Spectral sums of the Dirac-Wilson Operator and their relation to the Polyakov loop

TL;DR

This paper explores spectral sums of the Wilson lattice Dirac operator in SU(3) gauge theory, showing some act as order parameters for phase transitions and relate to the Polyakov loop, with potential continuum limits.

Contribution

It identifies spectral sums that serve as order parameters for confinement-deconfinement transition and are proportional to the Polyakov loop, some with a well-defined continuum limit.

Findings

Spectral sums act as order parameters for phase transition.

Main contribution from the IR end of the spectrum.

Some spectral sums have a well-defined continuum limit.

Abstract

We investigate and compute spectral sums of the Wilson lattice Dirac operator for quenched SU(3) gauge theory. It is demonstrated that there exist sums which serve as order parameters for the confinement-deconfinement phase transition and get their main contribution from the IR end of the spectrum. They are approximately proportional to the Polyakov loop. In contrast to earlier studied spectral sums some of them are expected to have a well-defined continuum limit.