Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs
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| Format: | Preprint |
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2024
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| _version_ | 1866911870520131584 |
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| author | Putrov, Pavel Radhakrishnan, Rajath |
| author_facet | Putrov, Pavel Radhakrishnan, Rajath |
| contents | We study the anomalies of non-invertible symmetries in 1+1D QFTs using gapped boundaries of its SymTFT. We establish the explicit relation between Lagrangian algebras which determine gapped boundaries of the SymTFT, and algebras which determine non-anomalous/gaugeable topological line operators in the 1+1D QFT. If the Lagrangian algebras in the SymTFT are known, this provides a method to compute algebras in all fusion categories that share the same SymTFT. We find necessary conditions that a line operator in the SymTFT must satisfy for the corresponding line operator in the 1+1D QFT to be non-anomalous. We use this constraint to show that a non-invertible symmetry admits a 1+1D trivially gapped phase if and only if the SymTFT admits a magnetic Lagrangian algebra. We define a process of transporting non-anomalous line operators between fusion categories which share the same SymTFT and apply this method to the three Haagerup fusion categories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_04619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs Putrov, Pavel Radhakrishnan, Rajath High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra We study the anomalies of non-invertible symmetries in 1+1D QFTs using gapped boundaries of its SymTFT. We establish the explicit relation between Lagrangian algebras which determine gapped boundaries of the SymTFT, and algebras which determine non-anomalous/gaugeable topological line operators in the 1+1D QFT. If the Lagrangian algebras in the SymTFT are known, this provides a method to compute algebras in all fusion categories that share the same SymTFT. We find necessary conditions that a line operator in the SymTFT must satisfy for the corresponding line operator in the 1+1D QFT to be non-anomalous. We use this constraint to show that a non-invertible symmetry admits a 1+1D trivially gapped phase if and only if the SymTFT admits a magnetic Lagrangian algebra. We define a process of transporting non-anomalous line operators between fusion categories which share the same SymTFT and apply this method to the three Haagerup fusion categories. |
| title | Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2405.04619 |