Five-loop anomalous dimension at critical wrapping order in N=4 SYM

TL;DR

This paper calculates the five-loop anomalous dimension of a length-five operator in N=4 SYM, confirming a conjectured formula using perturbative and Y-system methods, advancing understanding of critical wrapping effects.

Contribution

It provides the first explicit five-loop calculation of a length-five operator's anomalous dimension in N=4 SYM, confirming a previously conjectured formula with two independent methods.

Findings

Perturbative five-loop anomalous dimension matches the conjecture.

Y-system approach independently confirms the perturbative result.

Results enhance understanding of wrapping effects at critical order.

Abstract

We compute the anomalous dimension of a length-five operator at five-loop order in the SU(2) sector of N=4 SYM theory in the planar limit. This is critical wrapping order at five loops. The result is obtained perturbatively by means of N=1 superspace techniques. Our result from perturbation theory confirms explicitly the formula conjectured in arXiv:0901.4864 for the five-loop anomalous dimension of twist-three operators. We also explicitly obtain the same result by employing the recently proposed Y-system.