About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane

TL;DR

This paper explores the deep connection between noncommutative self-dual Chern-Simons systems and Toda field theories, providing methods to construct exact solutions, including specific solutions for the noncommutative Liouville model.

Contribution

It demonstrates how to derive Toda field theories from the NCSDCS system and constructs exact solutions using a noncommutative extension of the uniton method.

Findings

Exact solutions of noncommutative Toda theories are obtained.

Specific solutions for the noncommutative Liouville model are explicitly constructed.

The connection between NCSDCS and noncommutative chiral models is established.

Abstract

The relation of the noncommutative self-dual Chern-Simons (NCSDCS) system to the noncommutative generalizations of Toda and of affine Toda field theories is investigated more deeply. This paper continues the programme initiated in $JHEP {\bf 10} (2005) 071$, where it was presented how it is possible to define Toda field theories through second order differential equation systems starting from the NCSDCS system. Here we show that using the connection of the NCSDCS to the noncommutative chiral model, exact solutions of the Toda field theories can be also constructed by means of the noncommutative extension of the uniton method proposed in $JHEP {\bf 0408} (2004) 054$ by Ki-Myeong Lee. Particularly some specific solutions of the nc Liouville model are explicit constructed.