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Yangian Symmetry for Fishnet Feynman Graphs Deliang Zhong LPTENS - PowerPoint PPT Presentation

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Yangian Symmetry for Fishnet Feynman Graphs Deliang Zhong LPTENS Paris With Dmitry Chicherin, Vladimir Kazakov, Florian Loebbert, Dennis Mller arXiv: 1704.01967, 1708.00007 & work in progress 4D N = 4 Super Yang-Mills Superconformal

  1. Yangian Symmetry for Fishnet Feynman Graphs Deliang Zhong LPTENS Paris With Dmitry Chicherin, Vladimir Kazakov, Florian Loebbert, Dennis Müller arXiv: 1704.01967, 1708.00007 & work in progress

  2. 4D N = 4 Super Yang-Mills ❖ Superconformal symmetry ❖ Planar integrability • Origin: mysterious ❖ AdS/CFT correspondence

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sha1_base64="xqpYuP6uGvmHXgJwDJONYva+I=">ACIXicbVBNS8MwGE7n15xfVY9egkPwIKMdgu429OJxgnWDtZY0TbewNC1JKoy3+LFv+LFg8pu4p8x6yro5gPhfI870vyPkHKqFSW9WlUVlbX1jeqm7Wt7Z3dPXP/4F4mcDEwQlLRC9AkjDKiaOoYqSXCoLigJFuMLqe+d1HIiRN+J0ap8SL0YDTiGKktOSbLRcPqT9yKYdu7qa2dFac6L/eCGaDAgolR/ru7EN+tWwyoAl4ldkjo0fHNqRsmOIsJV5ghKfu2lSovR0JRzMik5maSpAiP0ID0NeUoJtLixUn8EQrIYwSoQ9XsFB/T+QolnIcB7ozRmoF72Z+J/Xz1R06eWUp5kiHM8fijIGVQJnecGQCoIVG2uCsKD6rxAPkUBY6VRrOgR7ceVl4jQbrYZ9e15vX5VpVMEROAanwAYXoA1uQAc4AIMn8ALewLvxbLwaH8Z03loxyplD8AfG1zcMBaOY</latexit> γ − twisted 4D N = 4 Super Yang-Mills Bi-scalar limit [Gürdo ğ an, Kazakov ’15] ❖ Chiral, non-unitary theory 2 ∂ µ φ 2 + ξ 2 φ † ∂ µ φ † 1 ∂ µ φ 1 + ∂ µ φ † 1 φ † � � L φ = N c Tr 2 φ 1 φ 2 . ❖ 1-1 correspondence: correlator and fishnet Feynman diagram K ( x 1 , . . . , x n ) = h Tr[ χ 1 ( x 1 ) . . . χ n ( x n )] i . ⇔ χ k ∈ { φ 1 , φ 2 , φ † 1 , φ † 2 }

  4. γ − twisted 4D N = 4 Super Yang-Mills Bi-scalar limit [Gürdo ğ an, Kazakov ’15] ❖ Conformal symmetry for specific choice of couplings [Sieg-Wilhelm ’16] ❖ Planar integrability [Grabner, Gromov, Kazakov, Korchemsky ’17] • From first principle • Yangian symmetry for individual Feynman diagrams ❖ Is there an AdS dual?

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