Simplifying the Tree-level Superstring Massless Five-point Amplitude

TL;DR

This paper simplifies the derivation of the tree-level massless five-point amplitude in superstring theory using the pure spinor formalism and establishes a fundamental connection between string theory OPE identities and BCJ kinematic relations.

Contribution

It provides a streamlined calculation of the five-point amplitude and a first principles derivation of BCJ identities from string theory principles.

Findings

Streamlined derivation of five-point amplitude using pure spinor formalism

Proof of equivalence between OPE identities and BCJ relations

Derivation of remaining BCJ identities from integration regions

Abstract

We use the pure spinor formalism to obtain the supersymmetric massless five-point amplitude at tree-level in a streamlined fashion. We also prove the equivalence of an OPE identity in string theory with a subset of the Bern-Carrasco-Johansson five-point kinematic relations, and demonstrate how the remaining BCJ identities follow from the different integration regions over the open string world-sheet, therefore providing a first principles derivation of the (supersymmetric) BCJ identities.