Mutual Influence of Symmetries and Topological Field Theories
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918139284946944 |
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| author | Teixeira, Daniel Yu, Matthew |
| author_facet | Teixeira, Daniel Yu, Matthew |
| contents | We study how the fusion 2-category symmetry of a fermionic (2+1)d QFT can be affected when one allows for stacking with TQFTs to be an equivalence relation for QFTs. Focusing on a simple kind of fermionic fusion 2-category described purely by group theoretical data, our results reveal that by allowing for stacking with $\mathrm{Spin}(n)_1$ as an equivalence relation enables a finite set of inequivalent modifications to the original fusion 2-categorical-symmetry. To put our results in a broader context, we relate the order of the symmetry modifications to the image of a map between groups of minimal nondegenerate extensions, and to the tangential structure set by the initial categorical symmetry on the background manifold for the QFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mutual Influence of Symmetries and Topological Field Theories Teixeira, Daniel Yu, Matthew Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra 18M20, 18N10 We study how the fusion 2-category symmetry of a fermionic (2+1)d QFT can be affected when one allows for stacking with TQFTs to be an equivalence relation for QFTs. Focusing on a simple kind of fermionic fusion 2-category described purely by group theoretical data, our results reveal that by allowing for stacking with $\mathrm{Spin}(n)_1$ as an equivalence relation enables a finite set of inequivalent modifications to the original fusion 2-categorical-symmetry. To put our results in a broader context, we relate the order of the symmetry modifications to the image of a map between groups of minimal nondegenerate extensions, and to the tangential structure set by the initial categorical symmetry on the background manifold for the QFT. |
| title | Mutual Influence of Symmetries and Topological Field Theories |
| topic | Mathematical Physics Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra 18M20, 18N10 |
| url | https://arxiv.org/abs/2507.06304 |