The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy

TL;DR

This paper constructs a five-loop four-point integrand for N=8 supergravity using a generalized double-copy method, involving systematic modifications and consistency checks, advancing the understanding of supergravity's ultraviolet behavior.

Contribution

It introduces a novel five-loop integrand for N=8 supergravity via a generalized double-copy approach, incorporating contact terms and unitarity cuts, crucial for future ultraviolet studies.

Findings

Successfully constructed the five-loop integrand for N=8 supergravity.

Derived formulas relating contact terms to gauge-theory dual Jacobi violations.

Performed consistency checks confirming the integrand's validity.

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.