Remarks on Non-BPS String Amplitudes and Their All Order $\alpha'$ Contact Interactions in IIB, IIA

Abstract

We explore the entire form of S-Matrix elements of a potential $C_{n-1}$ Ramond-Ramond (RR) form field, a tachyon and two transverse scalar fields on both world volume and transverse directions of type IIB and IIA superstring theories. Apart from $<V_{C^{-2}}V_{\phi^{0}}V_{\phi ^{0}}V_{T ^{0}}>$ the other scattering amplitude, namely $<V_{C^{-1}}V_{\phi^{-1}}V_{\phi ^{0}}V_{T ^{0}}>$ is also revealed. We then start to compare all singularity structures of symmetric and asymmetric analysis, generating all infinite singularity structures as well as all order $\alpha'$ contact interactions on the whole directions. This leads to deriving various new contact terms and several new restricted Bianchi identities in both type IIB and IIA. It is also shown that just some of the new couplings of type IIB (IIA) string theory can be re-verified in an Effective Field Theory (EFT) by pull-back of branes. To construct the rest of S-matrix elements one needs to first derive restricted world volume (or bulk) Bianchi identities and then discover new EFT couplings in both type IIB and IIA. Finally the presence of commutator of scalar fields inside the exponential of Wess-Zumino action for non-BPS branes has been confirmed as well.