The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N} = 4$ Sudakov Form Factor

TL;DR

This paper analytically derives the complete four-loop cusp anomalous dimension in $ ext{N}=4$ supersymmetric Yang-Mills theory using the Sudakov form factor, confirming recent independent results.

Contribution

It provides the first full analytic derivation of the four-loop cusp anomalous dimension in $ ext{N}=4$ SYM from the form factor, with uniformly transcendental master integrals.

Findings

Confirmed recent independent four-loop cusp anomalous dimension result.

Provided uniformly transcendental master integrals up to weight six.

Developed parametric integration method for extracting the cusp anomalous dimension.

Abstract

We present an analytic derivation of the full four-loop cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory from the Sudakov form factor. To extract the cusp anomalous dimension, we calculate the $\epsilon^{-2}$ pole of the form factor using parametric integrations of finite integrals. We provide uniformly transcendental results for the master integrals through to weight six and confirm a very recent independent analytic result for the full four-loop cusp anomalous dimension of the $\mathcal{N}=4$ model.