Scattering of closed strings from many D-branes

TL;DR

This paper develops an operator formalism to analyze scattering of closed strings from many D-branes in bosonic string theory, introducing a boundary state that inserts a boundary and saturates the multi-Reggeon vertex to generate all multi-brane amplitudes. It shows that amplitudes with $h$ D-branes are formally akin to $h-1$ open-string loops, establishing a bridge between closed-string scattering on D-branes and open-string loop dynamics. The key constructs are a BRST-invariant boundary state $|B\rangle$ and a boundary operator $B$, enabling explicit expressions for the generator ${\bf V}_{M;h}$ in terms of Schottky moduli, prime forms, and the period matrix; the approach reproduces known results (e.g., Polchinski's two-brane interaction) and provides a framework for superstring generalizations and more general brane configurations.

Abstract

We develop an operator formalism to compute scattering amplitudes of arbitrary bosonic string states in the background of many D-branes. Specifically, we construct a suitable boundary state which we use to saturate the multi-Reggeon vertex in order to obtain the generator of multi-membrane scattering amplitudes. We explicitly show that the amplitudes with $h$ parallel D-branes are similar to amplitudes with $h-1$ open string loops.