Vortices with source, FQHE and nontrivial statistics in 2+1 dimensions

TL;DR

This paper studies vortex solutions in 2+1D scalar gauge theories with sources, exploring their classification, non-Abelian cases, non-relativistic limits, and applications to FQHE and related models, revealing new vortex structures.

Contribution

It introduces a comprehensive classification of vortex solitons in 2+1D gauge theories with sources, including non-Abelian and non-relativistic cases, and applies these findings to models relevant for FQHE.

Findings

Classified vortex solutions for various potentials.

Discovered new vortex solutions in non-Abelian and non-relativistic models.

Connected vortex solutions to FQHE and related condensed matter phenomena.

Abstract

We investigate vortex soliton solutions in 2+1 dimensional scalar gauge theories, in the presence of source terms in the action. Concretely, this would be applied to anyons, as well as the Fractional Quantum Hall Effect (FQHE). We classify solitons for renormalizable potentials, as well as some nonrenormalizable examples that could be relevant for the FQHE. The non-Abelian case, specifically for theories with global non-Abelian symmetries, is also investigated, as is the non-relativistic limit of the above theories, when we get a modification of the Jackiw-Pi model, with an interesting new vortex solution. We explore the application to the ABJM model, as well as more general SYM-CS models in 2+1 dimensions.