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Non-invertible Symmetries of Class $\mathcal{S}$ Theories

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arxiv 2211.05138 v2 pith:E5XWSDJ3 submitted 2022-11-09 hep-th

classification hep-th
keywords non-invertiblesymmetriessymmetrytheoriesclassmathcalobtainedtheory
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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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Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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