Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors

TL;DR

This paper uses pure spinor formalism to establish identities linking different loop-level kinematic factors in massless four-point amplitudes, simplifying the computation of supersymmetric amplitudes.

Contribution

It derives identities that connect tree-level, one-loop, and two-loop kinematic factors, enabling immediate determination of higher-loop amplitudes from tree-level data.

Findings

Two-loop amplitudes match RNS formalism results up to a coefficient

Identities simplify supersymmetric amplitude calculations

Complete supersymmetric one- and two-loop amplitudes are determined from tree-level

Abstract

Using the pure spinor formalism we prove identities which relate the tree-level, one-loop and two-loop kinematic factors for massless four-point amplitudes. From these identities it follows that the complete supersymmetric one- and two-loop amplitudes are immediately known once the tree-level kinematic factor is evaluated. In particular, the two-loop equivalence with the RNS formalism (up to an overall coefficient) is obtained as a corollary.