Non-planar anomalous dimension of twist-2 operators: Higher moments at four loops

We compute the non-planar contribution to the anomalous dimension of the eighth moment of the twist-2 operators in N=4N=4 supersymmetric Yang–Mills theory at four loops. This result was obtained from the calculations of some elements of the anomalous dimension matrix for twist-2 operators with the help of the relations between its elements and eigenvalues. The properties of the obtained result and possible relations with a planar results are discussed.