Correlation functions for orbifolds of the type M^N/S^N

The D1-D5 system, which arises in black hole physics, gives rise to a 2-d CFT which is the low energy limit of a sigma model with target space an orbifold (M₄)^N/S^N. (M₄ is a 4-d manifold which can be T⁴ or K3, and S^N is the permutation group on N elements). With this motivation, we develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M^N/S_N, where M is an arbitrary manifold. We find intriguing relations between the CFT correlators and the gravity theory that is conjectured to be dual to the D1-D5 system.