Fully local Reshetikhin-Turaev theories
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arXiv
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| Format: | Preprint |
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2026
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| author | Freed, Daniel S. Scheimbauer, Claudia I. Teleman, Constantin |
| author_facet | Freed, Daniel S. Scheimbauer, Claudia I. Teleman, Constantin |
| contents | We define a symmetric tensor enhancement $\mathrm{E}\mathbb{F}$ with full duals of the 3-category $\mathbb{F}$ of fusion categories in which every Reshetikhin--Turaev theory has a fully local realization. Our $\mathrm{E}\mathbb{F}$ is a direct sum of invertible $\mathbb{F}$-modules, indexed by a $μ_6$-extension of the Witt group $W$ of non-degenerate braided fusion categories. Similarly, we enhance the 3-category $S\mathbb{F}$ of fusion super-categories to a symmetric tensor 3-category $\mathrm{E} S\mathbb{F}$ with full duals, which is a sum of invertible $S\mathbb{F}$-modules, indexed by an extension of the super-Witt group $SW$ with kernel the Pontrjagin dual of the stable stem $π_3^s$. The unit spectrum of $\mathrm{E}S\mathbb{F}$ is the connective cover of the Pontrjagin dual of $\mathbb{S}^{-3}$. We discuss tangential structures and central charges of the resulting TQFTs. We establish Spin-invariance of fusion supercategories and relate SO-invariance structures to modular and spherical structures. This confirms some conjectures from arxiv:1312.7188. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_05518 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fully local Reshetikhin-Turaev theories Freed, Daniel S. Scheimbauer, Claudia I. Teleman, Constantin Quantum Algebra Mathematical Physics 57R56 (Primary), 18M20 (Secondary) We define a symmetric tensor enhancement $\mathrm{E}\mathbb{F}$ with full duals of the 3-category $\mathbb{F}$ of fusion categories in which every Reshetikhin--Turaev theory has a fully local realization. Our $\mathrm{E}\mathbb{F}$ is a direct sum of invertible $\mathbb{F}$-modules, indexed by a $μ_6$-extension of the Witt group $W$ of non-degenerate braided fusion categories. Similarly, we enhance the 3-category $S\mathbb{F}$ of fusion super-categories to a symmetric tensor 3-category $\mathrm{E} S\mathbb{F}$ with full duals, which is a sum of invertible $S\mathbb{F}$-modules, indexed by an extension of the super-Witt group $SW$ with kernel the Pontrjagin dual of the stable stem $π_3^s$. The unit spectrum of $\mathrm{E}S\mathbb{F}$ is the connective cover of the Pontrjagin dual of $\mathbb{S}^{-3}$. We discuss tangential structures and central charges of the resulting TQFTs. We establish Spin-invariance of fusion supercategories and relate SO-invariance structures to modular and spherical structures. This confirms some conjectures from arxiv:1312.7188. |
| title | Fully local Reshetikhin-Turaev theories |
| topic | Quantum Algebra Mathematical Physics 57R56 (Primary), 18M20 (Secondary) |
| url | https://arxiv.org/abs/2601.05518 |