Scattering of massive open strings in pure spinor

TL;DR

This paper advances the understanding of massive open string scattering amplitudes within the pure spinor framework, aiming to facilitate two-loop renormalization on D-branes and explore new mathematical identities.

Contribution

It demonstrates the computation of massive open superstring scattering amplitudes in the pure spinor formulation, aligning with NSR results and setting groundwork for higher-loop analyses.

Findings

Reproduced NSR scattering amplitudes in pure spinor formulation.

Worked out examples of massive string scattering.

Suggested potential discovery of new Riemann identities.

Abstract

In {\em Phys.\ Lett.} {\bf B 660}, 583 (2008), it was proposed that the D-brane geometry could be produced by open string quantum effects. In an effort to verify the proposal, we consider scattering amplitudes involving {\em massive} open superstrings. The main goal of this paper is to set the ground for two-loop "renormalization" of an oriented open superstring on a D-brane and to strengthen our skill in the pure spinor formulation of a superstring, an effective tool for multi-loop string diagrams. We start by reviewing scattering amplitudes of massless states in the 2D component method of the NSR formulation. A few examples of massive string scattering are worked out. The NSR results are then reproduced in the pure spinor formulation. We compute the amplitudes using the massive vertex operator constructed by Berkovits and Chandia in {\em JHEP} {\bf 0208}, 040 (2002). We point out that it may be possible to discover new Riemann type identities involving Jacobi $\vartheta$-functions by comparing a NSR computation and the corresponding pure spinor computation.