Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

TL;DR

This study investigates the relationship between chiral symmetry restoration and deconfinement in SU(2) and SU(3) Yang-Mills theories by analyzing gauge-invariant order parameters derived from lattice and Dyson-Schwinger methods.

Contribution

It provides a comparative analysis of chiral and deconfinement transitions in SU(2) and SU(3) using correlation functions and lattice data, highlighting differences in their transition behaviors.

Findings

Deconfinement and chiral transitions are closely related but show differences between SU(2) and SU(3).

The gluon and quark propagators serve as effective probes for phase transitions.

The study identifies specific signatures of the phase transition in the propagators.

Abstract

We study a gauge invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang-Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson-Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.