The non-planar contribution to the four-loop universal anomalous dimension in N=4 Supersymmetric Yang-Mills theory

TL;DR

This paper calculates the non-planar four-loop anomalous dimension in N=4 SYM, revealing it is proportional to zeta(5) and exhibits a double-logarithmic growth for large spin values.

Contribution

It provides the first direct calculation of the non-planar four-loop anomalous dimension, showing its proportionality to zeta(5) and extending previous results to arbitrary Lorentz spin.

Findings

Non-planar contribution contains only zeta(5) term.

Proportionality to zeta(5) extends to arbitrary spin.

Results imply a double-logarithmic asymptotic for large spin.

Abstract

We present the result of a full direct component calculation for the non-planar contribution to the four-loop anomalous dimension of the Konishi operator in N =4 Supersymmetric Yang-Mills theory. The result contains only zeta(5) term and is proportional to zeta(5) contribution in the planar case, which comes purely from wrapping corrections. We have extended also our previous calculations for the leading transcendental contribution arXiv:0811.0607 on non-planar case and have found the same results up to a common factor. It allows us to suggest that the non-planar contribution to the four-loop universal anomalous dimension for the twist-2 operators with arbitrary Lorentz spin is proportional to $S_1^2(j) \zeta(5)$. This result gives unusual double-logarithmic asymptotic $\ln^2 j$ for large j.