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

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.

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

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Cited by in corpus (16)

• On form factors in N=4 sym
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• The Exact Effective Couplings of 4D N=2 gauge theories
• Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• Integrability in N=2 superconformal gauge theories
• The complete one-loop dilatation operator of planar real beta-deformed N=4 SYM theory
• From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators
• A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory
• On the Integrability of Planar N=2 Superconformal Gauge Theories
• Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory
• The two-loop dilatation operator of N=4 super Yang-Mills theory in the SO(6) sector
• The Complete One-loop Spin Chain of N =1 SQCD
• Four-loop anomalous dimensions in Leigh-Strassler deformations
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations