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

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

2010-08-19

arxiv.org/abs/1008.3351v2

Phys.Rev.D84:045014,2011

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 33 pages, v2: formulations improved, references added, final version

Scientific paper

10.1103/PhysRevD.84.045014

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.

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