Worldsheet scattering in AdS3/CFT2

We confront the recently proposed exact S-matrices for AdS3/CFT2 with direct worldsheet calculations. Utilizing the BMN and Near Flat Space (NFS) expansions for strings on AdS3 × S3 × S3 × S1 and AdS3 × S3 × T4 we compute both tree-level and one-loop scattering amplitudes. Up to some minor issues we find nice agreement in the tree-level sector. At the one-loop level however we find that certain non-zero tree-level processes, which are not visible in the exact solution, contribute, via the optical theorem, and give an apparent mismatch for certain amplitudes. Furthermore we find that a proposed one-loop modification of the dressing phase correctly reproduces the worldsheet calculation while the standard Hernandez-Lopez phase does not. We also compute several massless to massless processes.