High Energy Scattering in the AdS/CFT Correspondence (original) (raw)

By the AdS/CFT correspondence, the eikonal amplitude in AdS is related to the four point function of CFT primary operators in the regime of large 't Hooft coupling, including all terms of the 1/N expansion. We then show that the eikonal amplitude determines the behavior of the CFT four point function for small values of the cross ratios in a Lorentzian regime and that this controls its high spin and dimension conformal partial wave decomposition. These results allow us to determine the anomalous dimension of high spin and dimension double trace primary operators, by relating it to the AdS eikonal phase shift. Finally we find that, at large energies and large impact parameters in AdS, the gravitational interaction dominates all other interactions, as in flat space. Therefore, the anomalous dimension of double trace operators, associated to graviton exchange in AdS, yields a universal prediction for CFT's with AdS gravitational duals.