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

TL;DR

This paper computes the nonplanar four-loop anomalous dimensions of twist-two operators in N=4 SYM theory up to spin j=20, confirming a previously conjectured all-j formula and deriving the cusp anomalous dimension independently.

Contribution

It extends the direct diagrammatic calculation of nonplanar anomalous dimensions to higher spins and confirms the all-j conjecture, enabling a new derivation of the cusp anomalous dimension.

Findings

Confirmed the all-j conjecture for nonplanar anomalous dimensions

Extended calculations up to spin j=20, beyond previous limits

Derived the nonplanar four-loop cusp anomalous dimension independently

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.