Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace

TL;DR

This paper presents a new BRST-closed expression for 5-point super-Yang-Mills amplitudes in pure spinor superspace, linking string theory and field theory, and proposes a method to extend to higher points.

Contribution

It introduces a simple, cyclic invariant amplitude expression in pure spinor superspace and suggests an empirical approach for higher-point amplitudes based on pole structures.

Findings

BRST-closed 5-point amplitude expression in pure spinor superspace

Empirical method for higher-point amplitude construction

Explicit 6- and 7-gluon amplitude expansions

Abstract

A simple BRST-closed expression for the color-ordered super-Yang-Mills 5-point amplitude at tree-level is proposed in pure spinor superspace and shown to be BRST-equivalent to the field theory limit of the open superstring 5-pt amplitude. It is manifestly cyclic invariant and each one of its five terms can be associated to the five Feynman diagrams which use only cubic vertices. Its form also suggests an empirical method to find superspace expressions in the cohomology of the pure spinor BRST operator for higher-point amplitudes based on their kinematic pole structure. Using this method, Ansaetze for the 6- and 7-point 10D super-Yang-Mills amplitudes which map to their 14 and 42 color-ordered diagrams are conjectured and their 6- and 7-gluon expansions are explicitly computed.