# Four-graviton scattering to three loops in ${\mathcal N}=8$ supergravity

## TL;DR

This paper presents an analytic computation of the three-loop four-graviton scattering amplitude in ${\mathcal N}=8$ supergravity, revealing simple structures and uniform weight functions at this loop order.

## Contribution

It provides the first explicit three-loop amplitude in ${\mathcal N}=8$ supergravity with closed-form expressions using harmonic poly-logarithms.

## Key findings

- Amplitude expressed as Laurent series in dimensional regularisation
- Coefficients are harmonic poly-logarithms with uniform weight
- Results suggest a pattern of uniform weight functions at each loop order

## Abstract

We compute the three-loop scattering amplitude of four gravitons in ${\mathcal N}=8$ supergravity. Our results are analytic formulae for a Laurent expansion of the amplitude in the regulator of dimensional regularisation. The coefficients of this series are closed formulae in terms of well-established harmonic poly-logarithms. Our results display a remarkable degree of simplicity and represent an important stepping stone in the exploration of the structure of scattering amplitudes. In particular, we observe that to this loop order the four graviton amplitude is given by uniform weight $2L$ functions, where $L$ is the loop order.