Condition for confinement in non-Abelian gauge theories

TL;DR

This paper demonstrates that a confinement criterion based on BRST invariance applies in four-dimensional non-Abelian gauge theories, confirming confinement through exact solutions and linking it to BRST invariance and asymptotic freedom.

Contribution

The paper provides a direct verification of the Kugo-Ojima confinement criterion in four dimensions using exact solutions, strengthening the theoretical understanding of confinement mechanisms.

Findings

Non-Abelian gauge theories are confining under the BRST invariance criterion.

The confinement condition is validated in four-dimensional theories.

Confinement is shown to be rooted in BRST invariance and asymptotic freedom.

Abstract

We show that a criterion for confinement, based on the BRST invariance, holds in four dimensions, by solving a non-Abelian gauge theory with a set of exact solutions. The confinement condition we consider was obtained by Kugo and Ojima some decades ago. The current understanding of gauge theories permits us to apply the techniques straightforwardly for checking the validity of this criterion. In this way, we are able to show that the non-Abelian gauge theory is confining and that confinement is rooted in the BRST invariance and asymptotic freedom.