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

## TL;DR

This paper computes the two-loop five-point amplitude in $
$N=8 supergravity using a novel d-dimensional unitarity approach, revealing its uniform transcendentality and similarities to N=4 super-Yang-Mills theory.

## Contribution

Introduces a d-dimensional unitarity-based method for constructing amplitudes' rational structures, applicable beyond supergravity.

## Key findings

- Amplitude is uniformly transcendental.
- Rational prefactors are double copies of Yang-Mills ones.
- Discovered new relations between N=4 super-Yang-Mills amplitudes.

## Abstract

We compute the symbol of the two-loop five-point amplitude in $\mathcal N=8$ 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 $\mathcal N=8$ 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 $\mathcal N=4$ 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 $\mathcal N=4$ super-Yang-Mills theory.