Unitary Categorical Symmetries
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915242681827328 |
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| author | Bartsch, Thomas |
| author_facet | Bartsch, Thomas |
| contents | Global invertible symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to non-invertible symmetries by considering unitary actions of higher fusion category symmetries $\mathcal{C}$ on twisted sector local operators. We propose that the latter transform in $\ast$-representations of the tube algebra associated to $\mathcal{C}$, which we introduce and classify using the notion of higher $S$-matrices of higher braided fusion categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unitary Categorical Symmetries Bartsch, Thomas High Energy Physics - Theory Mathematical Physics Category Theory Quantum Algebra Global invertible symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to non-invertible symmetries by considering unitary actions of higher fusion category symmetries $\mathcal{C}$ on twisted sector local operators. We propose that the latter transform in $\ast$-representations of the tube algebra associated to $\mathcal{C}$, which we introduce and classify using the notion of higher $S$-matrices of higher braided fusion categories. |
| title | Unitary Categorical Symmetries |
| topic | High Energy Physics - Theory Mathematical Physics Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2502.04440 |