Eikonal approximation in Ads/CFT: from shock waves to four-point functions

We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function epsilon similar to < O1O1 > shock in the presence of a shock wave in Anti-de Sitter, where 01 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A similar to < O1O2O1O2 >, where O-2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing epsilon in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.