One- and two-loop checks for the AdS(3) x S(3) x T(4) superstring with mixed flux

TL;DR

This paper computes one- and two-loop corrections to the superstring in AdS(3) x S(3) x T(4) with mixed flux, confirming some theoretical predictions and revealing decoupling of massless modes in certain regimes.

Contribution

It provides the first one-loop S-matrix calculation for this background with mixed flux and tests the proposed exact dispersion relations at two loops.

Findings

One-loop S-matrix agrees with symmetry-based predictions.

Massless modes decouple from massive mode scattering at one loop.

Two-loop dispersion relation matches the proposed exact form for massive modes.

Abstract

We compute the one-loop worldsheet S-matrix for the superstring in AdS(3) x S(3) x 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 AdS(5) x S(5) and AdS(2) x S(2) x T(6) are used for comparison.