Non-Abelian monopoles in the Higgs phase

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 correspondence 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.