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

Henn, J. (0000 0001 2375 0603, Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805, München, Germany) ; Mistlberger, B. (0000 0001 2341 2786, Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A.)

07 May 2019

Abstract: We compute the three-loop scattering amplitude of four gravitons in N = 8 $\mathcal{N}=8$ 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 2 L functions, where L is the loop order.

Published in: JHEP 1905 (2019) 023