Non-Abelian, Self-Dual Chern-Simons Vortices Coupled to Gravity

TL;DR

This paper investigates non-Abelian Chern-Simons vortices coupled to gravity in three dimensions, deriving first-order Bogomol'nyi equations for cylindrically symmetric solutions with a specific potential.

Contribution

It introduces a new class of solutions in $SU(2)$ Chern-Simons/Higgs theory coupled to gravity, deriving first-order equations for vortex configurations.

Findings

First-order Bogomol'nyi equations derived for vortex solutions.

Reduction of Einstein and field equations to simpler form.

Identification of specific potential enabling these solutions.

Abstract

In this article we consider $SU(2)$ Chern-Simons/Higgs theory coupled to gravity in three-dimensions. It is shown that for a cylindrically symmetric vortex both the Einstein equations and the field equations can be reduced to a set of first-order Bogomol'nyi equations provided that we choose a specific eighth-order potential.