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 sup- plementary material.
Highlights
A key insight underpinning a number of those developments was the realization that the computation of perturbative scattering amplitudes can be divided into two steps: that of ‘summing Feynman diagrams’ to obtain a representative loop integrand —a rational differential form on the space of internal loop momenta; and that of tackling the more difficult problem of loop integration
We have prepared plain-text definitions of each integrand and coefficient needed for the representation of two-loop six-point MHV amplitudes in supersymmetric Yang-Mills (sYM) and SUGRA, and we have provided additional functionality for Mathematica users
In this paper we have constructed the four-dimensional integrands for two-loop six-point MHV amplitudes in maximally supersymmetric Yang-Mills theory and supergravity
Summary
Our results for the two-loop six-particle MHV amplitudes in N = 4 sYM and N = 8 SUGRA follow from the basic principles of generalized unitarity [2,3,4,5], and its refined form of prescriptive unitarity [47].
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