Infrared Limit of Gluon Amplitudes at Strong Coupling

TL;DR

The paper addresses how infrared divergences of gluon scattering amplitudes behave at strong coupling in ${\cal N}=4$ SYM via the AdS/CFT correspondence. It proposes that IR data are encoded entirely by local cusp data on the string worldsheet boundary, enabling a per-cusp minimal-surface calculation in AdS with dimensional regularization. The resulting per-cusp contribution $S_{i,i+1}(\epsilon)$ yields an additive, universal IR structure that matches the all-loop field-theory form, with the cusp anomalous dimension $f(\lambda)\sim \sqrt{\lambda}$ at strong coupling and a subleading $g(\lambda)$. The analysis recovers the known strong-coupling four-gluon IR divergence computed by Alday and Maldacena, supporting the BDS-type iterative structure at strong coupling and suggesting a new route to the finite remainder ${\cal F}_n$. Overall, the work clarifies how cusp-local AdS data encode the IR behavior of holographic gauge theories, reinforcing the connection between strong-coupling gravity duals and field-theory IR physics.

Abstract

In this note, we propose that the infrared structure of gluon amplitudes at strong coupling can be fully extracted from a local consideration near cusps. This is consistent with field theory and correctly reproduces the infrared divergences of the four-gluon amplitude at strong coupling calculated recently by Alday and Maldacena.

Figures (2)

• Figure 1: The boundary of the worldsheet of the $n$-gluon amplitude. For simplicity, we removed the factors of $2 \pi$ multiplying each $k_{i}$.
• Figure 2: The graphical representation of the infrared divergences. Each cusp represents the boundary of the minimal worldsheet.