Scattering of Closed String States from a Quantized D-Particle

TL;DR

This paper develops a path-integral formalism in bosonic string theory to compute the scattering amplitude of closed strings from a quantized D-particle, capturing recoil effects and enabling extensions to multi-D-particle processes.

Contribution

It introduces a novel formalism for quantizing D-particle recoil in string scattering, aligning with existing boundary states and allowing for more complex process analysis.

Findings

Agreement with BRST invariant boundary state at leading order

Formalism naturally incorporates D-particle recoil

Extendable to multi-D-particle interactions

Abstract

By developing an appropriate path-integral formalism, we compute, in bosonic string theory, the disk amplitude for the scattering of closed string states from a D-particle, in which the collective coordinate of the D-particle is fully quantized. As a consequence, the recoil of the D-particle is naturally taken into account. Our result can be readily factorized in the closed string channel to yield the boundary state describing the recoiling D-particle. This turned out to agree with the BRST invariant vertex recently proposed by Ishibashi to the leading order in the derivative expansion, but it will receive corrections in subsequent orders. The advantage of our formalism is that it is extendable to deal with more general processes involving multiple D-particles. A viewpoint regarding our work as describing a dynamical transition of CFT's is also discussed.