  We introduce the impact-parameter representation for conformal field theory
correlators of the form A ~ < O_1 O_2 O_1 O_2 >. This representation is
appropriate in the eikonal kinematical regime, and approximates the conformal
partial-wave decomposition in the limit of large spin and dimension of the
exchanged primary. Using recent results on the two-point function < O_1 O_1
>_{shock} in the presence of a shock wave in Anti-de Sitter, and its relation
to the discontinuity of the four-point amplitude A across a kinematical
branch-cut, we find the high spin and dimension conformal partial- wave
decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that,
as in flat space, the eikonal kinematical regime is dominated by the T-channel
exchange of the massless particle with highest spin (graviton dominance). We
also compute the anomalous dimensions of the high-spin O_1 O_2 composites.
Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to
all orders in the gravitational coupling.
