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

TL;DR

This paper develops a generalized eikonal approximation in AdS/CFT, relating shock wave two-point functions to four-point functions and extending to black hole horizons, providing new tools for Planckian physics analysis.

Contribution

It introduces a novel approach to compute amplitudes in AdS using shock waves, connecting two-point and four-point functions, and extends the framework to black hole horizons.

Findings

Relates shock wave two-point functions to four-point function discontinuities.

Extends the shock wave analysis to Schwarzschild BTZ black holes.

Provides new methods for studying Planckian physics in AdS spacetime.

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 ~ < 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.