Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space

TL;DR

This paper constructs explicit soliton solutions in noncommutative Chern-Simons gauge theories and related integrable models, revealing their structure and dynamics on noncommutative space.

Contribution

It introduces a generalized uniton method for noncommutative chiral models, providing explicit Chern-Simons solitons and extending Toda and Liouville models to noncommutative space.

Findings

Explicit Chern-Simons solitons as rings of charge and spin

Generalization of Toda and Liouville models to noncommutative space

First order moduli space dynamics of solitons is trivial

Abstract

We consider the Dunne-Jackiw-Pi-Trugenberger model of a U(N) Chern-Simons gauge theory coupled to a nonrelativistic complex adjoint matter on noncommutative space. Soliton configurations of this model are related the solutions of the chiral model on noncommutative plane. A generalized Uhlenbeck's uniton method for the chiral model on noncommutative space provides explicit Chern-Simons solitons. Fundamental solitons in the U(1) gauge theory are shaped as rings of charge `n' and spin `n' where the Chern-Simons level `n' should be an integer upon quantization. Toda and Liouville models are generalized to noncommutative plane and the solutions are provided by the uniton method. We also define affine Toda and sine-Gordon models on noncommutative plane. Finally the first order moduli space dynamics of Chern-Simons solitons is shown to be trivial.