Non-Abelian Monopoles in the Higgs Phase

TL;DR

This paper explores the relationship between non-Abelian monopoles and kinks in supersymmetric gauge theories, revealing a correspondence that offers new methods for constructing and studying non-Abelian monopoles and their quantum properties.

Contribution

It demonstrates a one-to-one correspondence between non-Abelian kinks and monopoles in certain supersymmetric theories, providing an alternative construction method and insights into quantum aspects.

Findings

Moduli spaces of non-Abelian kinks and monopoles are in one-to-one correspondence.

Non-Abelian kinks acquire orientational degrees of freedom in degenerate mass cases.

The correspondence holds generally, enabling new approaches to study non-Abelian monopoles.

Abstract

We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N = 2 supersymmetric U(N) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus on the case of degenerate masses. In these special cases vortices acquire new orientational degrees of freedom, and become "non-Abelian". Kinks acquire new degrees of freedom too, and we will refer to them as "non-Abelian". As already noticed for the Abelian case, non-Abelian kinks must correspond to non-Abelian monopoles of the unbroken phase of SU(N) Yang-Mills. We show, in some special cases, that the moduli spaces of the two objects are in one-to-one correspondence. We argue that the corre- spondence holds in the most general case. The consequence of our result is two-fold. First, it gives an alternative way to construct non-Abelian monopoles, in addition to other well- known techniques (Nahm transform, spectral curves, rational maps). Second, it opens the way to the study of the quantum physics of non- Abelian monopoles, by considering the simpler non-Abelian kinks.