Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops

TL;DR

This paper develops a new method called prescriptive unitarity to compute six-particle two-loop amplitudes in non-planar theories like super Yang-Mills and gravity, providing a local integrand basis that captures infrared properties.

Contribution

It extends prescriptive unitarity to non-planar six-particle amplitudes, constructing a diagonalized integrand basis that matches all soft-collinear singularities and separates infrared-divergent parts.

Findings

Constructed a local, diagonalized integrand basis for six-particle amplitudes.

Ensured the basis matches all soft-collinear singularities.

Provided insights into infrared divergence exponentiation.

Abstract

We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and gravity. The integrand basis we construct is diagonalized on a spanning set of non-vanishing leading singularities that ensures the manifest matching of all soft-collinear singularities in both theories. As a consequence, this integrand basis naturally splits into infrared-finite and infrared-divergent parts, with hints toward an integrand-level exponentiation of infrared divergences. Importantly, we use the same basis of integrands for both theories, so that the presence or absence of residues at infinite loop momentum becomes a feature detectable by inspecting the cuts of the theory. Complete details of our results are provided as ancillary files. This work has been updated to take into account the results of [arXiv:1911.09106], which leads to a simpler and more uniform representation of these amplitudes.