The Feyn-structure of Yangian symmetry
Abstract Yangian-type differential operators are shown to constrain Feynman integrals beyond the restriction to integrable graphs. In particular, we prove that all position-space Feynman diagrams at tree level feature a Yangian level-one momentum symmetry as long as their external coordinates are di...
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2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)112 |
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| author | Florian Loebbert Harshad Mathur |
| author_facet | Florian Loebbert Harshad Mathur |
| author_sort | Florian Loebbert |
| collection | DOAJ |
| description | Abstract Yangian-type differential operators are shown to constrain Feynman integrals beyond the restriction to integrable graphs. In particular, we prove that all position-space Feynman diagrams at tree level feature a Yangian level-one momentum symmetry as long as their external coordinates are distinct. This symmetry is traced back to a set of more elementary bilocal operators, which annihilate the integrals. In dual momentum space, the considered Feynman graphs represent multi-loop integrals without ‘loops of loops’, generalizing for instance the family of so-called train track or train track network diagrams. The extension of these results to integrals with massive propagators on the boundary of the Feynman graph is established. When specializing to the dual conformal case, where propagator powers sum up to the spacetime dimension at each position-space vertex, the symmetry extends to the full dual conformal Yangian. Hence, our findings represent a generalization of the statements on the Yangian symmetry of Feynman integrals beyond integrability and reveal its origin lying in a set of more elementary bilocal annihilators. Previous applications of the Yangian suggest to employ the resulting differential equations for bootstrapping multi-loop integrals beyond the dual conformal case. The considered bilocal constraints on Feynman integrals resemble the definition of conformal partial waves via Casimir operators, but are based on a different algebraic structure. |
| format | Article |
| id | doaj-art-c9c79bbeb09d4340b8028aa8ae6fb84b |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-c9c79bbeb09d4340b8028aa8ae6fb84b2025-02-09T12:07:04ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025113510.1007/JHEP01(2025)112The Feyn-structure of Yangian symmetryFlorian Loebbert0Harshad Mathur1Bethe Center for Theoretical Physics, Universität BonnBethe Center for Theoretical Physics, Universität BonnAbstract Yangian-type differential operators are shown to constrain Feynman integrals beyond the restriction to integrable graphs. In particular, we prove that all position-space Feynman diagrams at tree level feature a Yangian level-one momentum symmetry as long as their external coordinates are distinct. This symmetry is traced back to a set of more elementary bilocal operators, which annihilate the integrals. In dual momentum space, the considered Feynman graphs represent multi-loop integrals without ‘loops of loops’, generalizing for instance the family of so-called train track or train track network diagrams. The extension of these results to integrals with massive propagators on the boundary of the Feynman graph is established. When specializing to the dual conformal case, where propagator powers sum up to the spacetime dimension at each position-space vertex, the symmetry extends to the full dual conformal Yangian. Hence, our findings represent a generalization of the statements on the Yangian symmetry of Feynman integrals beyond integrability and reveal its origin lying in a set of more elementary bilocal annihilators. Previous applications of the Yangian suggest to employ the resulting differential equations for bootstrapping multi-loop integrals beyond the dual conformal case. The considered bilocal constraints on Feynman integrals resemble the definition of conformal partial waves via Casimir operators, but are based on a different algebraic structure.https://doi.org/10.1007/JHEP01(2025)112AdS-CFT CorrespondenceConformal and W SymmetryQuantum GroupsScattering Amplitudes |
| spellingShingle | Florian Loebbert Harshad Mathur The Feyn-structure of Yangian symmetry Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Quantum Groups Scattering Amplitudes |
| title | The Feyn-structure of Yangian symmetry |
| title_full | The Feyn-structure of Yangian symmetry |
| title_fullStr | The Feyn-structure of Yangian symmetry |
| title_full_unstemmed | The Feyn-structure of Yangian symmetry |
| title_short | The Feyn-structure of Yangian symmetry |
| title_sort | feyn structure of yangian symmetry |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Quantum Groups Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP01(2025)112 |
| work_keys_str_mv | AT florianloebbert thefeynstructureofyangiansymmetry AT harshadmathur thefeynstructureofyangiansymmetry AT florianloebbert feynstructureofyangiansymmetry AT harshadmathur feynstructureofyangiansymmetry |