Non-Abelian Chern-Simons-Higgs vortices with a quartic potential

TL;DR

This paper numerically constructs and analyzes non-Abelian vortices in an SU(2) Chern-Simons-Higgs theory with a quartic potential, revealing new features and solution classifications not seen with higher-order potentials.

Contribution

It introduces a detailed numerical analysis of non-Abelian vortices with a quartic Higgs potential, uncovering unexpected features and solution properties.

Findings

Non-Abelian solutions generally have lower energy than Abelian ones.

Existence of non-Abelian solutions with maximal angular momentum.

Uniqueness violation for vortex number n≥3 with identical global charges.

Abstract

We have constructed numerically non-Abelian vortices in an SU(2) Chern-Simons-Higgs theory with a quartic Higgs potential. We have analyzed these solutions in detail by means of improved numerical codes and found some unexpected features we did not find when a sixth-order Higgs potential was used. The generic non-Abelian solutions have been generated by using their corresponding Abelian counterparts as initial guess. Typically, the energy of the non-Abelian solutions is lower than that of the corresponding Abelian one (except in certain regions of the parameter space). Regarding the angular momentum, the Abelian solutions possess the maximal value, although there exist non-Abelian solutions which reach that maximal value too. In order to classify the solutions it is useful to consider the non-Abelian solutions with asymptotically vanishing $A_t$ component of the gauge potential, which may be labelled by an integer number $m$. For vortex number $n=3$ and above, we have found uniqueness violation: two different non-Abelian solutions with all the global charges equal. Finally, we have investigated the limit of infinity Higgs self-coupling parameter and found a piecewise Regge-like relation between the energy and the angular momentum.