Integrable sigma models with complex and generalized complex structures

Using the general method presented by Mohammedi [15] for the integrability of a sigma model on a manifold, we investigate the conditions for having an integrable deformation of the general sigma model on a manifold with a complex structure. On a Lie group, these conditions are satisfied by using the zeros of the Nijenhuis tensor. We then extend this formalism to a manifold, especially a Lie group, with a generalized complex structure and in this manner we present new integrable sigma models. Then we demonstrate that, for the examples of integrable sigma models with generalized complex structures on the Lie groups $A_{4,8}$ and $A_{4,10}$, under special conditions, the perturbed terms of the actions are identical to the WZ terms.