Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917570299297792 |
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| author | Geer, Nathan Lauda, Aaron D. Patureau-Mirand, Bertrand Sussan, Joshua |
| author_facet | Geer, Nathan Lauda, Aaron D. Patureau-Mirand, Bertrand Sussan, Joshua |
| contents | We develop the categorical context for defining Hermitian non-semisimple TQFTs. We prove that relative Hermitian modular categories give rise to modified Hermitian WRT-TQFTs and provide numerous examples of these structures coming from the representation theory of quantum groups and quantum superalgebras. The Hermitian theory developed here for the modified Turaev-Viro TQFT is applied to define new pseudo-Hermitian topological phases that can be considered as non-semisimple analogs of Levin-Wen models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14566 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups Geer, Nathan Lauda, Aaron D. Patureau-Mirand, Bertrand Sussan, Joshua Quantum Algebra Strongly Correlated Electrons Geometric Topology Quantum Physics 57K16, 17B37, 81R50, 18M15 We develop the categorical context for defining Hermitian non-semisimple TQFTs. We prove that relative Hermitian modular categories give rise to modified Hermitian WRT-TQFTs and provide numerous examples of these structures coming from the representation theory of quantum groups and quantum superalgebras. The Hermitian theory developed here for the modified Turaev-Viro TQFT is applied to define new pseudo-Hermitian topological phases that can be considered as non-semisimple analogs of Levin-Wen models. |
| title | Non-semisimple Levin-Wen Models and Hermitian TQFTs from quantum (super)groups |
| topic | Quantum Algebra Strongly Correlated Electrons Geometric Topology Quantum Physics 57K16, 17B37, 81R50, 18M15 |
| url | https://arxiv.org/abs/2208.14566 |