Massless representation of massive superfields and tree amplitudes with the pure spinor formalism

TL;DR

This paper develops a pure spinor formalism approach to describe massive superstring states and computes related tree amplitudes, revealing new relations between amplitudes with massive and massless states.

Contribution

It constructs the first mass level unintegrated vertex operator from massless vertices and generalizes amplitude relations involving massive states within the pure spinor framework.

Findings

Derived the unintegrated vertex operator at the first mass level.

Expressed the three-point amplitude with one massive state in pure spinor superspace.

Established relations between n-point amplitudes with massive and massless states.

Abstract

We construct the unintegrated vertex operator at the first mass level of the open superstring from the OPE of massless vertices. Using BRST cohomology manipulations, the tree amplitude of two massless and one massive state is rewritten in terms of the pure spinor superspace kinematic expression of the massless four-point amplitude at the ${\alpha^\prime}^2$ level. A generalization relating the partial $n$-point tree amplitudes with one massive state and linear combinations of the ${\alpha^\prime}^2$ corrections to n+1 massless amplitudes is found and shown to be consistent with unitarity.