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
4D N = 4 Super Yang-Mills ❖ Superconformal symmetry ❖ Planar integrability • Origin: mysterious ❖ AdS/CFT correspondence
<latexit sha1_base64="Fde3I1S7l2LSHflQ/wLNC1ajzIk=">AB93icbVBNS8NAEN34WetHox69LBbBU0lEUG9FLx48VDC20Iay2W7apZvdsDtRaugv8eJBxat/xZv/xm2bg7Y+GHi8N8PMvCgV3IDnfTtLyura+uljfLm1vZOxd3duzcq05QFVAmlWxExTHDJAuAgWCvVjCSRYM1oeDXxmw9MG67kHYxSFiakL3nMKQErd1K54bFoHl/AERr9dh1q17NmwIvEr8gVSg0XW/Oj1Fs4RJoIY0/a9FMKcaOBUsHG5kxmWEjokfda2VJKEmTCfHj7GR1bp4VhpWxLwVP09kZPEmFES2c6EwMDMexPxP6+dQXwe5lymGTBJZ4viTGBQeJIC7nHNKIiRJYRqbm/FdEA0oWCzKtsQ/PmXF0lwUruo+ben1fplkUYJHaBDdIx8dIbq6Bo1UIAoytAzekVvzpPz4rw7H7PWJaeY2Ud/4Hz+AKCok0U=</latexit> <latexit sha1_base64="Fde3I1S7l2LSHflQ/wLNC1ajzIk=">AB93icbVBNS8NAEN34WetHox69LBbBU0lEUG9FLx48VDC20Iay2W7apZvdsDtRaugv8eJBxat/xZv/xm2bg7Y+GHi8N8PMvCgV3IDnfTtLyura+uljfLm1vZOxd3duzcq05QFVAmlWxExTHDJAuAgWCvVjCSRYM1oeDXxmw9MG67kHYxSFiakL3nMKQErd1K54bFoHl/AERr9dh1q17NmwIvEr8gVSg0XW/Oj1Fs4RJoIY0/a9FMKcaOBUsHG5kxmWEjokfda2VJKEmTCfHj7GR1bp4VhpWxLwVP09kZPEmFES2c6EwMDMexPxP6+dQXwe5lymGTBJZ4viTGBQeJIC7nHNKIiRJYRqbm/FdEA0oWCzKtsQ/PmXF0lwUruo+ben1fplkUYJHaBDdIx8dIbq6Bo1UIAoytAzekVvzpPz4rw7H7PWJaeY2Ud/4Hz+AKCok0U=</latexit> <latexit sha1_base64="Fde3I1S7l2LSHflQ/wLNC1ajzIk=">AB93icbVBNS8NAEN34WetHox69LBbBU0lEUG9FLx48VDC20Iay2W7apZvdsDtRaugv8eJBxat/xZv/xm2bg7Y+GHi8N8PMvCgV3IDnfTtLyura+uljfLm1vZOxd3duzcq05QFVAmlWxExTHDJAuAgWCvVjCSRYM1oeDXxmw9MG67kHYxSFiakL3nMKQErd1K54bFoHl/AERr9dh1q17NmwIvEr8gVSg0XW/Oj1Fs4RJoIY0/a9FMKcaOBUsHG5kxmWEjokfda2VJKEmTCfHj7GR1bp4VhpWxLwVP09kZPEmFES2c6EwMDMexPxP6+dQXwe5lymGTBJZ4viTGBQeJIC7nHNKIiRJYRqbm/FdEA0oWCzKtsQ/PmXF0lwUruo+ben1fplkUYJHaBDdIx8dIbq6Bo1UIAoytAzekVvzpPz4rw7H7PWJaeY2Ud/4Hz+AKCok0U=</latexit> <latexit sha1_base64="Fde3I1S7l2LSHflQ/wLNC1ajzIk=">AB93icbVBNS8NAEN34WetHox69LBbBU0lEUG9FLx48VDC20Iay2W7apZvdsDtRaugv8eJBxat/xZv/xm2bg7Y+GHi8N8PMvCgV3IDnfTtLyura+uljfLm1vZOxd3duzcq05QFVAmlWxExTHDJAuAgWCvVjCSRYM1oeDXxmw9MG67kHYxSFiakL3nMKQErd1K54bFoHl/AERr9dh1q17NmwIvEr8gVSg0XW/Oj1Fs4RJoIY0/a9FMKcaOBUsHG5kxmWEjokfda2VJKEmTCfHj7GR1bp4VhpWxLwVP09kZPEmFES2c6EwMDMexPxP6+dQXwe5lymGTBJZ4viTGBQeJIC7nHNKIiRJYRqbm/FdEA0oWCzKtsQ/PmXF0lwUruo+ben1fplkUYJHaBDdIx8dIbq6Bo1UIAoytAzekVvzpPz4rw7H7PWJaeY2Ud/4Hz+AKCok0U=</latexit> <latexit sha1_base64="ie6VLT5r35QrW3+QMtcDwLOzDTk=">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</latexit> <latexit sha1_base64="ie6VLT5r35QrW3+QMtcDwLOzDTk=">ACNHicbVBPS8MwHE3nvzn/T16CQ5hgzFaEdSDMPQi6GHC5gZrKWmWbWFpWpJUNsq+lBe/hyc9eFDx6mcw7XrQzQeBx/u9X5L3vJBRqUz1cgtLa+sruXCxubW9s7xd29exlEApMWDlgOh6ShFOWoqRjqhIMj3Gl7o6tk3n4gQtKAN9UkJI6PBpz2KUZKS27x9qY8dq2q3QuUrI7dmE8rFzZDfMCI7SM1FH7cFNOujYfUtRJrJbXCVOBa4BXHFqm/VnCLJbNmpoCLxMpICWRouMVnfRuOfMIVZkjKrmWGyomRUBQzMi3YkSQhwiM0IF1NOfKJdOI09RQeaUH+4HQhyuYqr83YuRLOfE97UySyPlZIv4360aqf+bElIeRIhzPHupHDKoAJhXCHhUEKzbRBGFB9V8hHiKBsNJFJyVY85EXSeu4dl6z7k5K9cusjTw4AIegDCxwCurgGjRAC2DwCF7AO/gwnow349P4mlzRrazD/7A+P4BfjSq3A=</latexit> <latexit sha1_base64="ie6VLT5r35QrW3+QMtcDwLOzDTk=">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</latexit> <latexit sha1_base64="ie6VLT5r35QrW3+QMtcDwLOzDTk=">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</latexit> <latexit sha1_base64="xqpYuP6uGvmHXgJwDJONYva+I=">ACIXicbVBNS8MwGE7n15xfVY9egkPwIKMdgu429OJxgnWDtZY0TbewNC1JKoy3+LFv+LFg8pu4p8x6yro5gPhfI870vyPkHKqFSW9WlUVlbX1jeqm7Wt7Z3dPXP/4F4mcDEwQlLRC9AkjDKiaOoYqSXCoLigJFuMLqe+d1HIiRN+J0ap8SL0YDTiGKktOSbLRcPqT9yKYdu7qa2dFac6L/eCGaDAgolR/ru7EN+tWwyoAl4ldkjo0fHNqRsmOIsJV5ghKfu2lSovR0JRzMik5maSpAiP0ID0NeUoJtLixUn8EQrIYwSoQ9XsFB/T+QolnIcB7ozRmoF72Z+J/Xz1R06eWUp5kiHM8fijIGVQJnecGQCoIVG2uCsKD6rxAPkUBY6VRrOgR7ceVl4jQbrYZ9e15vX5VpVMEROAanwAYXoA1uQAc4AIMn8ALewLvxbLwaH8Z03loxyplD8AfG1zcMBaOY</latexit> <latexit sha1_base64="xqpYuP6uGvmHXgJwDJONYva+I=">ACIXicbVBNS8MwGE7n15xfVY9egkPwIKMdgu429OJxgnWDtZY0TbewNC1JKoy3+LFv+LFg8pu4p8x6yro5gPhfI870vyPkHKqFSW9WlUVlbX1jeqm7Wt7Z3dPXP/4F4mcDEwQlLRC9AkjDKiaOoYqSXCoLigJFuMLqe+d1HIiRN+J0ap8SL0YDTiGKktOSbLRcPqT9yKYdu7qa2dFac6L/eCGaDAgolR/ru7EN+tWwyoAl4ldkjo0fHNqRsmOIsJV5ghKfu2lSovR0JRzMik5maSpAiP0ID0NeUoJtLixUn8EQrIYwSoQ9XsFB/T+QolnIcB7ozRmoF72Z+J/Xz1R06eWUp5kiHM8fijIGVQJnecGQCoIVG2uCsKD6rxAPkUBY6VRrOgR7ceVl4jQbrYZ9e15vX5VpVMEROAanwAYXoA1uQAc4AIMn8ALewLvxbLwaH8Z03loxyplD8AfG1zcMBaOY</latexit> <latexit sha1_base64="xqpYuP6uGvmHXgJwDJONYva+I=">ACIXicbVBNS8MwGE7n15xfVY9egkPwIKMdgu429OJxgnWDtZY0TbewNC1JKoy3+LFv+LFg8pu4p8x6yro5gPhfI870vyPkHKqFSW9WlUVlbX1jeqm7Wt7Z3dPXP/4F4mcDEwQlLRC9AkjDKiaOoYqSXCoLigJFuMLqe+d1HIiRN+J0ap8SL0YDTiGKktOSbLRcPqT9yKYdu7qa2dFac6L/eCGaDAgolR/ru7EN+tWwyoAl4ldkjo0fHNqRsmOIsJV5ghKfu2lSovR0JRzMik5maSpAiP0ID0NeUoJtLixUn8EQrIYwSoQ9XsFB/T+QolnIcB7ozRmoF72Z+J/Xz1R06eWUp5kiHM8fijIGVQJnecGQCoIVG2uCsKD6rxAPkUBY6VRrOgR7ceVl4jQbrYZ9e15vX5VpVMEROAanwAYXoA1uQAc4AIMn8ALewLvxbLwaH8Z03loxyplD8AfG1zcMBaOY</latexit> <latexit 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 }
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?
Recommend
More recommend