Exact Superconformal and Yangian Symmetry of Scattering Amplitudes

Abstract

We review recent progress in the understanding of symmetries for scattering amplitudes in N=4 superconformal Yang-Mills theory. It is summarized how the superficial breaking of superconformal symmetry by collinear anomalies and the renormalization process can be cured at tree and loop level. This is achieved by correcting the representation of the superconformal group on amplitudes. Moreover, we comment on the Yangian symmetry of scattering amplitudes and how it inherits these correction terms from the ordinary Lie algebra symmetry. Invariants under this algebra and their relation to the Grassmannian generating function for scattering amplitudes are discussed. Finally, parallel developments in N=6 superconformal Chern-Simons theory are summarized. This article is an invited review for a special issue of Journal of Physics A devoted to Scattering Amplitudes in Gauge Theories.

28 Pages, 6 Figures. Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", v2: references added

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Cited by in corpus (19)

• Basics of Generalized Unitarity
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Lectures on Yangian Symmetry
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• An Introduction to On-shell Recursion Relations
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• On Yangian-invariant regularisation of deformed on-shell diagrams in N=4 super-Yang-Mills theory
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• SUSY Ward identities, Superamplitudes, and Counterterms
• Yangian Bootstrap for Massive Feynman Integrals
• Massive Fishnets
• Tree-level amplitudes and dual superconformal symmetry
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Grassmannian Integrals in Minkowski Signature, Amplitudes, and Integrability
• 6D dual superconformal algebra
• Bilocal phase operators in beta-deformed super Yang-Mills