Scattering equations, supergravity integrands, and pure spinors

TL;DR

This paper develops a worldsheet theory approach to compute supergravity scattering amplitudes, extending to higher genus surfaces, and provides evidence supporting the conjecture that these correlators yield loop integrands consistent with superstring theory.

Contribution

It introduces a non-minimal worldsheet formalism for supergravity amplitudes that manifest supersymmetry and supports the conjecture with genus-one and genus-two evidence.

Findings

Correlators on higher genus worldsheets can compute supergravity loop integrands.

The formalism shows a close match with pure spinor superstring theory.

Evidence supports the conjecture at genus one and two with four external states.

Abstract

The tree-level S-matrix of type II supergravity can be computed in scattering equation form by correlators in a worldsheet theory analogous to a chiral, infinite tension limit of the pure spinor formalism. By defining a non-minimal version of this theory, we give a prescription for computing correlators on higher genus worldsheets which manifest space-time supersymmetry. These correlators are conjectured to provide the loop integrands of supergravity scattering amplitudes, supported on the scattering equations. We give non-trivial evidence in support of this conjecture at genus one and two with four external states. Throughout, we find a close correspondence with the pure spinor formalism of superstring theory, particularly regarding regulators and zero-mode counting.