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We extend the applications of prescriptive unitarity beyond the planar limitto provide local, polylogarithmic, integrand-level representations ofsix-particle MHV scattering amplitudes in both maximally supersymmetricYang-Mills theory and gravity. The integrand basis we construct is diagonalizedon a spanning set of non-vanishing leading singularities that ensures themanifest matching of all soft-collinear singularities in both theories. As aconsequence, this integrand basis naturally splits into infrared-finite andinfrared-divergent parts, with hints toward an integrand-level exponentiationof infrared divergences. Importantly, we use the same basis of integrands forboth theories, so that the presence or absence of residues at infinite loopmomentum 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 ofthese amplitudes.

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