# Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory

## TL;DR

This paper computes the first non-planar four-loop correction to the cusp anomalous dimension in N=4 supersymmetric Yang-Mills theory, revealing the breakdown of quadratic Casimir scaling and advancing understanding of infrared divergences.

## Contribution

It provides the first numerical calculation of the non-planar four-loop cusp anomalous dimension in N=4 SYM, extending integrability results beyond three loops.

## Key findings

- Non-planar correction at four loops obtained numerically
- Quadratic Casimir scaling breaks down at four loops
- Methods applicable to controlling integrals' number-theoretic aspects

## Abstract

The light-like cusp anomalous dimension is a universal function that controls infrared divergences in quite general quantum field theories. In the maximally supersymmetric Yang-Mills theory this function is fixed fully by integrability to the three-loop order. At four loops a non-planar correction appears which we obtain for the first time from a numerical computation of the Sudakov form factor. Key ingredients are widely applicable methods to control the number-theoretic aspects of the appearing integrals. Our result shows explicitly that quadratic Casimir scaling breaks down at four loops.