Non-Abelian Yang-Mills-Higgs vortices

TL;DR

This paper introduces new non-Abelian vortex solutions in SU(2) Yang-Mills-Higgs theory with a single scalar field, revealing their properties and behavior as the Higgs potential coupling varies, including their relation to self-dual vortices.

Contribution

The paper presents the first explicit non-Abelian vortex solutions in SU(2) Yang-Mills-Higgs theory with an isovector scalar, expanding understanding of vortex structures beyond Abelian cases.

Findings

Non-Abelian vortices branch from Abelian solutions at specific coupling values.

Their energies are lower than Abelian vortices for all coupling values.

In the limit of infinite coupling, vortices become non-interacting and relate to O(3) sigma model vortices.

Abstract

In this Letter we present new, genuinely non-Abelian vortex solutions in SU(2) Yang-Mills--Higgs theory with only one {\it isovector} scalar field. These non-Abelian solutions branch off their Abelian counterparts (Abrikosov-Nielsen-Olesen vortices) for precise values of the Higgs potential coupling constant $\lambda$. For all values of $\lambda$, their energies lie below those of the Abelian energy profiles, the latter being logarithmically divergent as $\lambda\to\infty$. The non-Abelian branches plateau in the limit $\lambda\to\infty$ and their number increases with $\lambda$, this number becoming infinite. For each vorticity, the gaps between the plateauing energy levels become constant. In this limit the non-Abelian vortices are non-interacting and are described by the {\it self-dual} vortices of the O(3) sigma model. In the absence of a topological lower bound, we expect these non-Abelian vortices to be {\it sphalerons}.