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$\mathbb{Q}/\mathbb{Z}$ symmetry
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abstract
We summarize basic features of quantum field theories with discrete symmetry $\mathbb{Q}/\mathbb{Z}$ (possibly higher form, global or gauged). The classification of representations and anomalies is quite rich and involves the ring of profinite integers. As a main example we consider in detail 3d topological Dijkgraaf-Witten $\mathbb{Q}/\mathbb{Z}$ gauge theories. We also briefly discuss relevance for some previously considered physical systems. In particular we comment on a relation to the recently discovered non-invertible symmetry in 4d QED and the problem of categorification of Chern-Simons TQFT.
Forward citations
Cited by 3 Pith papers
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Non-Local Conserved Currents and Continuous Non-Invertible Symmetries
Non-local conserved currents attached to topological lines generate continuous non-invertible symmetries in 1+1d CFTs, with new examples in SU(2)_k WZW and minimal model products.
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SymTFT, Protected Gaplessness, and Spontaneous Breaking of Non-invertible Symmetries
The authors classify, via Galois theory of cyclotomic polynomials, when finite duality symmetry groups of 4d BF-type SymTFTs admit invariant Lagrangian boundary conditions, thereby determining when symmetry-preserving...
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The Higher Structure of Symmetries of Axion-Maxwell Theory
The paper determines the fusion interfaces and F-symbols for the non-invertible electric 1-form symmetry of 4d axion-Maxwell theory.
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