The Confinement Mechanism in Yang-Mills Theory?

TL;DR

This paper proposes a non-linear gauge approach to Yang-Mills theory, demonstrating that confinement arises from classical, statistical effects of scalar fields on Gribov horizons, rather than purely quantum phenomena.

Contribution

It introduces a non-linear gauge condition revealing confinement mechanisms through classical scalar fields on Gribov horizons, offering a new perspective on non-perturbative effects in Yang-Mills theory.

Findings

Area law behavior of Wilson loop confirmed

Linear dependence of gluon propagator shown

Confinement explained via classical scalar fields on horizons

Abstract

Using the recently proposed non-linear gauge condition, we show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the non-linear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The non-linear sector is actually composed of "Gribov horizons" on the surfaces parallel to the Coulomb surface. In this sector, the gauge field can be expressed in terms of a scalar field and a new vector field. The effective dynamics of the scalar field suggests non-perturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) scalar fields are classical solutions and averaging these solutions using a qaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "horizons" of the surfaces parallel to the Coulomb surface.