Static quark-antiquark potential and Dirac eigenvector correlators

TL;DR

This paper explores how the spectral sum of Dirac eigenvector correlators can describe the static quark-antiquark potential and its change across the confinement-deconfinement transition in lattice QCD.

Contribution

It introduces a spectral representation of the Polyakov loop correlator using Dirac eigenvector correlators and analyzes their role in the confinement transition.

Findings

Normalized Dirac eigenvector correlators decay similarly in both phases.

Amplitude changes in correlators drive the transition from confining to deconfining potential.

Spectral sum representation captures the deconfinement mechanism.

Abstract

We represent the Polyakov loop correlator as a spectral sum of correlators of eigenvectors of the lattice Dirac operator. This spectral representation is studied numerically using quenched SU(3) configurations below and above the deconfinement temperature. We analyze whether the individual Dirac eigenvector correlators differ in the confined and deconfined phases. The decay properties of the normalized Dirac eigenvector correlators turn out to be essentially identical in the two phases, but the amplitudes change. This change of the amplitudes shifts the relative contributions of the individual Dirac eigenvector correlators and is the driving mechanism for the transition from the confining static potential into the deconfining one.