Noncommmutative solitons and kinks in the affine Toda model coupled to matter

TL;DR

This paper explores noncommutative extensions of integrable models, specifically the affine Toda model coupled to matter, revealing new soliton and kink solutions and their dualities with massive Thirring theories.

Contribution

It introduces a noncommutative version of the affine Toda model coupled to matter and demonstrates its relation to the double sine-Gordon model, expanding the understanding of noncommutative integrable systems.

Findings

Noncommutative affine Toda model coupled to matter formulated.

Duality between NC generalized sine-Gordon and NC Thirring models established.

Reduction to NC double sine-Gordon model demonstrated.

Abstract

Some properties of the non-commutative (NC) versions of the generalized sine-Gordon model (NCGSG) and its dual massive Thirring theory are studied. Our method relies on the NC extension of integrable models and the master lagrangian approach to deal with dual theories. The master lagrangian turns out to be the NC version of the so-called affine Toda model coupled to matter related to the group GL(n), in which the Toda field $g \subset GL(n), (n=2, 3)$. Moreover, as a reduction of GL(3) NCGSG one gets a NC version of the remarkable double sine-Gordon model.