2017/04/06 by Dmitry Chicherin, Vladimir Kazakov, Florian Loebbert +2
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Quantum #Quantum electrodynamics #Quantum mechanics #Scalar (mathematics) #Scattering amplitude #Twistor theory #Yangian #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep05(2018)003
published as JHEP05(2018)003 · 40 pages, 20 figures
arxiv created 2017/04/06 · openalex publication_date 2018/05/01 · arxiv updated 2018/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract 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 γ -twisted weakly coupled N=4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> 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.