Quark Confinement from Correlation Functions

TL;DR

This paper investigates quark confinement by analyzing the Polyakov loop potential in Yang--Mills theory using various non-perturbative functional continuum methods, linking confinement to low-momentum correlator behavior.

Contribution

It extends previous studies by combining functional renormalisation group, Dyson--Schwinger equations, and two-particle-irreducible functionals to identify a confinement criterion based on low-momentum Green functions.

Findings

Confinement criterion expressed through low-momentum correlators.

Unified framework connecting different non-perturbative approaches.

Identification of low-momentum behavior as key to confinement.

Abstract

We study quark confinement by computing the Polyakov loop potential in Yang--Mills theory within different non-perturbative functional continuum approaches [1]. We extend previous studies in the formalism of the functional renormalisation group and complement those with findings from Dyson--Schwinger equations and two-particle-irreducible functionals. These methods are formulated in terms of low order Green functions. This allows to identify a criterion for confinement solely in terms of the low-momentum behaviour of correlators.