Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange

TL;DR

This paper develops a generalized Regge theory for conformal field theories, analyzing high-spin exchanges in Lorentzian correlators, and applies it to string duals like N=4 super-Yang-Mills, including multi-reggeon effects.

Contribution

It introduces complex-spin techniques to analyze Lorentzian CFT correlators with arbitrary spin exchanges and applies impact parameter methods to multi-reggeon exchanges in the eikonal limit.

Findings

High-spin conformal partial waves dominate Lorentzian limits.

Regge poles correspond to gravireggeon exchanges in string duals.

Multi-reggeon exchanges are analyzed using impact parameter representation.

Abstract

We analyze conformal field theory 4-point functions of the form A ~ O_1(x_1) O_2(x_2) O_1(x_3) O_2(x_4), where the operators O_i are scalar primaries. We show that, in the Lorentzian regime, the limit x_1 -> x_3 is dominated by the exchange of conformal partial waves of highest spin. When partial waves of arbitrary spin contribute to A, the behavior of the Lorentzian amplitude for x_1 -> x_3 must be analyzed using complex-spin techniques, leading to a generalized Regge theory for CFT's. Whenever the CFT is dual to a string theory, the string tree-level contribution A_tree to the amplitude A presents a Regge pole corresponding the a gravi-reggeon exchange. In this case, we apply the impact parameter representation for CFT amplitudes, previously developed, to analyze multiple reggeon exchanges in the eikonal limit. As an example, we apply these general techniques to N=4 super-Yang-Mills theory in d=4 in the limit of large 't Hooft coupling, including the leading string corrections to pure graviton exchange.