Orbifolds by 2-groups and decomposition

Abstract

In this paper we study three-dimensional orbifolds by 2-groups with a trivially-acting one-form symmetry group BK. These orbifolds have a global two-form symmetry, and so one expects that they decompose into (are equivalent to) a disjoint union of other three-dimensional theories, which we demonstrate. These theories can be interpreted as sigma models on 2-gerbes, whose formal structures reflect properties of the orbifold construction.

arXiv commentLaTeX, 53 pages; v2: typos fixed, references added

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• Symmetry TFTs for 3d QFTs from M-theory
• Anomalies of Generalized Symmetries from Solitonic Defects
• Disconnected 0-Form and 2-Group Symmetries
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Decomposition and the Gross-Taylor string theory
• Three-dimensional orbifolds by 2-groups
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• Dilaton shifts, probability measures, and decomposition
• Decomposition squared
• Decomposition in 2d non-invertible gaugings