Some tree-level string amplitudes in the NSR formalism

TL;DR

This paper computes tree-level open and closed string scattering amplitudes in the NSR formalism, introducing a streamlined method and deriving new five-point fermionic amplitudes consistent with supersymmetric effective actions.

Contribution

It presents a simplified, symmetry-based approach to calculating tree-level string amplitudes and derives new five-point fermionic amplitudes within the NSR formalism.

Findings

Confirmed five-point gluon amplitude matches previous results.

Derived new five-point amplitudes involving fermions.

Validated results against supersymmetric $F^4$ effective action expectations.

Abstract

We calculate tree level scattering amplitudes for open strings using the NSR formalism. We present a streamlined symmetry-based and pedagogical approach to the computations, which we first develop by checking two-, three-, and four-point functions involving bosons and fermions. We calculate the five-point amplitude for massless gluons and find agreement with an earlier result by Brandt, Machado and Medina. We then compute the five-point amplitudes involving two and four fermions respectively, the general form of which has not been previously obtained in the NSR formalism. The results nicely confirm expectations from the supersymmetric $F^4$ effective action. Finally we use the prescription of Kawai, Lewellen and Tye (KLT) to compute the amplitudes for the closed string sector.