Worldsheet operator product expansions and p-point functions in AdS3/CFT2

We construct the operator product expansions (OPE) of the chiral primary operators in the worldsheet theory for strings on AdS_3 x S^3 x T^4. As an interesting application, we will use the worldsheet OPEs to derive a recursion relation for a particular class of extremal p-point correlators on the sphere. We compare our result with the corresponding recursion relation previously found in the symmetric orbifold theory on the boundary of AdS_3.