Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions
Abstract
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 E ~ < O1 O1 >shock in the presence of a shock wave in Anti-de Sitter, where O1 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 ~ < O1 O2 O1 O2 >, where O2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E 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.
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