The two-loop five-point amplitude in $ \mathcal{N}=8$ supergravity

DOI10.1007/JHEP03(2019)123zbMATH Open1414.83094arXiv1901.08563OpenAlexW2912348714MaRDI QIDQ2421129

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Publication date: 8 June 2019

Published in: (Search for Journal in Brave)

Abstract: We compute the symbol of the two-loop five-point amplitude in $mathcalN=8$ supergravity. We write an ansatz for the amplitude whose rational prefactors are based on not only 4-dimensional leading singularities, but also $d$-dimensional ones, as the former are insufficient. Our novel $d$-dimensional unitarity-based approach to the systematic construction of an amplitude's rational structures is likely to have broader applications, for example to analogous QCD calculations. We fix parameters in the ansatz by performing numerical integration-by-parts reduction of the known integrand. We find that the two-loop five-point $mathcalN=8$ supergravity amplitude is uniformly transcendental. We then verify the soft and collinear limits of the amplitude. There is considerable similarity with the corresponding amplitude for $mathcalN=4$ super-Yang-Mills theory: all the rational prefactors are double copies of the Yang-Mills ones and the transcendental functions overlap to a large degree. As a byproduct, we find new relations between color-ordered loop amplitudes in $mathcalN=4$ super-Yang-Mills theory.

Full work available at URL: https://arxiv.org/abs/1901.08563

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