Two dimensional Nambu sigma model

TL;DR

This paper introduces a two-dimensional sigma model based on Nambu structures, explores its relation to WZW models, and demonstrates integrability in specific Lie group cases.

Contribution

It develops a novel sigma model framework using Nambu structures and identifies conditions for equivalence to WZW models and integrability in certain Lie groups.

Findings

Model constructed from Nambu structure of order three can be equivalent to WZW models.

The model on the four-dimensional Heisenberg Lie group is demonstrated.

The model on the central extension of the 2D Poincare group is shown to be integrable.

Abstract

We present two dimensional sigma model by using the Nambu structure on a manifold in general, and on a Lie group as a special case. Then, we consider model constructed from Nambu structure of order three and obtain conditions under which this model is equivalent to a WZW model. Furthermore, we present an example for this case on the four dimensional Heisenberg Lie group. Finally, as another example we show that the model constructed with Nambu structure of order three on the central extension of the 2D Poincare Lie group is integrable.