Some properties of the integrable noncommutative sine-Gordon system

TL;DR

This paper explores the properties of an integrable noncommutative sine-Gordon system, revealing its constraints, derivation from noncommutative Yang-Mills theory, and its non-causal S-matrix despite integrability.

Contribution

It introduces a new noncommutative sine-Gordon model with specific constraints, derived from noncommutative Yang-Mills theory, and analyzes its unique properties.

Findings

The system has an extra constraint for integrability.

The equations derive from a sum of two WZNW actions.

The S-matrix is acausal with particle production.

Abstract

In this paper we continue the program, initiated in Ref. hep-th/0112246, to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in order to guarantee classical integrability. We show that the system of constraint plus dynamical equation of motion can be obtained by a suitable reduction of a noncommutative version of 4d self-dual Yang-Mills theory. The field equations can be derived from an action which is the sum of two WZNW actions with cosine potentials corresponding to a complexified noncommutative U(1) gauge group. A brief discussion of the relation with the bosonized noncommutative Thirring model is given. In spite of integrability we show that the S-matrix is acasual and particle production takes place.