On BPS World Volume, RR Couplings, and Their α ′ Corrections in Type IIB

We compute the asymmetric and symmetric correlation functions of a four-point amplitude of a gauge field, a scalar field, and a
closed string Ramond-Ramond (RR) for different nonvanishing BPS branes. All world volume, the Taylor and pull-back
couplings, and their all-order α′ corrections have also been explored. Due to various symmetry structures, different restricted
BPS Bianchi identities have also been constructed. The prescription of exploring all the corrections of two closed string RR
couplings in type IIB is given. We obtain the closed form of the entire S-matrix elements of two closed string RRs and a
gauge field on the world volume of BPS branes in type IIB. All the correlation functions of VA0ðx1ÞVC−1ðz1,�z1ÞVC−1ðz2,�z2Þ are
also revealed accordingly. The algebraic forms for the most general case of the integrations Ð
d2zjz − ijajz + ijbðz − �zÞcðz + �zÞd on the upper half plane are derived in terms of Pochhammer and some analytic functions. Lastly, we generate various
singularity structures in both effective field theory and IIB string theory, producing different contact interactions as well as their
α′ higher derivative corrections.