Remarks on the mixed Ramond -Ramond, open string scattering amplitudes of BPS, non-BPS and brane-anti brane

TL;DR

This paper computes and analyzes mixed Ramond-Ramond and open string scattering amplitudes in type IIA and IIB superstring theories, highlighting differences between BPS and non-BPS branes and emphasizing the importance of certain momentum terms for gauge invariance.

Contribution

It provides detailed calculations of mixed scattering amplitudes involving RR and open strings, revealing new insights into the equations applicable to BPS versus non-BPS branes and the role of transverse RR momentum.

Findings

Certain equations valid for BPS branes do not apply to non-BPS cases.

Transverse RR momentum terms are crucial for gauge invariance.

Explicit S-matrix elements for specific scattering processes are derived.

Abstract

From the world-sheet point of view we compute three, four and five point BPS and non-BPS scattering amplitudes of type IIA and IIB superstring theory. All these the mixed S-matrix elements including a closed string Ramond-Ramond (RR) in the bulk and a scalar/gauge or tachyons with their all different pictures ( including RR in asymmetric and symmetric pictures) have been carried out. We have also shown that in asymmetric pictures various equations must be kept fixed. More importantly, by direct calculations on upper half plane, it is realized that some of the equations (that must be true) for BPS branes can not be necessarily applied to non-BPS amplitudes. We also derive the S-Matrix elements of $<V_C^{-2} V_{\phi}^{0}V _A^{0} V_T^{0} >$ and clarify the fact that in the presence of the scalar field and RR, the terms carrying momentum of RR in transverse directions play important role in the entire form of the S-matrix and their presence is needed in order to have gauge invariance for the entire S-matrix elements of type IIA (IIB) superstring theory.