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

Understand

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.