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.
Highlights
In a very important paper [1], it has been extensively clarified that the sources for all different kinds of D-branes are Ramond–Ramond (RR) fields
It is well known that if one wants to work with the effective actions of type IIA, IIB string theory, one needs to deal with DBI and Chern–Simons effective actions, which can be found in [6,7,8,9]
It is explained in detail that for BPS branes all the corrections to D-brane effective actions can just be derived by having the entire form of S-matrix and not by any other tools like T-duality transformation
Summary
In a very important paper [1], it has been extensively clarified that the sources for all different kinds of D-branes are Ramond–Ramond (RR) fields. For a scattering amplitude of the brane–anti-brane system (including a scalar, tachyons and an RR), we have three different choices.5 For these particular amplitudes there is no Ward identity and a priori one does not know which specific picture gives us the correct S-matrix, where we claim and establish the fact that already at the level of S-matrix for a brane/anti-brane, one needs to know some generalised Bianchi identities to be able to produce all the effective field theory couplings. The motivation for doing this computation in different pictures is that there is no Ward identity for the mixed RR and a scalar field, and one might wonder what happens in higher point functions of all mixed amplitudes including an RR, scalar field and tachyons (but not gauge fields), or one might ask which particular picture is going to give us the complete S-matrix elements including all the infinite contact interactions of string theory.
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