Non-planar cusp and transcendental anomalous dimension at four loops in N=4 supersymmetric Yang-Mills theory

TL;DR

This paper calculates the nonplanar four-loop contributions to anomalous dimensions in N=4 supersymmetric Yang-Mills theory, providing new analytic results for arbitrary spin and confirming previous findings for specific cases.

Contribution

It presents the first computation of nonplanar four-loop anomalous dimensions for twist-two operators in N=4 SYM, including analytic expressions for arbitrary Lorentz spin.

Findings

Confirmed previous results for lightlike cusp anomalous dimension.

Derived analytic expressions for nonplanar contributions at four loops.

Provided new insights into transcendental parts of anomalous dimensions.

Abstract

We compute the nonplanar contribution to the universal anomalous dimension of the SU(4)-singlet twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops through Lorentz spin 18. From this, we numerically evaluate the nonplanar contribution to the four-loop lightlike cusp anomalous dimension and derive the transcendental $\zeta_3$ and $\zeta_5$ parts of the universal anomalous dimension for arbitrary Lorentz spin in analytic form. As for the lightlike cusp anomalous dimension and the $\zeta_5$ part of the universal anomalous dimension, we confirm previous results.