Five-loop four-point integrand of N=8 supergravity as a generalized double copy

Zvi Bern, John Joseph Carrasco, Wei Ming Chen, Henrik Johansson, Radu Roiban, Mao Zeng

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99 Scopus citations

Abstract

We use the recently developed generalized double-copy procedure to construct an integrand for the five-loop four-point amplitude of N=8 supergravity. This construction starts from a naive double copy of the previously computed corresponding amplitude of N=4 super-Yang-Mills theory. This is then systematically modified by adding contact terms generated in the context of the method of maximal unitarity cuts. For the simpler generalized cuts, whose corresponding contact terms tend to be the most complicated, we derive a set of formulas relating the contact contributions to the violations of the dual Jacobi identities in the relevant gauge-theory amplitudes. For more complex generalized unitarity cuts, which tend to have simpler contact terms associated with them, we use the method of maximal cuts more directly. The five-loop four-point integrand is a crucial ingredient towards future studies of ultraviolet properties of N=8 supergravity at five loops and beyond. We also present a nontrivial check of the consistency of the integrand, based on modern approaches for integrating over the loop momenta in the ultraviolet region.

Original languageEnglish (US)
Article number126012
JournalPhysical Review D
Volume96
Issue number12
DOIs
StatePublished - Dec 15 2017

Funding

We thank Jacob Bourjaily, Lance Dixon, Alex Edison, Michael Enciso, Enrico Hermann, David Kosower, Julio Parra-Martinez, Chia-Hsien Shen, Jaroslav Trnka and Yang Zhang for many useful and interesting discussions. This work is supported by the Department of Energy under Awards No. DE-SC0009937 and No. DE-SC0013699. We acknowledge the hospitality of KITP at UC Santa Barbara in the program “Scattering Amplitudes and Beyond,” during various stages of this work. While at KITP this work was also supported by the U.S. NSF under Grant No. PHY11-25915. J. J. M. C. is supported by the European Research Council under ERC-STG-639729, preQFT: Strategic Predictions for Quantum Field Theories. The research of H. J. is supported in part by the Swedish Research Council under Grant No. 621-2014-5722, the Knut and Alice Wallenberg Foundation under Grant No. KAW 2013.0235, and the Ragnar Söderberg Foundation under Grant S1/16.

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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