Chern--Simons Vortices in the Gudnason Model

TL;DR

This paper proves the existence of multiple vortex solutions in a supersymmetric Chern--Simons gauge theory model, using minimization techniques in both full plane and periodic settings, revealing solutions with identical vortex distributions but different gauge configurations.

Contribution

It introduces new existence theorems for multiple vortex solutions in the Gudnason model, including conditions for multiple gauge-distinct solutions with the same vortex distribution.

Findings

Existence of multiple vortex solutions in the Gudnason model.

Conditions for at least two gauge-distinct solutions with same vortex distribution.

Application of minimization methods to elliptic systems with exponential nonlinearity.

Abstract

We present a series of existence theorems for multiple vortex solutions in the Gudnason model of the ${\cal N}=2$ supersymmetric field theory where non-Abelian gauge fields are governed by the pure Chern--Simons dynamics at dual levels and realized as the solutions of a system of elliptic equations with exponential nonlinearity over two-dimensional domains. In the full plane situation, our method utilizes a minimization approach, and in the doubly periodic situation, we employ an-inequality constrained minimization approach. In the latter case, we also obtain sufficient conditions under which we show that there exist at least two gauge-distinct solutions for any prescribed distribution of vortices. In other words, there are distinct solutions with identical vortex distribution, energy, and electric and magnetic charges.