Self-Dual Chern-Simons Solitons with Non-Compact Groups

TL;DR

This paper demonstrates how to couple non-relativistic matter to Chern-Simons gauge fields from non-compact groups, specifically $SL(2,\mathbb{R})$ and $ISO(2,1)$, and finds soliton solutions under certain self-interactions.

Contribution

It introduces a method to couple matter with non-compact Chern-Simons gauge fields and explicitly constructs soliton solutions for specific groups.

Findings

Successfully coupled matter to non-compact Chern-Simons gauge fields.

Constructed explicit soliton solutions for $SL(2,\mathbb{R})$ and $ISO(2,1)$ groups.

Identified conditions for self-interactions to admit solitons.

Abstract

It is shown how to couple non-relativistic matter with a Chern--Simons gauge field that belongs to a non-compact group. We treat in some details the $SL(2,{\bf R})$ and the Poincar\'e $ISO(2,1)$ groups. For suitable self-interactions, we are able to exhibit soliton solutions.