Three-dimensional orbifolds by 2-groups

Abstract

In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in physics, state a version of the decomposition conjecture, and then compute in numerous examples, checking that decomposition works as advertised.

arXiv comment37 pages, LaTeX; v2: typos fixed, pictures added, new example added

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• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Dilaton shifts, probability measures, and decomposition
• Decomposition squared
• Chern-Simons theory, decomposition, and the A model
• Decomposition in 2d non-invertible gaugings