Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory

TL;DR

This paper computes the four-loop collinear anomalous dimension in N=4 Yang-Mills theory, providing precise numerical results that support string theory predictions via AdS/CFT correspondence.

Contribution

It presents the first four-loop calculation of the collinear anomalous dimension in N=4 SYM using the method of obstructions, advancing understanding of infrared structures in gauge theories.

Findings

Four-loop anomalous dimension g^4 = -1240.9 with 0.02% uncertainty

Supports the string theory prediction for strong coupling behavior

Enhances the precision of infrared divergence calculations in N=4 SYM

Abstract

We report a calculation in N = 4 Yang-Mills of the four-loop term g^4 in the collinear anomalous dimension g(lambda) which governs the universal subleading infrared structure of gluon scattering amplitudes. Using the method of obstructions to extract this quantity from the 1/epsilon singularity in the four-gluon iterative relation at four loops, we find g^4 = -1240.9 with an estimated numerical uncertainty of 0.02%. We also analyze the implication of our result for the strong coupling behavior of g(lambda), finding support for the string theory prediction computed recently by Alday and Maldacena using AdS/CFT.