A Numerical Study of Gluon Scattering Amplitudes in N=4 Super Yang-Mills Theory at Strong Coupling

TL;DR

This paper numerically investigates gluon scattering amplitudes in N=4 super Yang-Mills theory at strong coupling using the AdS/CFT correspondence, focusing on minimal surfaces in AdS space for various point amplitudes.

Contribution

It provides a numerical approach to evaluate minimal surfaces for gluon scattering amplitudes at strong coupling, confirming analytical infrared singularity results with high precision.

Findings

Infrared singularities match analytical predictions within 5%

Numerical solutions are stable and accurate at high lattice resolution

Method applicable to higher-point amplitudes in AdS/CFT context

Abstract

We study gluon scattering amplitudes in N=4 super Yang-Mills theory at strong coupling via the AdS/CFT correspondence. We solve numerically the discretized Euler-Lagrange equations on the square worldsheet for the minimal surface with light-like boundaries in AdS spacetime. We evaluate the area of the surface for the 4, 6 and 8-point amplitudes using worldsheet and radial cut-off regularizations. Their infrared singularities in the cut-off regularization are found to agree with the analytical results near the cusp less than 5% at 520x520 lattice points.