Relation between chiral symmetry breaking and confinement in YM-theories

TL;DR

This paper explores the connection between chiral symmetry breaking and confinement in Yang-Mills theories by analyzing spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop, including continuum and lattice formulations.

Contribution

It generalizes Gattringer's approach to mode sums reconstructing the Polyakov loop locally and studies their convergence and effectiveness in different gauge theories and phases.

Findings

Mode sums approximate the static quark potential well at large distances.

Good agreement between mode sum approximation and static potential in confinement and plasma phases.

The approach is validated in continuum and lattice formulations of Yang-Mills theories.

Abstract

Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop are thoroughly investigated. The approach by Gattringer is generalized to mode sums which reconstruct the Polyakov loop locally. This opens the possibility to study the mode sum approximation to the Polyakov loop correlator. The approach is re-derived for the ab initio continuum formulation of Yang-Mills theories, and the convergence of the mode sum is studied in detail. The mode sums are then explicitly calculated for the Schwinger model and SU(2) gauge theory in a homogeneous background field. Using SU(2) lattice gauge theory, the IR dominated mode sums are considered and the mode sum approximation to the static quark anti-quark potential is obtained numerically. We find a good agreement between the mode sum approximation and the static potential at large distances for the confinement and the high temperature plasma phase.