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

TL;DR

The paper computes the massive-sector worldsheet S-matrix at one loop for AdS_n x S^n x T^{10-2n} (n=2,3,5) in the near-BMN expansion. After accounting for wave-function renormalization and using a symmetry-preserving regularization, the one-loop S-matrix is UV finite and agrees with integrability-based predictions: HL dressing phases for AdS5xS5 and BOSST-type phases for AdS3xS3xT^4, with massless modes decoupling in the n=2,3 cases so the massive-sector results match the coset sigma-model. These findings reinforce the consistency between worldsheet perturbation theory and the algebraic/ crossing-based S-matrix program, and set the stage for two-loop investigations and extensions to mixed flux backgrounds.

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.