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

## TL;DR

This paper computes the first two-loop five-particle amplitude in $
=8$ supergravity, expressing it in terms of known integrals and symbols, and analyzing its factorization, soft divergences, and multi-Regge limit.

## Contribution

It provides the first explicit calculation of the two-loop five-particle amplitude in $
=8$ supergravity, including a compact representation and analysis of its properties.

## Key findings

- Amplitude expressed in terms of uniform weight four symbols.
- Soft divergences exponentiate and a finite remainder is extracted.
- Explicit multi-Regge limit with leading logarithmic terms provided.

## Abstract

We compute for the first time the two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity. Starting from the known integrand, we perform an integration-by-parts reduction and express the answer in terms of uniform weight master integrals. The latter are known to evaluate to non-planar pentagon functions, described by a 31-letter symbol alphabet. We express the final result for the amplitude in terms of uniform weight four symbols, multiplied by a small set of rational factors. The amplitude satisfies the expected factorization properties when one external graviton becomes soft, and when two external gravitons become collinear. We verify that the soft divergences of the amplitude exponentiate, and extract the finite remainder function. The latter depends on fewer rational factors, and is independent of one of the symbol letters. By analyzing identities involving rational factors and symbols we find a remarkably compact representation in terms of a single seed function, summed over all permutations of external particles. Finally, we work out the multi-Regge limit, and present explicitly the leading logarithmic terms in the limit. The full symbol of the IR-subtracted hard function is provided as an ancillary file.