Nonplanar Cusp and Transcendental Anomalous Dimension at Four Loops in N=4 Supersymmetric Yang-Mills Theory

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 ζ3 and ζ5 parts of the universal anomalous dimension for arbitrary Lorentz spin in analytic form. As for the lightlike cusp anomalous dimension and the ζ5 part of the universal anomalous dimension, we confirm previous results.