Non-planar 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 ${\zeta }_3$ 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.

Comments: 6 pages, 1 figure, minor changes, reference added, accepted for publication in Phys. Rev. Lett