On RR Couplings, Singularity Structures and all order $\alpha'$ contact interactions to BPS String Amplitudes

Abstract

We evaluate five point world-sheet string theory amplitudes of one transverse scalar field, two world volume gauge fields ( and two transverse scalars, a gauge field) in the presence of a closed string Ramond-Ramond vertex operator in its symmetric picture. We carry out all the entire S-matrix elements of five point mixed RR-scalars/gauge fields $<C^{-1}\phi ^{0}A^{-1} A^{0}>$, $<C^{-1}\phi ^{-1}A^{0} A^{0}>$, $<C^{-1}A^{0}\phi ^{-1}\phi^{0}>$ and $<C^{-1}A^{-1}\phi ^{0}\phi^{0}>$ in detail and start comparing all order $\alpha'$ contact interactions and singularities in both transverse and world volume directions. We explore the presence of various new couplings in string theory effective actions and find out their all order $\alpha'$ higher derivative corrections in both type IIA and IIB. Ultimately we make various remarks for the singularities and contact terms whose RR momenta are embedded in transverse directions. $\alpha'$ corrections to some of Myers terms are also addressed.