Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions

TL;DR

This paper develops an impact-parameter representation for conformal correlators in AdS/CFT, enabling analysis of high-spin exchanges and leading to new insights into the structure of four-point functions at finite N.

Contribution

It introduces a novel impact-parameter approach for conformal partial waves in the eikonal regime, connecting shock wave results to four-point correlators and proposing a resummation of Witten diagrams.

Findings

High-spin conformal partial-wave decomposition derived for AdS Witten diagrams.

Demonstration of graviton dominance in the eikonal regime.

Conjecture of a resummation formula for crossed-ladder diagrams.

Abstract

We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ < O_1 O_2 O_1 O_2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function < O_1 O_1 >_{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.