Linking confinement to spectral properties of the Dirac operator

TL;DR

This paper explores how the spectral properties of the lattice Dirac operator relate to the confinement-deconfinement transition in gauge theories, linking spectral sums to Polyakov loops and quark potentials.

Contribution

It introduces a spectral representation of Polyakov loops and correlators, connecting spectral eigenvalues and eigenmodes to confinement phenomena in lattice gauge theories.

Findings

Deconfinement transition characterized by changes in eigenvalue response to boundary conditions.

Polyakov loops expressed as spectral sums of Dirac eigenvalues.

Quark potential linked to spatial correlations of Dirac eigenvectors.

Abstract

We represent Polyakov loops and their correlators as spectral sums of eigenvalues and eigenmodes of the lattice Dirac operator. The deconfinement transition of pure gauge theory is characterized as a change in the response of moments of eigenvalues to varying the boundary conditions of the Dirac operator. We argue that the potential between static quarks is linked to spatial correlations of Dirac eigenvectors.