Ramond-Ramond field strength couplings on D-branes

TL;DR

This work derives explicit Ramond–Ramond–NSNS couplings on D$_p$-branes at order $O(\alpha'^2)$ by matching disk-level S-matrix elements with worldvolume actions and enforcing T-duality. Linear T-duality fixes on-shell ambiguities and constrains the dilaton’s appearance to the string-frame metric, while nonlinear T-duality necessitates using the invariant RR field strength ${\cal F}=d{\cal C}$ with ${\cal C}=e^{B}C$. The resulting couplings involve derivatives of RR fluxes $F^{(p)}$, $F^{(p+2)}$, $F^{(p+4)}$ and their interactions with NSNS fluxes, curvature, and the dilaton. This aligns the worldvolume action with duality symmetries and clarifies the interplay between RR and NSNS sectors at higher-derivative levels, with potential confirmation from future disk amplitude calculations.

Abstract

By examining in details the disk level S-matrix element of one massless RR and one NSNS states at order O(α'^2), we find the coupling of one RR and one NSNS fields on the world volume of a D$_p$-brane. The non-zero couplings involve the first derivative of the RR field strengths F^{(p)}, F^{(p+2)} and F^{(p+4)}. We then fix the on-shell ambiguity of the couplings by requiring consistency with the linear T-duality transformations. Moreover, consistency with the non-linear T-duality requires that the RR field strength in the above couplings to be {\cal F}=d{\cal C} where {\cal C}=e^{B}C.