Complete spectra of the Dirac operator and their relation to confinement

TL;DR

This paper computes the full spectra of the lattice Dirac operator in SU(3) gauge theory, revealing how eigenvalues differ between confined and deconfined phases and their influence on the Polyakov loop.

Contribution

It provides a detailed analysis of the complete Dirac spectra and their relation to confinement, highlighting the UV eigenvalues' dominant role in the Polyakov loop.

Findings

Eigenvalues respond differently to boundary conditions in confined vs. deconfined phases

Polyakov loop is mainly influenced by UV eigenvalues

Spectral sums can represent the Polyakov loop effectively

Abstract

We compute complete spectra of the staggered lattice Dirac operator for quenched SU(3) gauge configurations below and above the critical temperature. The confined and the deconfined phase are characterized by a different response of the Dirac eigenvalues to a change of the fermionic boundary conditions. We analyze the role of the eigenvalues in recently developed spectral sums representing the Polyakov loop. We show that the Polyakov loop gets its main contributions from the UV end of the spectrum.