Non-Local Conserved Currents and Continuous Non-Invertible Symmetries
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915447225450496 |
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| author | Delmastro, Diego Sharon, Adar Zheng, Yunqin |
| author_facet | Delmastro, Diego Sharon, Adar Zheng, Yunqin |
| contents | We embark on a systematic study of continuous non-invertible symmetries, focusing on 1+1d CFTs. We describe a generalized version of Noether's theorem, where continuous non-invertible symmetries are associated to $\textit{non-local}$ conserved currents: point-like operators attached to extended topological defects. The generalized Noether's theorem unifies several constructions of continuous non-invertible symmetries in the literature, and allows us to exhibit many more examples in diverse theories of interest. We first review known examples which are non-intrinsic (i.e., invertible up to gauging), and then describe $\textit{new}$ examples in Wess-Zumino-Witten models and products of minimal models. For some of these new examples, we show that these continuous non-invertible symmetries are intrinsic if we demand that a certain global symmetry is preserved. The continuous non-invertible symmetries in products of minimal models also allow us to construct new examples of defect conformal manifolds in a single copy of a minimal model. Finally, we comment on continuous non-invertible symmetries in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22976 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Local Conserved Currents and Continuous Non-Invertible Symmetries Delmastro, Diego Sharon, Adar Zheng, Yunqin High Energy Physics - Theory We embark on a systematic study of continuous non-invertible symmetries, focusing on 1+1d CFTs. We describe a generalized version of Noether's theorem, where continuous non-invertible symmetries are associated to $\textit{non-local}$ conserved currents: point-like operators attached to extended topological defects. The generalized Noether's theorem unifies several constructions of continuous non-invertible symmetries in the literature, and allows us to exhibit many more examples in diverse theories of interest. We first review known examples which are non-intrinsic (i.e., invertible up to gauging), and then describe $\textit{new}$ examples in Wess-Zumino-Witten models and products of minimal models. For some of these new examples, we show that these continuous non-invertible symmetries are intrinsic if we demand that a certain global symmetry is preserved. The continuous non-invertible symmetries in products of minimal models also allow us to construct new examples of defect conformal manifolds in a single copy of a minimal model. Finally, we comment on continuous non-invertible symmetries in higher dimensions. |
| title | Non-Local Conserved Currents and Continuous Non-Invertible Symmetries |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.22976 |