On SYM theory and all order Bulk Singularity Structures of BPS Strings in type II theory

The complete forms of the S-matrix elements of a transverse scalar field, two world volume gauge fields, and a Potential $C_{n-1}$ Ramond-Ramond (RR) form field are investigated. In order to find an infinite number of $t,s, (t+s+u)$-channel bulk singularity structures of this particular mixed open-closed amplitude, we employ all the conformal field theory techniques to $<V_{C^{-2}}V_{\phi ^{0}} V_{A^{0}} V_{A^{0}}>$, exploring all the entire correlation functions and all order $\alpha'$ contact interactions to these supersymmetric Yang-Mills (SYM) couplings. Singularity and contact term comparisons with the other symmetric analysis, $<V_{C^{-1}}V_{\phi ^{0}} V_{A^{-1}} V_{A^{0}}>$ and $<V_{C^{-1}}V_{\phi ^{-1}} V_{A^{0}} V_{A^{0}}>$ are also carried out in detail. Various couplings from pull-Back of branes, Myers terms and several generalized Bianchi identities should be taken into account to be able to reconstruct all order $\alpha'$ bulk singularities of type IIB (IIA) superstring theory. Finally, we make a comment on how to derive without any ambiguity all order $\alpha'$ contact terms of this S-matrix which carry momentum of RR in transverse directions.