Non Abelian Chern-Simons-Higgs solutions in (2+1) dimensions

TL;DR

This paper constructs and analyzes non-Abelian vortices in a 2+1 dimensional SU(2) Chern-Simons-Higgs theory, revealing novel features such as lower energy states and unique mass-spin relations compared to Abelian solutions.

Contribution

It provides the first numerical construction of non-Abelian vortices in this theory and uncovers their distinct properties and stability features.

Findings

Non-Abelian vortices can have lower energy than Abelian ones.

Existence of a nontrivial mass-spin relation for non-Abelian vortices.

Identification of Abelian embeddings within the non-Abelian solutions.

Abstract

Non Abelian vortices of a SU(2) Chern-Simons--Higgs theory in 2+1 dimensions are constructed numerically. They represent natural counterparts of the U(1) solutions considered by Hong, Kim and Pac, and, by Jackiw and Weinberg. The Abelian embeddings are identified, for all values of the Higgs selfinteraction strength $\nu$, resulting in both attractive and repulsive phases. A detailed analysis of the properties of the solutions reveals the existence ofa number of unexpected features. For a certain range of the parameter $\nu$, it is shown that the non Abelian vortices have lower energy than their topologically stable Abelian counterparts, resulting in an effective energy lower bound on the SU(2) configurations. The angular momentum of these vortices is analysed and it is found that unlike the Abelian ones, whose angular momentum and energy are unrelated, there is a nontrivial mass--spin relation of the non Abelian vortices.