Eikonal Approach to N=4 SYM Regge Amplitudes in the AdS/CFT Correspondence

TL;DR

This paper investigates the high-energy behavior of N=4 SYM elastic amplitudes at strong coupling using the AdS/CFT correspondence, employing an eikonal method and comparing different minimal surface approaches to reveal universal Regge behavior.

Contribution

It introduces an eikonal approach with a generalized helicoid minimal surface in hyperbolic space and compares it to existing methods, showing universality in Regge trajectories at strong coupling.

Findings

Eikonal amplitudes are dominated by the Euclidean cusp contribution.

High-energy amplitudes exhibit Regge behavior with universal trajectories.

Results are consistent across different scattering particle types.

Abstract

The high-energy behavior of N=4 SYM elastic amplitudes at strong coupling is studied by means of the AdS/CFT correspondence. We consider the eikonal method proposed by Janik and one of the authors, where the relevant minimal surface is a "generalized helicoid" in hyperbolic space ("Euclidean AdS_5"), from which the physical amplitude is obtained after an appropriate analytic continuation. We then compare our results with those obtained, using a minimal surface in AdS_5 momentum space, by Alday and Maldacena for gluon-gluon scattering, and by Barnes and Vaman for quark-quark scattering ("Alday-Maldacena approach"). Exploiting a conformal transformation, we show that the eikonal amplitudes are dominated by the Euclidean version of the cusp contribution found in the Alday-Maldacena approach. The amplitudes in the two approaches are of Regge type at high-energy and with the same logarithmic Regge trajectory independently of the kind of colliding particles, in agreement with the expected universality of Regge trajectories.