Non-Invertible Symmetry Webs

Abstract

Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with $G$ 0-form symmetry, and we propose a description of sequential partial gaugings of sub-symmetries. The gauging implements the theta-symmetry defects of the companion paper [1]. The resulting network of symmetry structures related by this gauging will be called a non-invertible symmetry web. Our formulation makes direct contact with fusion 2-categories, and we uncover numerous interesting structures such as symmetry fractionalization in this categorical setting. The complete symmetry web is derived for several groups $G$, and we propose extensions to higher dimensions. The highlight of this analysis is the complete categorical symmetry web, including non-invertible symmetries, for 3d pure gauge theories with orthogonal gauge groups and its extension to arbitrary dimensions.

115 pages

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Cited by in corpus (33)

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• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
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• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
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• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Boundary SymTFT
• Fiber 2-Functors and Tambara-Yamagami Fusion 2-Categories
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• Fusion 3-Categories for Duality Defects
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• Symmetry fractionalization and duality defects in Maxwell theory
• Self-$G$-ality in 1+1 dimensions
• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Entropic Order Parameters for Categorical Symmetries in 2D-CFT