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

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.

21 pages, no figures at all

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Cited by in corpus (5)

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• Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator
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• Double logarithms in $\mathcal{N}\ge 4$ supergravity: weak gravity and Shapiro's time delay