Chiral and deconfinement transition from Dyson-Schwinger equations

TL;DR

This paper investigates the chiral and deconfinement phase transitions in quenched QCD using Dyson-Schwinger equations, analyzing order parameters like the quark condensate and Polyakov loop across temperature and quark mass variations.

Contribution

It introduces a method to study the chiral and deconfinement transitions via Dyson-Schwinger equations with gauge-invariant quantities, comparing lattice and continuum results, and exploring different order parameters.

Findings

Transition temperatures for chiral and deconfinement are close at finite quark masses.

In the chiral limit, the chiral and deconfinement transitions coincide.

The dual scalar quark dressing provides an alternative deconfinement order parameter.

Abstract

We determine the quark condensate and the dressed Polyakov loop from the finite temperature Landau gauge quark propagator evaluated with U(1)-valued boundary conditions in an approximation to quenched QCD. These gauge invariant quantities allow for an investigation of the chiral and deconfinement transition. We compare results from Dyson-Schwinger equations on a lattice with infinite volume continuum results and study the temperature and quark mass dependence of both quantities. In particular we investigate the chiral condensate and the dressed Polyakov loop in the chiral limit. We also consider an alternative order parameter for the deconfinement transition, the dual scalar quark dressing, and compare with the dressed Polyakov loop. As a result we find only slightly different transition temperatures for the chiral and the deconfinement transition at finite quark masses; in the chiral limit both transitions coincide.