Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory

Abstract

We show that appropriately supersymmetrized smooth Maldacena-Wilson loop operators in N=4 super Yang-Mills theory are invariant under a Yangian symmetry Y[psu(2,2|4)] built upon the manifest superconformal symmetry algebra of the theory. The existence of this hidden symmetry is demonstrated at the one-loop order in the weak coupling limit as well as at leading order in the strong coupling limit employing the classical integrability of the dual AdS_5 x S^5 string description. The hidden symmetry generators consist of a canonical non-local second order variational derivative piece acting on the superpath, along with a novel local path dependent contribution. We match the functional form of these Yangian symmetry generators at weak and strong coupling and find evidence for an interpolating function. Our findings represent the smooth counterpart to the Yangian invariance of scattering superamplitudes dual to light-like polygonal super Wilson loops in the N=4 super Yang-Mills theory.

36 pages, 1 figure. v2: Typos corrected, version to be published in JHEP

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• Yangian Symmetry of String Theory on $Ad{S}_3\times S^3\times S^3\times S^1$ with Mixed 3-form Flux
• One-loop Wilson loops and the particle-interface potential in AdS/dCFT
• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• Integrability of Smooth Wilson Loops in N=4 Superspace
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Smooth Wilson Loops in N=4 Non-Chiral Superspace
• Bonus Symmetry for Super Wilson Loops
• Master Symmetry for Holographic Wilson Loops
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
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• Yangian Algebra and Correlation Functions in Planar Gauge Theories
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• Minimal area surfaces in AdS_{n+1} and Wilson loops
• Dual conformal transformations of smooth holographic Wilson loops
• Supersymmetric Wilson Loops via Integral Forms
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• Master symmetry in the $Ad{S}_5\times S^5$ pure spinor string
• Euclidean Wilson loops and Minimal Area Surfaces in Minkowski AdS3
• $\mathcal{N}=3$ Harmonic Super-Wilson Loop
• Wilson Loops and Integrability
• S-duality transformation of $\mathcal{N}$ $=4$ SYM theory at the operator level
• Dilogarithm ladders from Wilson loops
• Twistor Parametrization of Locally BPS Super-Wilson Loops