A tale of two exponentiations in $\mathcal{N}=8$ supergravity

Abstract

The structure of scattering amplitudes in supergravity theories continues to be of interest. Recently, the amplitude for $2\to 2$ scattering in $\mathcal{N}=8$ supergravity was presented at three-loop order for the first time. The result can be written in terms of an exponentiated one-loop contribution, modulo a remainder function which is free of infrared singularities, but contains leading terms in the high energy Regge limit. We explain the origin of these terms from a well-known, unitarity-restoring exponentiation of the high-energy gravitational $S$-matrix in impact-parameter space. Furthermore, we predict the existence of similar terms in the remainder function at all higher loop orders. Our results provide a non-trivial cross-check of the recent three-loop calculation, and a necessary consistency constraint for any future calculation at higher loops.

14 pages, 2 figures. Minor updates