Non-Abelian Chern-Simons vortices with generic gauge groups

TL;DR

This paper explores non-Abelian Chern-Simons vortices with generic gauge groups, analyzing their moduli spaces, deriving master equations, and numerically studying magnetic field configurations, revealing complex splitting behaviors.

Contribution

It generalizes the study of non-Abelian Chern-Simons vortices to arbitrary gauge groups and provides a detailed analysis of their moduli spaces and magnetic field structures.

Findings

Magnetic field splitting occurs when coupling constants vary.

Negative magnetic field density near vortex centers can occur.

Moduli space and master equations are derived for general gauge groups.

Abstract

We study non-Abelian Chern-Simon BPS-saturated vortices enjoying N=2 supersymmetry in d=2+1 dimensions, with generic gauge groups of the form U(1) x G', with G' being a simple group, allowing for orientational modes in the solutions. We will keep the group as general as possible and utilizing the powerful moduli matrix formalism to provide the moduli spaces of vortices and derive the corresponding master equations. Furthermore, we study numerically the vortices applying a radial Ansatz to solve the obtained master equations and we find especially a splitting of the magnetic fields, when the coupling constants for the trace-part and the traceless part of the Chern-Simons term are varied, such that the Abelian magnetic field density can become negative near the origin of the vortex while the non-Abelian part stays positive, and vice versa.