Superspace calculation of the three-loop dilatation operator of N=4 SYM theory

TL;DR

This paper computes the three-loop dilatation operator for a specific sector of N=4 SYM theory using superspace Feynman diagrams, confirming integrability predictions and revealing universal cancellation mechanisms.

Contribution

It provides the first direct Feynman diagram calculation of the three-loop dilatation operator in N=4 SYM, confirming integrability-based results and introducing finiteness conditions to simplify calculations.

Findings

Transcendentality three contributions cancel out, leaving a rational result.

Finiteness conditions help avoid evaluating many Feynman graphs.

All higher-order poles cancel, ensuring consistency.

Abstract

We derive the three-loop dilatation operator of the flavor SU(2) subsector of N=4 supersymmetric Yang-Mills theory in the planar limit by a direct Feynman diagram calculation in N=1 superspace. The transcendentality three contributions which appear in intermediate steps cancel among each other, leaving a rational result which confirms the predictions from integrability. We derive finiteness conditions that allow us to avoid the explicit evaluation of entire classes of Feynman graphs and also yield constraints on the D-algebra manipulations. Based on these results, we discover universal cancellation mechanisms. As a check for the consistency of our result, we verify the cancellation of all higher-order poles.