  The loop expansion for the n-point functions of N=4 Yang-Mills theory and N=8
supergravity can be formulated as the loop expansion of scalar field theory
with an infinite subclass being the ladder diagrams. We consider the sum of
ladder diagrams for gluon-gluon and graviton-graviton scattering in the Regge
limit. The reggeization of the gluon and the graviton is discussed in this
context and that of hep-th/0701217. If the Bern, Dixon, Smirnov conjecture for
planar gluon-gluon scattering is correct, then the ladder sum for SU(N) gauge
theory at large N, correctly gives the Regge limit, with Regge trajectory
function proportional to the cusp anomalous dimension.
  In graviton-graviton scattering it is argued that the graviton lies on a
Regge trajectory. Regge cuts are also present due to infinite sums of
non-planar graphs. The multiple exchange of Regge poles in non-planar graphs
can give a countable infinite number of moving Regge cuts which accumulate near
s=0. It is conjectured that this may be related to the infinite number of
non-perturbative massless states which remain in the limit discussed by Green,
Ooguri and Schwarz.
