Relativistic Chern--Simons--Higgs Vortex Equations

TL;DR

This paper proves the existence of solutions to non-Abelian relativistic Chern--Simons--Higgs vortex equations over a periodic domain for gauge group SU(N), expanding understanding of vortex solutions in gauge theories.

Contribution

It establishes an existence theorem for solutions to these vortex equations for the first time in the general SU(N) gauge group case.

Findings

Existence of solutions is proven for the non-Abelian relativistic Chern--Simons--Higgs vortex equations.

Results apply to the most general and important prototype gauge group SU(N).

The theorem advances mathematical understanding of vortex solutions in gauge theories.

Abstract

An existence theorem is established for the solutions to the non-Abelian relativistic Chern--Simons--Higgs vortex equations over a doubly periodic domain when the gauge group $G$ assumes the most general and important prototype form, $G=SU(N)$