Regge behavior of gluon scattering amplitudes in N=4 SYM theory

TL;DR

The paper establishes Reggeization of the planar four-gluon amplitude in ${\cal N}=4$ SYM by combining the BDS ansatz with Alday–Maldacena's strong-coupling results. It shows that the leading Regge trajectory $\alpha(s)$ and residue $\beta(s)$ are controlled by the same coupling functions $f(\lambda)$ and $g(\lambda)$ that govern IR divergences and the finite $\log^2(s/t)$ piece, enabling a Regge form ${\cal A}_4 \to \beta(s)[(u/(-s))^{\alpha(s)}+\cdots]$ in the Regge limit. In the weak coupling, $f(\lambda)$ and $g(\lambda)$ reproduce known perturbative structures, while at strong coupling $\exp[ (\sqrt{\lambda})/(8\pi)\log^2(s/t) ]$ governs the amplitude, yielding a logarithmic, not linear, $\alpha(s)$ and signaling no Regge recurrences in a conformal theory. The results bridge perturbative and AdS/CFT descriptions, showing Reggeization persists across couplings and clarifying high-energy behavior in a conformal gauge theory.

Abstract

It is shown that the four-gluon scattering amplitude for N=4 supersymmetric Yang-Mills theory in the planar limit can be written, in both the weak- and strong-coupling limits, as a reggeized amplitude, with a parent trajectory and an infinite number of daughter trajectories. This result relies crucially on the fact that the leading IR-divergence and the finite log^2(s/t)-dependent piece of the amplitude are characterized by the same function for all values of the coupling, as conjectured by Bern, Dixon, and Smirnov, and proved by Alday and Maldacena in the strong-coupling limit. We use the Alday-Maldacena result to determine the strong-coupling Regge trajectory.