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Yangian Symmetry for Bi-Scalar Loop Amplitudes

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arxiv 1704.01967 v1 pith:S2SL3QOD submitted 2017-04-06 hep-th math-phmath.MP

Dmitry Chicherin , Vladimir Kazakov , Florian Loebbert , Dennis Müller , De-liang Zhong This is my paper
classification hep-thmath-phmath.MP
keywords amplitudesyangianbi-scalarsymmetrytheoryconformaldiscaction
verification ladder T0 review T1 audit T2 compute T3 formal
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We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of gamma-twisted weakly coupled N=4 SYM theory. Each amplitude with a certain order of scalar particles is given by a single fishnet Feynman graph of disc topology cut out of a regular square lattice. The Yangian can be realized by the action of a product of Lax operators with a specific sequence of inhomogeneity parameters on the boundary of the disc. Based on this observation, the Yangian generators of level one for generic bi-scalar amplitudes are explicitly constructed. Finally, we comment on the relation to the dual conformal symmetry of these scattering amplitudes.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Yangian Symmetry Escapes from the Fishnet

    hep-th 2025-11 unverdicted novelty 7.0 of 10

    Yangian symmetry holds classically in fishnet models under restricted evaluation parameters but does not extend to generic quantum correlators in the bi-scalar model, with counterexamples indicating that non-zero dual...

  2. Integrable systems: From the ice rule to supersymmetric fishnet Feynman diagrams

    hep-th 2025-09 conditional novelty 7.0 of 10

    A dissertation extends the integrability correspondence between lattice models and fishnet Feynman graphs to fermionic, supersymmetric, and boundary cases, yielding new exact critical couplings and a conjectured box p...

  3. Yangian Symmetry Escapes from the Fishnet

    hep-th 2025-11 unverdicted novelty 5.0 of 10

    Yangian symmetry is realized classically in fishnet models under restricted parameter choices but does not extend to generic quantum correlators, indicating an obstacle from non-zero dual Coxeter number.

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