Vortices which do not Abelianize dynamically: Semi-classical origin of non-Abelian monopoles

TL;DR

This paper explores the semi-classical origins of non-Abelian monopoles, focusing on non-Abelian vortices that retain their non-Abelian nature and their role in dual gauge symmetry, contrasting with Abelianized vortices.

Contribution

It introduces a new class of non-Abelian vortices with $CP^{n-1} imes CP^{r-1}$ moduli that do not fully Abelianize, revealing their connection to monopole dual gauge degrees of freedom.

Findings

Non-Abelian vortices with specific moduli do not fully Abelianize.

Fluctuations of vortex moduli can be absorbed by monopoles, acting as dual gauge fields.

Contrasts with earlier models where vortices become effectively Abelian.

Abstract

After briefly reviewing the problems associated with non-Abelian monopoles, we turn our attention to the development in our understanding of non-Abelian {\it vortices} in the last several years. In the U(N) model with $N_{f}=N$ flavors in which they were first found, the fluctuations of the orientational modes along the vortex length and in time become strongly coupled at long distances. They effectively reduce to Abelian ANO vortices. We discuss then a very recent work on non-Abelian vortices with $CP^{n-1}\times CP^{r-1}$ orientational moduli, which, unlike the ones so far extensively studied, do not dynamically Abelianize completely. The surviving vortex orientational moduli, fluctuating along the vortex length and in time, gets absorbed by the monopoles at the ends, turning into the dual gauge degrees of freedom for the latter.