The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: First moments in image SYM and non-singlet QCD Original Research Article

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 image supersymmetric Yang–Mills theory. Obtained result completes our previous calculations in 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 image and image 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.