On Bulk Singularity Structures and all order $\alpha'$ Contact Terms of BPS String Amplitudes

TL;DR

This paper derives the complete amplitude structure for specific BPS string interactions, revealing new contact terms and couplings through all-order ' corrections, verified via effective field theory methods.

Contribution

It provides the first complete algebraic form of certain integrals and constructs an infinite series of bulk singularity structures with all-order ' corrections for BPS string amplitudes.

Findings

Derived the full amplitude for three SYM and RR fields.

Identified new contact interactions and couplings.

Constructed all-order ' corrections and singularity structures.

Abstract

The entire form of the amplitude of three SYM ( involving two transverse scalar fields, a gauge field) and a potential $C_{n-1}$ Ramond-Ramond (RR) form field is found out. We first derive $<V_{C^{-2}} V_{A^{0}} V_{\phi ^{0}} V_{\phi ^{0}}>$ and then start constructing an infinite number of $t,s$ channel bulk singularity structures by means of all order $\alpha'$ corrections to pull-back of brane in an Effective Field Theory (EFT). Due to presence of the complete form of S-matrix, several new contact interactions as well as new couplings are explored. It is also shown that these couplings can be verified at the level of EFT by either the combinations of Myers terms, pull-back, Taylor expanded of scalar fields or the mixed combination of the couplings of this paper as well as employed Bianchi identities. For the first time, we also derive the algebraic and the complete form of the integrations for some arbitrary combinations of Mandelstam variables and for the most general case $\int d^2z |1-z|^{a} |z|^{b} (z - \bar{z})^{c} (z + \bar{z})^{3}$ on upper half plane as well.