Quantum groups as global symmetries
Abstract We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the general constraints of the quantum group symmetry, gi...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2025)087 |
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| _version_ | 1849333840768663552 |
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| author | Barak Gabai Victor Gorbenko Jiaxin Qiao Bernardo Zan Aleksandr Zhabin |
| author_facet | Barak Gabai Victor Gorbenko Jiaxin Qiao Bernardo Zan Aleksandr Zhabin |
| author_sort | Barak Gabai |
| collection | DOAJ |
| description | Abstract We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the general constraints of the quantum group symmetry, given by Ward identities, that correlation functions of the theory should satisfy. We also show that generators of the symmetry can be represented by topological lines with some novel properties. We then discuss a particular example of U q (sl 2) symmetric CFT, which we solve using bootstrap techniques and relying on the symmetry. We finally show strong evidence that for a special value of q a subsector of this theory reproduces the fermionic formulation of the Ising model. This suggests that a quantum group can act on local operators as well, however, it generically transforms them into non-local ones. |
| format | Article |
| id | doaj-art-538f80be641c4c8a9e376f2eacebcc9f |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-538f80be641c4c8a9e376f2eacebcc9f2025-08-20T03:45:44ZengSpringerOpenJournal of High Energy Physics1029-84792025-08-012025817510.1007/JHEP08(2025)087Quantum groups as global symmetriesBarak Gabai0Victor Gorbenko1Jiaxin Qiao2Bernardo Zan3Aleksandr Zhabin4Laboratory for Theoretical Fundamental Physics, Institute of Physics, École Polytechnique Fédérale de LausanneLaboratory for Theoretical Fundamental Physics, Institute of Physics, École Polytechnique Fédérale de LausanneLaboratory for Theoretical Fundamental Physics, Institute of Physics, École Polytechnique Fédérale de LausanneDepartment of Applied Mathematics and Theoretical Physics, University of CambridgeLaboratory for Theoretical Fundamental Physics, Institute of Physics, École Polytechnique Fédérale de LausanneAbstract We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the general constraints of the quantum group symmetry, given by Ward identities, that correlation functions of the theory should satisfy. We also show that generators of the symmetry can be represented by topological lines with some novel properties. We then discuss a particular example of U q (sl 2) symmetric CFT, which we solve using bootstrap techniques and relying on the symmetry. We finally show strong evidence that for a special value of q a subsector of this theory reproduces the fermionic formulation of the Ising model. This suggests that a quantum group can act on local operators as well, however, it generically transforms them into non-local ones.https://doi.org/10.1007/JHEP08(2025)087Global SymmetriesQuantum GroupsConformal and W SymmetryField Theories in Lower Dimensions |
| spellingShingle | Barak Gabai Victor Gorbenko Jiaxin Qiao Bernardo Zan Aleksandr Zhabin Quantum groups as global symmetries Journal of High Energy Physics Global Symmetries Quantum Groups Conformal and W Symmetry Field Theories in Lower Dimensions |
| title | Quantum groups as global symmetries |
| title_full | Quantum groups as global symmetries |
| title_fullStr | Quantum groups as global symmetries |
| title_full_unstemmed | Quantum groups as global symmetries |
| title_short | Quantum groups as global symmetries |
| title_sort | quantum groups as global symmetries |
| topic | Global Symmetries Quantum Groups Conformal and W Symmetry Field Theories in Lower Dimensions |
| url | https://doi.org/10.1007/JHEP08(2025)087 |
| work_keys_str_mv | AT barakgabai quantumgroupsasglobalsymmetries AT victorgorbenko quantumgroupsasglobalsymmetries AT jiaxinqiao quantumgroupsasglobalsymmetries AT bernardozan quantumgroupsasglobalsymmetries AT aleksandrzhabin quantumgroupsasglobalsymmetries |