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

TL;DR

This paper calculates the non-planar contributions to the four-loop anomalous dimensions of twist-2 operators in N=4 SYM and QCD, providing new explicit results for the first three moments and proposing a general form for certain zeta terms.

Contribution

It presents the first direct calculation of the non-planar four-loop anomalous dimensions for the first three moments in N=4 SYM and extends results to QCD, revealing new structural insights.

Findings

Explicit results for the first three moments in N=4 SYM.

First moment of non-planar contribution in QCD.

Proposed general form for zeta(5) and zeta(3) parts.

Abstract

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 complete our previous calculations in arXiv:0902.4646 and gives the usual result for the higher moments on the contrary to degenerate one in the case of Konishi. We have proposed a general form of zeta(5) and zeta(3) parts of the full non-planar anomalous dimension of twist-2 operators. As by product, we have obtained the first moment of the non-planar contribution to the non-singlet four-loop anomalous dimension of Wilson twist-2 operators in QCD.