On WZ and RR Couplings of BPS Branes and their all order $\alpha'$ Corrections in IIB, IIA

TL;DR

This paper computes all-order $\alpha'$ corrections to Wess-Zumino couplings of BPS D-branes in type IIB and IIA string theories, revealing structural and coefficient differences between the two theories and providing comprehensive S-matrix analyses.

Contribution

It provides the first complete all-order $\alpha'$ corrections to WZ couplings and S-matrices for BPS D-branes in both IIB and IIA, including new structural insights and contact term constructions.

Findings

Confirmed differences in $\alpha'$ correction structures between IIB and IIA.

Derived all-order S-matrices for RR fields and gauge/scalar fields.

Constructed all-order contact terms and analyzed singularity structures.

Abstract

We compute all three and four point couplings of BPS $D_{p}$-branes for all different nonzero $p$-values on the entire world volume and transverse directions. We start finding out all four point function supersymmetric Wess-Zumino (WZ) actions of one closed string Ramond-Ramond (RR) field with two fermions, either with the same (IIB) or different chirality (IIA) as well as their all order $\alpha'$ corrections. The closed form of S-matrices of two closed string RR in both IIB, IIA, including their all order $\alpha'$ corrections have also been addressed. Our results confirm that, not only the structures of $\alpha'$ corrections but also their coefficients of IIB are quite different from their IIA ones. The S-matrix of an RR and two gauge (scalar) fields and their all order corrections in antisymmetric picture of RR have been carried out as well. Various remarks on the restricted Bianchi identities as well as all order $\alpha'$ corrections to all different supersymmetric WZ couplings in both type IIA and IIB superstring theory are also released. Lastly, different singularity structures as well as all order contact terms for all non-vanishing traces in type II have also been constructed.