Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories

Abstract

In this article we establish the notion of classical Yangian symmetry for planar N=4 supersymmetric Yang-Mills theory and for related planar gauge theories. After revisiting Yangian invariance for the equations of motion, we describe how the bi-local generators act on the action of the model such that the latter becomes exactly invariant. In particular, we elaborate on the relevance of the planar limit and how to act non-linearly with bi-local generators on the cyclic action.

arXiv comment42 pages, in honor of Joe Polchinski; v2: minor corrections

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• Field Theories on Null Manifolds
• Interacting Conformal Carrollian Theories: Cues from Electrodynamics
• Galilean Gauge Theories from Null Reductions
• Massive Fishnets
• Bose-Fermi cancellations without supersymmetry
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Yangian Algebra and Correlation Functions in Planar Gauge Theories
• Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure
• Galilean Electrodynamics: Covariant formulation and Lagrangian
• Marginal deformations and quasi-Hopf algebras
• Yangian Symmetry in Five Dimensions
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• On Exact Solvability of $\mathcal{N}$=4 super Yang-Mills