Solitons in a Grassmannian sigma-model Coupled to Chern-Simons Term

TL;DR

This paper introduces an exactly solvable Grassmannian sigma-model coupled with Chern-Simons theory, revealing exact vortex solutions with physical topological charge, and extends the analysis to noncommutative spaces.

Contribution

It presents a new solvable model with topological terms that admits explicit vortex solutions and explores their properties in both commutative and noncommutative settings.

Findings

Exact self-dual vortex solutions identified

Topological charge corresponds to magnetic flux

Extension to noncommutative plane analyzed

Abstract

We propose an exactly solvable Grassmannian sigma-model coupled to the Chern-Simons theory. In the presence of a novel topological term our model admits exact self-dual vortex solutions which are identical to those of pure Grassmannian model, but the topological charge has a physical meaning as a magnetic flux since the gauge field is no longer auxiliary. We also extend the theory to a noncommutative plane and analyze the BPS solutions.