Equivalence of Extended $U(1)$ Chern-Simons and Reshetikhin-Turaev TQFTs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918468889083904 |
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| author | Galviz, Daniel |
| author_facet | Galviz, Daniel |
| contents | We establish the equivalence between $U(1)$ Chern-Simons and Reshetikhin-Turaev TQFTs associated with finite quadratic modules. For gauge group $U(1)$ and even level $k$, we prove that the corresponding Chern-Simons TQFT is naturally isomorphic to the Reshetikhin-Turaev TQFT determined by the pointed modular category $C(\mathbb Z_k,q_k)$. The equivalence holds both for closed $3$-manifolds and for bordisms with boundary, so that the two constructions define naturally isomorphic extended $(2+1)$-dimensional TQFTs. In particular, the finite quadratic module $(\mathbb Z_k,q_k)$ completely determines the $U(1)$ Chern-Simons theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivalence of Extended $U(1)$ Chern-Simons and Reshetikhin-Turaev TQFTs Galviz, Daniel Quantum Algebra Mathematical Physics Geometric Topology We establish the equivalence between $U(1)$ Chern-Simons and Reshetikhin-Turaev TQFTs associated with finite quadratic modules. For gauge group $U(1)$ and even level $k$, we prove that the corresponding Chern-Simons TQFT is naturally isomorphic to the Reshetikhin-Turaev TQFT determined by the pointed modular category $C(\mathbb Z_k,q_k)$. The equivalence holds both for closed $3$-manifolds and for bordisms with boundary, so that the two constructions define naturally isomorphic extended $(2+1)$-dimensional TQFTs. In particular, the finite quadratic module $(\mathbb Z_k,q_k)$ completely determines the $U(1)$ Chern-Simons theory. |
| title | Equivalence of Extended $U(1)$ Chern-Simons and Reshetikhin-Turaev TQFTs |
| topic | Quantum Algebra Mathematical Physics Geometric Topology |
| url | https://arxiv.org/abs/2603.27688 |