On the action of non-invertible symmetries on local operators in 3+1d
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911483596636160 |
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| author | Putrov, Pavel Radhakrishnan, Rajath |
| author_facet | Putrov, Pavel Radhakrishnan, Rajath |
| contents | Most of the known non-invertible symmetries of quantum field theories in three and four spacetime dimensions act invertibly on local operators. An exception is coset symmetries, which can be constructed from gauging a non-normal subgroup of an invertible symmetry. In this paper, we study the action of a general finite non-invertible symmetry on local operators in four dimensions. We show that non-invertible symmetries without topological line operators necessarily act invertibly on local operators. Using this result, we argue that the action of a general non-invertible symmetry in 3+1d on local operators can be decomposed into the invertible action of some operators composed with the action of a gauging interface. We use this result to study when such a symmetry is anomaly-free. We find a necessary condition for a finite non-invertible symmetry in 3+1d to be anomaly-free, and show that anomaly-free non-invertible symmetries without topological line operators are non-intrinsically non-invertible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03438 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the action of non-invertible symmetries on local operators in 3+1d Putrov, Pavel Radhakrishnan, Rajath High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra Most of the known non-invertible symmetries of quantum field theories in three and four spacetime dimensions act invertibly on local operators. An exception is coset symmetries, which can be constructed from gauging a non-normal subgroup of an invertible symmetry. In this paper, we study the action of a general finite non-invertible symmetry on local operators in four dimensions. We show that non-invertible symmetries without topological line operators necessarily act invertibly on local operators. Using this result, we argue that the action of a general non-invertible symmetry in 3+1d on local operators can be decomposed into the invertible action of some operators composed with the action of a gauging interface. We use this result to study when such a symmetry is anomaly-free. We find a necessary condition for a finite non-invertible symmetry in 3+1d to be anomaly-free, and show that anomaly-free non-invertible symmetries without topological line operators are non-intrinsically non-invertible. |
| title | On the action of non-invertible symmetries on local operators in 3+1d |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2603.03438 |