  The structure of scattering amplitudes in supergravity theories continues to
be of interest. Recently, the amplitude for $2\rightarrow 2$ scattering in
${\cal N}=8$ 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.

High Energy Physics - Theory