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

Understand

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.