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arXiv · 2507.22976

Non-Local Conserved Currents and Continuous Non-Invertible Symmetries

Diego Delmastro·Adar Sharon·Yunqin Zheng
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Abstract

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.

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Diego Delmastro, Adar Sharon, Yunqin Zheng. 2025-07-30. Non-Local Conserved Currents and Continuous Non-Invertible Symmetries. https://arxiv.org/abs/2507.22976

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