Drinfel’d double symmetry of the 4d Kitaev model
Abstract Following the general theory of categorified quantum groups developed by the author previously, we construct the Drinfel’d double 2-bialgebra associated to a finite group N = G 0. For N = ℤ 2, we explicitly compute the braided 2-categories of 2-representations of certain version of this Dri...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP09(2023)141 |
| _version_ | 1797371240600567808 |
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| author | Hank Chen |
| author_facet | Hank Chen |
| author_sort | Hank Chen |
| collection | DOAJ |
| description | Abstract Following the general theory of categorified quantum groups developed by the author previously, we construct the Drinfel’d double 2-bialgebra associated to a finite group N = G 0. For N = ℤ 2, we explicitly compute the braided 2-categories of 2-representations of certain version of this Drinfel’d double 2-bialgebra, and prove that they characterize precisely the 4d toric code and its spin-ℤ 2 variant. This result relates the two descriptions (categorical vs. field theoretical) of 4d gapped topological phases in existing literature and displays an instance of higher Tannakian duality for braided 2-categories. In particular, we show that particular twists of the underlying Drinfel’d double 2-bialgebra is responsible for much of the higher-structural properties that arise in 4d topological orders. |
| first_indexed | 2024-03-08T18:17:03Z |
| format | Article |
| id | doaj.art-d466f40159e340218c32e1363ca37e7f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T18:17:03Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-d466f40159e340218c32e1363ca37e7f2023-12-31T12:07:11ZengSpringerOpenJournal of High Energy Physics1029-84792023-09-012023915410.1007/JHEP09(2023)141Drinfel’d double symmetry of the 4d Kitaev modelHank Chen0Department of Applied Mathematics, University of WaterlooAbstract Following the general theory of categorified quantum groups developed by the author previously, we construct the Drinfel’d double 2-bialgebra associated to a finite group N = G 0. For N = ℤ 2, we explicitly compute the braided 2-categories of 2-representations of certain version of this Drinfel’d double 2-bialgebra, and prove that they characterize precisely the 4d toric code and its spin-ℤ 2 variant. This result relates the two descriptions (categorical vs. field theoretical) of 4d gapped topological phases in existing literature and displays an instance of higher Tannakian duality for braided 2-categories. In particular, we show that particular twists of the underlying Drinfel’d double 2-bialgebra is responsible for much of the higher-structural properties that arise in 4d topological orders.https://doi.org/10.1007/JHEP09(2023)141Discrete SymmetriesQuantum GroupsSigma ModelsTopological States of Matter |
| spellingShingle | Hank Chen Drinfel’d double symmetry of the 4d Kitaev model Journal of High Energy Physics Discrete Symmetries Quantum Groups Sigma Models Topological States of Matter |
| title | Drinfel’d double symmetry of the 4d Kitaev model |
| title_full | Drinfel’d double symmetry of the 4d Kitaev model |
| title_fullStr | Drinfel’d double symmetry of the 4d Kitaev model |
| title_full_unstemmed | Drinfel’d double symmetry of the 4d Kitaev model |
| title_short | Drinfel’d double symmetry of the 4d Kitaev model |
| title_sort | drinfel d double symmetry of the 4d kitaev model |
| topic | Discrete Symmetries Quantum Groups Sigma Models Topological States of Matter |
| url | https://doi.org/10.1007/JHEP09(2023)141 |
| work_keys_str_mv | AT hankchen drinfelddoublesymmetryofthe4dkitaevmodel |