PSL(n|n) sigma model as a conformal field theory

We discuss the sigma model on the PSL(n|n) supergroup manifold. We demonstrate that this theory is exactly conformal. The chiral algebra of this model is given by some extension of the Virasoro algebra, similar to the W algebra of Zamolodchikov. We also show that all group invariant correlation functions are coupling constant independent and can be computed in the free theory. The non-invariant correlation functions are highly non-trivial and coupling dependent. At the end we compare two- and three-point correlation functions of the PSL(1, 1|2) sigma model with the correlation functions in the boundary theory of AdS3 × S3 and find a qualitative agreement.