Superstring Scattering from D-Branes Bound States

TL;DR

This work computes covariant disk two-point amplitudes for massless closed strings scattering from D-brane bound states carrying a constant background field, using a background-dependent $D$-matrix and spinor $M$-matrix formalism with the doubling trick. The resulting amplitudes reveal massless $t$-channel poles that reproduce the long-range fields of extremally charged $(p+1)$- and $(p-1)$-brane bound states, and yield linear couplings that are precisely consistent with Born-Infeld and Chern-Simons actions in the background field. By matching with low-energy field theory, the paper derives explicit NS-NS and R-R sources, computes the corresponding long-range fields, and confirms the bound-state interpretation through charge and tension relations, including $T_{p,p-2}=T_p\sqrt{1+{\cal F}^2}$ and $Q_p, Q_{p-2}$ scaling. Overall, the results provide a concrete world-sheet realization of D-brane bound states and a calculational framework for their couplings to NS-NS and R-R sectors in type II theories.

Abstract

We derive fully covariant expressions for disk scattering amplitudes of any two massless closed strings in which mixed Neumann and Dirichlet world-sheet boundary conditions are included. From the two-point amplitudes, we derive the long range background fields and verify that they correspond to D$p$-brane bound state. Also, from the scattering amplitudes, we calculate the linear coupling of closed string fields to D-brane world-volume and show that they are consistent with Born-Infeld and Chern-Simons actions in the presence of a background field.