T-duality of the Riemann curvature corrections to supergravity

We examine the sigma model Riemann curvature corrections to the supergravity action under T-duality transformations. Using the compatibility of the effective action with on-shell linear T-duality and with the S-matrix calculations as guiding principles, we have incorporated in this action the couplings of four B-field strengths and the couplings of two Riemann curvatures and two B-field strengths at order α′3. Using the S-matrix calculations we have also found new dilaton couplings in the string frame at this order.