A three-loop test of the dilatation operator in N=4 SYM

TL;DR

This paper calculates the three-loop anomalous dimensions of specific operators in N=4 SYM, providing evidence for BMN scaling and refining the understanding of the dilatation operator at higher loops.

Contribution

It introduces a method to compute three-loop anomalous dimensions by reducing the problem to two loops using descendant ratios, confirming BMN scaling at three loops.

Findings

Confirmed BMN scaling at three loops

Reduced three-loop calculations to two loops

Determined the form of the dilatation operator

Abstract

We compute the three-loop anomalous dimension of the BMN operators with charges J=0 (the Konishi multiplet) and J=1 in N=4 super-Yang-Mills theory. We employ a method which effectively reduces the calculation to two loops. Instead of using the superconformal primary states, we consider the ratio of the two-point functions of suitable descendants of the corresponding multiplets. Our results unambiguously select the form of the N=4 SYM dilatation operator which is compatible with BMN scaling. Thus, we provide evidence for BMN scaling at three loops.