  We derive an eikonal approximation to high energy interactions in Anti-de
Sitter spacetime, by generalizing a position space derivation of the eikonal
amplitude in flat space. We are able to resum, in terms of a generalized phase
shift, ladder and cross ladder graphs associated to the exchange of a spin j
field, to all orders in the coupling constant. Using the AdS/CFT
correspondence, the resulting amplitude determines the behavior of the dual
conformal field theory four point function < O_1 O_2 O_1 O_2 > for small values
of the cross ratios, in a Lorentzian regime. Finally we show that the phase
shift is dominated by graviton exchange and computes, in the dual CFT, the
anomalous dimension of the double trace primary operators O_1 \partial ...
\partial O_2 of large dimension and spin, corresponding to the relative motion
of the two interacting particles. The results are valid at strong t'Hooft
coupling and are exact in the 1/N expansion.
