Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions

Details Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions

2006-11-10

arxiv.org/abs/hep-th/0611122v2

JHEP 0708:019,2007

Physics

High Energy Physics

High Energy Physics - Theory

JHEP3.cls, 34 pages, 10 figures; v2: added paragraph, footnote + reference, minor changes

Scientific paper

10.1088/1126-6708/2007/08/019

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 ~ < O_1 O_1 >_{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 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 ~ < O_1 O_2 O_1 O_2 >, where O_2 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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