Massive and Massless Monopoles and Duality

TL;DR

This paper reviews BPS monopoles and electric-magnetic duality, highlighting how monopoles behave in theories with various gauge symmetry breakings, including the emergence of massless monopoles as non-Abelian field clouds.

Contribution

It provides a detailed analysis of monopole solutions in theories with arbitrary gauge groups, especially the role of massless monopoles as non-Abelian clouds.

Findings

Massive monopoles correspond to fundamental monopoles in broken gauge theories.

Massless monopoles manifest as non-Abelian field clouds around massive monopoles.

Examples of monopole solutions with non-Abelian clouds are presented.

Abstract

I review some aspects of BPS magnetic monopoles and of electric-magnetic duality in theories with arbitrary gauge groups. When the symmetry is maximally broken to a U(1)^r subgroup, all magnetically charged configurations can be understood in terms of r species of massive fundamental monopoles. When the unbroken group has a non-Abelian factor, some of these fundamental monopoles become massless and can be viewed as the duals to the massless gauge bosons. Rather than appearing as distinct solitons, these massless monopoles are manifested as clouds of non-Abelian field surrounding one or more massive monopoles. I describe in detail some examples of solutions with such clouds.