Yangian Symmetry and Integrability of Planar N=4 Super-Yang-Mills Theory

Abstract

In this letter we establish Yangian symmetry of planar N=4 super-Yang-Mills theory. We prove that the classical equations of motion of the model close onto themselves under the action of Yangian generators. Moreover we propose an off-shell extension of our statement which is equivalent to the invariance of the action and prove that it is exactly satisfied. We assert that our relationship serves as a criterion for integrability in planar gauge theories by explicitly checking that it applies to integrable ABJM theory but not to non-integrable N=1 super-Yang-Mills theory.

9 pages, v2: minor changes, published version

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
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• Massive Fishnets
• Bose-Fermi cancellations without supersymmetry
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Yangian Algebra and Correlation Functions in Planar Gauge Theories
• Quantum noncommutative ABJM theory: first steps
• Untwisting the symmetries of $\beta$-deformed Super-Yang--Mills
• Galilean Electrodynamics: Covariant formulation and Lagrangian
• Marginal deformations and quasi-Hopf algebras
• Ambitwistor strings and reggeon amplitudes in N=4 SYM