Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry

Abstract

Scattering amplitudes in planar N=4 super Yang-Mills theory reveal a remarkable symmetry structure. In addition to the superconformal symmetry of the Lagrangian of the theory, the planar amplitudes exhibit a dual superconformal symmetry. The presence of this additional symmetry imposes strong restrictions on the amplitudes and is connected to a duality relating scattering amplitudes to Wilson loops defined on polygonal light-like contours. The combination of the superconformal and dual superconformal symmetries gives rise to a Yangian, an algebraic structure which is known to be related to the appearance of integrability in other regimes of the theory. We discuss two dual formulations of the symmetry and address the classification of its invariants.

22 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated, v3 added references, typos fixed

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Cited by in corpus (20)

• Heptagons from the Steinmann Cluster Bootstrap
• Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• Superspin chains and supersymmetric gauge theories
• The Two-Loop Remainder Function for Eight and Nine Particles
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Non-abelian fermionic T-duality in supergravity
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
• Fermionic T-Duality of $Ad{S}_n\times S^n(\times S^n)\times T^m$ using IIA Supergravity
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
• Hexagon Bootstrap in the Double Scaling Limit
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions