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| Format: | Preprint |
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2021
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| Online Access: | https://arxiv.org/abs/2108.13423 |
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| _version_ | 1866909287138197504 |
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| author | Sharpe, E. |
| author_facet | Sharpe, E. |
| contents | In this paper we discuss the relationship between noninvertible topological operators, one-form symmetries, and decomposition of two-dimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete torsion. As one component of our analysis, we study the ring of dimension-zero operators in two-dimensional theories exhibiting decomposition. From a commutative algebra perspective, the rings are naturally associated to a finite number of points, one point for each universe in the decomposition. Each universe is canonically associated to a representation, which defines a projector, an idempotent in the ring of dimension-zero operators. We discuss how bulk Wilson lines act as defects bridging universes, and how Wilson lines on boundaries of two-dimensional theories decompose, and compute actions of projectors. We discuss one-form symmetries of the rings, and related properties. We also give general formulas for projection operators, which previously were computed on a case-by-case basis. Finally, we propose a characterization of noninvertible higher-form symmetries in this context in terms of representations. In that characterization, non-isomorphic universes appearing in decomposition are associated with noninvertible one-form symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_13423 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Topological operators, noninvertible symmetries and decomposition Sharpe, E. High Energy Physics - Theory In this paper we discuss the relationship between noninvertible topological operators, one-form symmetries, and decomposition of two-dimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete torsion. As one component of our analysis, we study the ring of dimension-zero operators in two-dimensional theories exhibiting decomposition. From a commutative algebra perspective, the rings are naturally associated to a finite number of points, one point for each universe in the decomposition. Each universe is canonically associated to a representation, which defines a projector, an idempotent in the ring of dimension-zero operators. We discuss how bulk Wilson lines act as defects bridging universes, and how Wilson lines on boundaries of two-dimensional theories decompose, and compute actions of projectors. We discuss one-form symmetries of the rings, and related properties. We also give general formulas for projection operators, which previously were computed on a case-by-case basis. Finally, we propose a characterization of noninvertible higher-form symmetries in this context in terms of representations. In that characterization, non-isomorphic universes appearing in decomposition are associated with noninvertible one-form symmetries. |
| title | Topological operators, noninvertible symmetries and decomposition |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2108.13423 |