On twist-two operators in N=4 SYM

TL;DR

This paper introduces a novel method for calculating anomalous dimensions of higher-spin twist-two operators in N=4 SYM using ratios of correlation functions, simplifying higher-loop computations.

Contribution

It proposes a new technique based on correlation function ratios to determine anomalous dimensions at multiple loops, demonstrated with tree-level calculations.

Findings

Reproduced one-loop anomalous dimensions using only tree-level calculations.

Derived the complete form of first-generation descendants of twist-two operators.

Analyzed the scalar sector of second-generation descendants.

Abstract

We propose a mechanism for calculating anomalous dimensions of higher-spin twist-two operators in N=4 SYM. We consider the ratio of the two-point functions of the operators and of their superconformal descendants or, alternatively, of the three-point functions of the operators and of the descendants with two protected half-BPS operators. These ratios are proportional to the anomalous dimension and can be evaluated at n-1 loop in order to determine the anomalous dimension at n loops. We illustrate the method by reproducing the well-known one-loop result by doing only tree-level calculations. We work out the complete form of the first-generation descendants of the twist-two operators and the scalar sector of the second-generation descendants.