  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 nontrivial 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 $AdS_3 \times S^3$ and find a qualitative agreement.
