Magneto-static vortices in two dimensional Abelian gauge theories

TL;DR

This paper investigates the existence of magneto-static vortices in two-dimensional Abelian gauge theories, providing conditions for vortex existence using a penalization method due to embedding challenges.

Contribution

It introduces a novel approach to establish vortex existence in 2D Klein-Gordon-Maxwell equations under magneto-static conditions, overcoming embedding limitations.

Findings

Established sufficient conditions for vortex existence

Applied penalization method to overcome embedding issues

Extended understanding of vortices in 2D gauge theories

Abstract

We study the existence of vortices of the Klein-Gordon-Maxwell equations in the two dimensional case. In particular we find sufficient conditions for the existence of vortices in the magneto-static case, i.e when the electric potential $\phi=0$. This result, due to the lack of suitable embedding theorems for the vector potential $\A$ is achieved with the help of a penalization method.