A boundary characterization of Turaev-Viro TQFTs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908494730362880 |
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| author | Steffen, Max-Niklas Schweigert, Christoph |
| author_facet | Steffen, Max-Niklas Schweigert, Christoph |
| contents | We consider three-dimensional topological field theories on manifolds with boundary defects and identify explicit boundary locality conditions. These conditions imply a state sum construction of the given TQFT. As a consistency check, we prove that Turaev-Viro state sum models obey the boundary locality conditions. Recent progress (arXiv:2410.18049v1) in the description of defects in Dijkgraaf-Witten theories enables us to show that these theories likewise satisfy boundary locality. This directly implies that Dijkgraaf-Witten theories with boundary defects admit a state sum description. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_13759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A boundary characterization of Turaev-Viro TQFTs Steffen, Max-Niklas Schweigert, Christoph Quantum Algebra Geometric Topology We consider three-dimensional topological field theories on manifolds with boundary defects and identify explicit boundary locality conditions. These conditions imply a state sum construction of the given TQFT. As a consistency check, we prove that Turaev-Viro state sum models obey the boundary locality conditions. Recent progress (arXiv:2410.18049v1) in the description of defects in Dijkgraaf-Witten theories enables us to show that these theories likewise satisfy boundary locality. This directly implies that Dijkgraaf-Witten theories with boundary defects admit a state sum description. |
| title | A boundary characterization of Turaev-Viro TQFTs |
| topic | Quantum Algebra Geometric Topology |
| url | https://arxiv.org/abs/2508.13759 |