Worldsheet four-point functions in AdS3/CFT2

We calculate some extremal and non-extremal four-point functions on the sphere of certain chiral primary operators for strings on AdS3 × S3 × T4. The computation is done for small values of the spacetime cross-ratio where global SL(2) and SU(2) descendants may be neglected in the intermediate channel. Ignoring also current algebra descendants, we find that in the non-extremal case the integrated worldsheet correlators factorize into spacetime three-point functions, which is non-trivial due to the integration over the moduli space. We then restrict to the extremal case and compare our results with the four-point correlators recently computed in the dual boundary theory. We also discuss a particular non-extremal correlator involving two chiral and two anti-chiral operators.