Vortex Formation in a $U(1) \times U(1)'$, N=2, D=3 Supersymmetric Gauge Model

TL;DR

This paper investigates vortex formation in a three-dimensional N=2 supersymmetric gauge model with a U(1) x U(1)' symmetry, analyzing the role of Bogomol'nyi relations, magnetic flux, and topological charge.

Contribution

It introduces a detailed study of vortex mechanisms in a supersymmetric gauge model derived from higher dimensions, highlighting the interplay of multiple gauge fields and supersymmetry.

Findings

Vortex formation is characterized by Bogomol'nyi equations.

Magnetic flux and topological charge are computed for the vortices.

The model relates to vortices observed in superfluid films.

Abstract

In this work, we study a $U(1) \times U(1) ^{\prime}-$ model that results from a dimensional reduction of the N=1-D=4 supersymmetric version of the Cremer-Scherk-Kalb-Ramond model with non-minimal coupling to matter. Field truncations are not carried out, two Abelian symmetries coexist and three vector fields are present; two of them are gauge bosons. Then, by considering the full $N=2-D=3$ supersymmetric model, we study the mechanism for magnetic vortex formation by means of the Bogomol'nyi relations, the magnetic flux and the topological charge in the presence of the two gauge potentials. A short discussion on the relation between our $N=2-D=3$ supersymmetric model and vortices in superfluid films is also presented.