Towards massive field-theory amplitudes from the cohomology of pure spinor superspace

TL;DR

This paper proposes a new approach to compute massive field-theory amplitudes using pure spinor superspace cohomology, extending methods from massless string amplitudes and providing explicit derivations for certain n-point tree amplitudes.

Contribution

It introduces a conjecture that BRST cohomology in pure spinor superspace determines massive field-theory amplitudes and demonstrates this with explicit derivations for specific cases.

Findings

Derived the pure spinor superspace expression for massive n-point tree amplitudes.

Provided evidence supporting the conjecture through two independent derivations.

Connected the amplitude structure to ${\

Abstract

By analogy with the formula for the massless string disk amplitudes, we define massive field-theory tree amplitudes and conjecture that the BRST cohomology structure of pure spinor superspace fixes their form. We give evidence by deriving the pure spinor superspace expression of the massive field-theory n-point tree amplitude with one first-level massive and n-1 massless states in two ways: 1) from BRST cohomology arguments in pure spinor superspace and 2) from the ${\alpha^\prime}^2$ correction to the massless string amplitudes by inverting the unitarity constraint in superspace.