The Five-Loop Four-Point Integrand of N = 8 Supergravity as a Generalized Double Copy
Authors: Zvi Bern, John Joseph Carrasco, Wei-Ming Chen, Henrik Johansson, Radu Roiban, Mao Zeng Preprint Number: UUITP-29/17 We use the recently developed generalized double-copy procedure to construct an integrand for the five-loop four-point amplitude of N = 8 supergravity. [...] The five-loop four-point integrand is a crucial ingredient towards future determinations 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 loop integration in the ultraviolet region.
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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 corrected via a set of contact terms generated in the context of the method of maximal unitarity cuts. For the simpler generalized unitarity cuts which tend to have the most complicated contact terms associated with them, we derive a set of formulas for determining the N = 8 supergravity contact contribution in terms of violations of dual Jacobi identities in the corresponding N = 4 super-Yang–Mills amplitude. 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.