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

J M Henn,B Mistlberger

doi:10.1007/jhep05(2019)023

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.

Highlights

JHEP05(2019)023 symmetries, and the memory effect of gravitational radiation
We observe that to this loop order the four graviton amplitude is given by uniform weight 2L functions, where L is the loop order
We will express our result for amplitudes at different orders in the coupling expanded in the dimensional regulator in terms of harmonic poly-logarithms (HPLs) [56]

Summary

Notations and four-graviton amplitude at one loop

We briefly discuss the overall setup and introduce some definitions. We write the amplitude for scattering of gravitons in N = 8 super gravity in terms of. We will express our result for amplitudes at different orders in the coupling expanded in the dimensional regulator in terms of harmonic poly-logarithms (HPLs) [56]. In massless gauge theory one typically finds one double pole per loop order originating from simultaneous soft and collinear singularities At most a single pole is allowed per loop order We observed this cancellation already above in the case of the one-loop amplitude when expanding in the dimensional regulator and applying the kinematic constraint s+t+u = 0. Ultraviolet divergences in quantum gravity theories have received a lot of interest, culminating in a recent computation of the ultra-violet limit of N = 8 super-gravity scattering amplitudes up to five loops in ref. The three loop result F (3) obtained in this article has to be free of poles in the dimensional regulator — and it is

Analytic continuation to different physical regions

The four-graviton amplitude up to three loops

Soft and Regge limit

Conclusion and outlook