Braidings on topological operators, anomaly of higher-form symmetries and the SymTFT
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916655227994112 |
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| author | Putrov, Pavel Radhakrishnan, Rajath |
| author_facet | Putrov, Pavel Radhakrishnan, Rajath |
| contents | The anomaly of non-invertible higher-form symmetries is determined by the braiding of topological operators implementing them. In this paper, we study a method to classify braidings on topological line and surface operators by leveraging the fact that topological operators which admit a braiding are symmetries of their associated SymTFT. This perspective allows us to formulate an algorithm to explicitly compute all possible braidings on a given fusion category, bypassing the need to solve the hexagon equations. Additionally, using 3+1d SymTFTs, we determine braidings on various fusion 2-categories. We prove a necessary and sufficient condition for the fusion 2-categories $Σ\mathcal{C}$, 2Vec$_G^π$ and Tambara-Yamagami (TY) 2-categories TY$(A,π)$ to admit a braiding. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_13633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Braidings on topological operators, anomaly of higher-form symmetries and the SymTFT Putrov, Pavel Radhakrishnan, Rajath High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra The anomaly of non-invertible higher-form symmetries is determined by the braiding of topological operators implementing them. In this paper, we study a method to classify braidings on topological line and surface operators by leveraging the fact that topological operators which admit a braiding are symmetries of their associated SymTFT. This perspective allows us to formulate an algorithm to explicitly compute all possible braidings on a given fusion category, bypassing the need to solve the hexagon equations. Additionally, using 3+1d SymTFTs, we determine braidings on various fusion 2-categories. We prove a necessary and sufficient condition for the fusion 2-categories $Σ\mathcal{C}$, 2Vec$_G^π$ and Tambara-Yamagami (TY) 2-categories TY$(A,π)$ to admit a braiding. |
| title | Braidings on topological operators, anomaly of higher-form symmetries and the SymTFT |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2503.13633 |