The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: First moments in N=4 SYM and non-singlet QCD

We present the result of a full direct component calculation for the first three even moments of the non-planar contribution into the four-loop anomalous dimension of twist-2 operators in maximally extended N=4 supersymmetric Yang-Mills theory. Obtained result completes our previous calculations in arXiv:0902.4646 [9] and gives the usual result for the higher moments on the contrary to degenerate one in the case of Konishi. We propose a general form of ζ5 and ζ3 parts of the complete non-planar four-loop anomalous dimension of twist-2 operators. As by product, we have obtained the first even moment of the non-planar contribution to the non-singlet four-loop anomalous dimension of Wilson twist-2 operators in QCD.