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

TL;DR

This paper investigates RR couplings on D-branes using T-duality and S-matrix calculations, confirming and extending previous results to include $C^{(p-1)}$ couplings at order $O(eta'^2)$ through explicit string amplitude analysis.

Contribution

It extends the understanding of RR couplings on D-branes by explicitly deriving $C^{(p-1)}$ couplings from string amplitudes, confirming T-duality consistency.

Findings

String amplitudes reproduce the proposed RR couplings.

Consistency of T-dual S-matrix elements is verified.

Extension from $C^{(p-3)}$ to $C^{(p-1)}$ couplings is demonstrated.

Abstract

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.