Abstract
We study the non-invertible symmetries of class \( \mathcal{S} \) theories obtained by compactifying the type \( {\mathfrak{a}}_{p-1} \) 6d (2,0) theory on a genus g Riemann surface with no punctures. After setting up the general framework, we describe how such symmetries can be classified up to genus 5. Of central interest to us is the question of whether a non-invertible symmetry is intrinsic, i.e. whether it can be related to an invertible symmetry by discrete gauging. We then describe the higher-dimensional origin of our results, and explain how the Anomaly and Symmetry TFTs, as well as N-ality defects, of class \( \mathcal{S} \) theories can be obtained from compactification of a 7d Chern-Simons theory. Interestingly, we find that the Symmetry TFT for theories with intrinsically non-invertible symmetries can only be obtained by coupling the 7d Chern-Simons theory to topological gravity.
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Acknowledgments
We would like to thank Christian Copetti, Luis Diogo, Alice Hedenlund, Kantaro Ohmori, Jian Qiu, Gabi Zafrir, and Yunqin Zheng for many useful conversations. We also thank Yunqin Zheng for a careful reading of the manuscript. The work of MDZ and AH is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 851931). MDZ also acknowledges support from the Simons Foundation Grant #888984 (Simons Collaboration on Global Categorical Symmetries). VB is supported from the Knut and Alice Wallenberg Foundation under grant KAW 2021.0170, VR grant 2018-04438 and the Olle Engkvists Stiftelse grant n. 2180108.
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Bashmakov, V., Del Zotto, M., Hasan, A. et al. Non-invertible symmetries of class S theories. J. High Energ. Phys. 2023, 225 (2023). https://doi.org/10.1007/JHEP05(2023)225
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DOI: https://doi.org/10.1007/JHEP05(2023)225