The one-loop worldsheet S-matrix for the AdS(n) x S(n) x T(10-2n) superstring

TL;DR

This paper calculates the one-loop worldsheet S-matrix for superstring theories in AdS(n) x S(n) x T(10-2n), demonstrating UV finiteness and consistency with symmetries, and showing decoupling of massless modes in certain cases.

Contribution

It provides the first one-loop computation of the massive-sector S-matrix for these superstring backgrounds, confirming symmetry predictions and massless mode decoupling.

Findings

One-loop S-matrix is UV finite after wave function renormalization.

The S-matrix matches symmetry-based predictions for n=3,5.

Massless modes decouple from the massive sector at one-loop for n=2,3.

Abstract

We compute the massive-sector worldsheet S-matrix for superstring theories in AdS(n) x S(n) x T(10-2n) (with n=2,3,5) in the near BMN expansion up to one-loop order in inverse string tension. We show that, after taking into account the wave function renormalization, the one-loop S-matrix is UV finite. In an appropriate regularization scheme the S-matrix is consistent with the underlying symmetries of the superstring theory, i.e. for the n=3,5 cases it coincides with the one implied by the light-cone gauge symmetries with the dressing phases determined from the crossing equations. For the n=2,3 cases we observe that the massless modes decouple from the one-loop calculation of massive mode scattering, i.e. the 2n-dimensional supercoset sigma model and the full 10-dimensional superstring happen to have the same massive one-loop S-matrix.