One- and two-loop checks for the AdS3 × S3 × T 4 superstring with mixed flux

We compute the one-loop worldsheet S-matrix for the superstring in AdS3 × S3 × T 4 supported by a combination of RR and NSNS flux in the massive sector. In the appropriate regularization scheme it agrees with the S-matrix found from symmetry considerations including the proposed dressing phases. As previously observed in other cases the massless modes decouple from the calculation of one-loop massive mode scattering. We also calculate the correction to the dispersion relation at two loops in the near-flat-space limit and find agreement with a proposal for the form of the exact dispersion relation for the massive modes. Somewhat surprisingly the massless modes again decouple from the calculation (in a suitable regularization scheme). We also compute the correction to the dispersion relation for the massless modes and compare to a suggestion for the exact dispersion relation, finding a small discrepancy. The corresponding calculations for AdS5 × S 5 and AdS2 × S2 × T 6 are used for comparison. (paper)