T-dual RR couplings on D-branes from S-matrix elements

Understand

Using the linear T-dual ward identity associated with the NSNS gauge transformations, some RR couplings on D$_p$-branes have been found at order $O(\alpha'^2)$.

• We examine the $C^{(p-1)}$ couplings with the S-matrix elements of one RR, one graviton and one antisymmetric B-field vertex operators.
• We find the consistency of T-dual S-matrix elements and explicit results of scattering string amplitude and show that the string amplitude reproduces these couplings as well as some other couplings.
• This illustration is found for $C^{(p-3)}$ couplings in the literature which is extended to the $C^{(p-1)}$ couplings in this paper.