Scattering three closed strings off a Dp-brane in pure spinor formalism

TL;DR

This paper calculates the three-closed-string disk amplitude in pure spinor formalism, revealing its relation to open string amplitudes and exploring Dp-brane couplings, thus advancing understanding of gravitational interactions in string theory.

Contribution

It provides a compact expression for three-closed-string amplitudes in terms of open superstring amplitudes and generalizes to any number of closed strings, enhancing computational methods in string theory.

Findings

Derived a compact expression for three-closed-string disk amplitude

Expressed the amplitude in terms of open superstring six-point amplitudes

Discussed low-energy expansion and Dp-brane couplings

Abstract

We compute the disk amplitude of three closed strings in the pure spinor formalism. Among others, this amplitude probes tree-level gravitational interactions in the presence of Dp-branes. After disentangling holomorphic and anti-holomorphic closed string coordinates on the disk by means of introducing monodromy phases we find a compact expression for the disk amplitude of three closed strings in terms of open superstring six-point amplitudes. Furthermore, we provide the low-energy expansion (in the inverse string tension) of our amplitude and discuss some relevant Dp-brane couplings associated to it. Finally, we write down an expression for the general structure of the disk amplitude of any number n_c of closed strings in terms of pure open string amplitudes involving 2n_c open strings.