Nonplanar Four-Loop Anomalous Dimensions of Twist-Two Operators in N=4 Super Yang-Mills Theory: Higher Moment, General Result, and Cusp Anomalous Dimension

Abstract

We consider the nonplanar universal anomalous dimension of twist-two operators at four loops in N=4 supersymmetric Yang-Mills theory and push its direct diagrammatic calculation through Lorentz spin j=20, one unit beyond the state of the art, so as to confirm the correctness of the general, all-j result conjectured previously by us [1] imposing certain constraints on its analytic form. Thanks to our new result, such constraints can be eliminated altogether. By the same token, this allows us to re-derive, in a completely independent way, the nonplanar four-loop cusp anomalous dimension by taking the large-j limit of the general result.