Unit inclusion in a non-semisimple braided tensor category and non-compact relative TQFTs
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912458978885632 |
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| author | Haïoun, Benjamin |
| author_facet | Haïoun, Benjamin |
| contents | The inclusion of the unit in a braided tensor category $\mathcal{V}$ induces a 1-morphism in the Morita 4-category of braided tensor categories $BrTens$. We give criteria for the dualizability of this morphism. When $\mathcal{V}$ is a semisimple (resp. non-semisimple) modular category, we show that the unit inclusion induces under the Cobordism Hypothesis a (resp. non-compact) relative 3-dimensional topological quantum field theory. Following Jordan-Safronov, we conjecture that these relative field theories together with their bulk theories recover Witten-Reshetikhin-Turaev (resp. De Renzi-Gainutdinov-Geer-Patureau-Mirand-Runkel) theories, in a fully extended setting. In particular, we argue that these theories can be obtained by the Cobordism Hypothesis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_12167 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Unit inclusion in a non-semisimple braided tensor category and non-compact relative TQFTs Haïoun, Benjamin Quantum Algebra Category Theory Geometric Topology 18M20, 57R56 The inclusion of the unit in a braided tensor category $\mathcal{V}$ induces a 1-morphism in the Morita 4-category of braided tensor categories $BrTens$. We give criteria for the dualizability of this morphism. When $\mathcal{V}$ is a semisimple (resp. non-semisimple) modular category, we show that the unit inclusion induces under the Cobordism Hypothesis a (resp. non-compact) relative 3-dimensional topological quantum field theory. Following Jordan-Safronov, we conjecture that these relative field theories together with their bulk theories recover Witten-Reshetikhin-Turaev (resp. De Renzi-Gainutdinov-Geer-Patureau-Mirand-Runkel) theories, in a fully extended setting. In particular, we argue that these theories can be obtained by the Cobordism Hypothesis. |
| title | Unit inclusion in a non-semisimple braided tensor category and non-compact relative TQFTs |
| topic | Quantum Algebra Category Theory Geometric Topology 18M20, 57R56 |
| url | https://arxiv.org/abs/2304.12167 |