The non-perturbative stringy interaction between NS-brane \& Dp brane

To our best knowledge, the leading non-perturbative stringy interaction between an NS brane and a Dp brane remains unknown. We here present the non-perturbative stringy amplitudes for a system of an F-string and a Dp brane and a system of an NS 5 brane and a Dp brane for $0 \le p \le 6$. In either case, the F or NS5 and the Dp are placed parallel at a separation. We obtain the respective amplitudes, starting from the amplitude for a system of a D1 and a D3 for the former and that for a system of a D5 and a D3 system for the latter, based on the IIB S-duality and various T-dualities plus the consistency of both, along with the respective known long-range amplitudes. We would like to point out that the amplitude for the D1/D3 or D3/D5 computed from the usual D-brane technique does not take into consideration of the non-perturbative contribution due to the exchange of virtual closed D-string emitted by the D3. As such the resulting amplitudes obtained from this one via the S-duality and followed by various T-dualities are not consistent with the IIB S-duality. We resolve this issue and obtain the corresponding consistent amplitudes. The implications of so obtained amplitudes are also discussed.