Anomalous dimensions from the $\mathcal{N}=4$ SYM hexagon

TL;DR

This paper computes the one-loop anomalous dimensions of certain operators in $ ext{N}=4$ super Yang-Mills theory using a hexagon approach, providing a novel method for analyzing correlators in this context.

Contribution

It introduces a hexagon-based method to extract anomalous dimensions from correlators in $ ext{N}=4$ SYM, advancing computational techniques in the field.

Findings

Successfully reproduces known one-loop anomalous dimensions.

Demonstrates the effectiveness of the hexagon approach for correlator analysis.

Provides a new computational framework for operator dimensions in supersymmetric theories.

Abstract

We consider the correlator $\langle \mathcal{L} \mathcal{K} \tilde{ \mathcal{K}} \rangle $ of the Lagrange operator of $\mathcal{N}=4$ super Yang-Mills theory and two conjugate two-excitation operators in an $su(2)$ sector. We recover the planar one-loop anomalous dimension of the renormalised operators from this hexagon computation.