The nonplanar cusp and collinear anomalous dimension at four loops in ${\mathcal N} = 4$ SYM theory

TL;DR

This paper computes the nonplanar cusp and collinear anomalous dimensions at four loops in ${\mathcal N}=4$ SYM theory, revealing the breakdown of quadratic Casimir scaling through numerical analysis of the Sudakov form factor.

Contribution

It provides the first numerical results for nonplanar four-loop anomalous dimensions in ${\mathcal N}=4$ SYM, demonstrating the failure of quadratic Casimir scaling.

Findings

Breakdown of quadratic Casimir scaling at four loops

Numerical values for nonplanar anomalous dimensions

Analysis of numerical uncertainties

Abstract

We present numerical results for the nonplanar lightlike cusp and collinear anomalous dimension at four loops in ${\mathcal N} = 4$ SYM theory, which we infer from a calculation of the Sudakov form factor. The latter is expressed as a rational linear combination of uniformly transcendental integrals for arbitrary colour factor. Numerical integration in the nonplanar sector reveals explicitly the breakdown of quadratic Casimir scaling at the four-loop order. A thorough analysis of the reported numerical uncertainties is carried out.