Anomalies in mirror symmetry enriched topological orders
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912108789104640 |
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| author | Ding, Zhaoyang Qi, Yang |
| author_facet | Ding, Zhaoyang Qi, Yang |
| contents | Two-dimensional mirror symmetry enriched topological (SET) orders can be studied using the folding approach: it can be folded along the mirror axis and turned into a bilayer system on which the mirror symmetry acts as a $\mathbb Z_2$ layer-exchange symmetry. How mirror symmetry enriches the topological order is then encoded at the mirror axis, which is a gapped boundary of the folded bilayer system. Based on anyon-condensation theory, we classify possible $\mathbb Z_2$-symmetric gapped boundaries of the folded system. In particular, we derive an $H^2$ obstruction function, which corresponds to an $H^3$ obstruction for topological orders enriched by the time-reversal symmetry instead of mirror symmetry. We demonstrate that states with a nontrivial $H^2$ obstruction function can be constructed on the surface of a three-dimensional mirror SET order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anomalies in mirror symmetry enriched topological orders Ding, Zhaoyang Qi, Yang Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Two-dimensional mirror symmetry enriched topological (SET) orders can be studied using the folding approach: it can be folded along the mirror axis and turned into a bilayer system on which the mirror symmetry acts as a $\mathbb Z_2$ layer-exchange symmetry. How mirror symmetry enriches the topological order is then encoded at the mirror axis, which is a gapped boundary of the folded bilayer system. Based on anyon-condensation theory, we classify possible $\mathbb Z_2$-symmetric gapped boundaries of the folded system. In particular, we derive an $H^2$ obstruction function, which corresponds to an $H^3$ obstruction for topological orders enriched by the time-reversal symmetry instead of mirror symmetry. We demonstrate that states with a nontrivial $H^2$ obstruction function can be constructed on the surface of a three-dimensional mirror SET order. |
| title | Anomalies in mirror symmetry enriched topological orders |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2406.16700 |