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

TL;DR

This paper analyzes the complete structure of bulk singularities in superstring scattering amplitudes involving BPS strings, using conformal field theory techniques to uncover all-order $\alpha'$ corrections in type II theories.

Contribution

It provides a comprehensive analysis of all-order bulk singularity structures of mixed open-closed string amplitudes in type II superstring theory, including contact interactions and couplings.

Findings

Derived all-order ' bulk singularity structures.

Compared singularities with other symmetric amplitude analyses.

Identified couplings from brane pull-back, Myers terms, and Bianchi identities.

Abstract

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.