those of Rome-Southampton collaboration, allowing a direct evaluation of the Banks-Casher relation. The relation between the resulting temperature-dependent Dirac eigenvalue spectrum and the possible restoration of $U(1)_A$ symmetry with increasing temperature is discussed.