Modular functors from non-semisimple 3d TFTs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910460974989312 |
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| author | Hofer, Aaron Runkel, Ingo |
| author_facet | Hofer, Aaron Runkel, Ingo |
| contents | Given a not necessarily semisimple modular tensor category C, we use the corresponding 3d TFT defined in [arXiv:1912.02063] to explicitly describe a modular functor as a symmetric monoidal 2-functor from a 2-category of oriented bordisms to a 2-category of finite linear categories. This recovers a result by Lyubashenko [arXiv:hep-th/9405168] obtained via generators and relations. Pulling back the modular functor for C to a 2-category of bordisms with orientation reversing involution cancels the gluing anomaly, and further pulling back to the original bordism category along a doubling functor leads to the modular functor for the Drinfeld centre Z(C). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18038 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modular functors from non-semisimple 3d TFTs Hofer, Aaron Runkel, Ingo Quantum Algebra High Energy Physics - Theory Geometric Topology Given a not necessarily semisimple modular tensor category C, we use the corresponding 3d TFT defined in [arXiv:1912.02063] to explicitly describe a modular functor as a symmetric monoidal 2-functor from a 2-category of oriented bordisms to a 2-category of finite linear categories. This recovers a result by Lyubashenko [arXiv:hep-th/9405168] obtained via generators and relations. Pulling back the modular functor for C to a 2-category of bordisms with orientation reversing involution cancels the gluing anomaly, and further pulling back to the original bordism category along a doubling functor leads to the modular functor for the Drinfeld centre Z(C). |
| title | Modular functors from non-semisimple 3d TFTs |
| topic | Quantum Algebra High Energy Physics - Theory Geometric Topology |
| url | https://arxiv.org/abs/2405.18038 |