On Unitary 2-Group Symmetries
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915141151358976 |
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| author | Bartsch, Thomas |
| author_facet | Bartsch, Thomas |
| contents | Global internal symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to extended observables by considering unitary actions of finite global 2-group symmetries $\mathcal{G}$ on line operators. We propose that the latter transform in unitary 2-representations of $\mathcal{G}$, which we classify up to unitary equivalence. Our results recover the known classification of ordinary 2-representations of finite 2-groups, but provide additional data interpreted as a type of reflection anomaly for $\mathcal{G}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Unitary 2-Group Symmetries Bartsch, Thomas Mathematical Physics High Energy Physics - Theory Category Theory Global internal symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to extended observables by considering unitary actions of finite global 2-group symmetries $\mathcal{G}$ on line operators. We propose that the latter transform in unitary 2-representations of $\mathcal{G}$, which we classify up to unitary equivalence. Our results recover the known classification of ordinary 2-representations of finite 2-groups, but provide additional data interpreted as a type of reflection anomaly for $\mathcal{G}$. |
| title | On Unitary 2-Group Symmetries |
| topic | Mathematical Physics High Energy Physics - Theory Category Theory |
| url | https://arxiv.org/abs/2411.05067 |