We observe that the replacement of the Riemann curvature with the generalized Riemann curvature in the corrections to type-II supergravity at order
03, which are in terms of the contractions of four Riemann curvatures R4, is not fully consistent with the S-matrix elements in the superstring theory. In particular, they produce nonzero S-matrix elements for an odd number of B-field strengths which are not consistent with the string theory results. Using the consistency of the couplings with the linear T duality as a guiding principle, we consider all T-duality-invariant couplings and fix their coefficients by requiring them to be consistent with the S-matrix elements. The new Lagrangian density is then equivalent to the placement of the generalized Riemann curvature into the expression t8t8R4.

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