Monopole Vacuum in Non-Abelian Theories

TL;DR

This paper explores the topological structure of monopoles in non-Abelian gauge theories, proposing a monopole vacuum model that could explain confinement and meson mass phenomena in QCD.

Contribution

It introduces a topological degeneracy of BPS monopoles and a new chromoelectric monopole variable, linking monopole vacuum structure to confinement and meson mass effects in QCD.

Findings

Monopole vacuum may cause a rising potential in QCD

Topological confinement is supported by the monopole model

Additional mass for the $ta_0$ meson is predicted

Abstract

It is shown that, in the theory of interacting Yang -Mills fields and a Higgs field, there is a topological degeneracy of Bogomol'nyi-Prasad-Sommerfield (BPS) monopoles and that there arises, in this case, a chromoelectric monopole characterized by a new topological variable that describes transitions between topological states of the monopole in the Minkowski space (in just the same way as an instanton describes such transitions in the Euclidean space). The limit of an infinitely large mass of the Higgs field at a finite density of the BPS monopole is considered as a model of the stable vacuum in the pure Yang-Mills theory. It is shown that, in QCD, such a monopole vacuum may lead to a rising potential, a topological confinement and an additional mass of the $\eta_0$ meson. The relationship between the result obtained here for the generating functional of perturbation theory and Faddeev-Popov integral is discussed.