Quark and gluon confinement from an effective model of Yang-Mills theory

TL;DR

This paper develops a gauge-invariant effective model of SU(2) Yang-Mills theory demonstrating confinement phenomena through the behavior of the gluon propagator, providing insights into the origin of confinement.

Contribution

It introduces a gauge-invariant low-energy effective model that captures quark and gluon confinement and relates the string tension to the gluon propagator.

Findings

Gluon propagator follows Gribov-Stingl form regardless of gauge.

The model exhibits area law for Wilson loop indicating confinement.

A formula for string tension from the gluon propagator matches estimates.

Abstract

We derive a gauge-invariant low-energy effective model of the SU(2) Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type, irrespective of the gauge choice. In the maximally Abelian gauge, especially, we demonstrate that the model exhibits both quark confinement and gluon confinement: the Wilson loop average has area law and the Schwinger function violates reflection positivity. Moreover, we give a formula for the string tension calculable from the gluon propagator of the gauge-invariant field strength and gives a good estimate for the string tension. We discuss if quark confinement and gluon confinement are of the same origin attributed to the gluon propagator in the deep infrared momentum region.