Two dimensional Nambu sigma model

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.