Gauging Noninvertible Defects: A 2-Categorical Perspective

Abstract

We generalize the notion of an anomaly for a symmetry to a noninvertible symmetry enacted by surface operators using the framework of condensation in 2-categories. Given a multifusion 2-category, potentially with some additional levels of monoidality, we prove theorems about the structure of the 2-category obtained by condensing a suitable algebra object. We give examples where the resulting category displays grouplike fusion rules and through a cohomology computation, find the obstruction to condensing further to the vacuum theory.

26 pages, v2 a new theorem about symmetric fusion 2-categories is added

References in corpus (5)

• Universal Non-Invertible Symmetries
• Non-Invertible Symmetries from Holography and Branes
• The Branes Behind Generalized Symmetry Operators
• Symmetry TFTs for 3d QFTs from M-theory
• Rigid and Separable Algebras in Fusion 2-Categories

Cited by in corpus (21)

• Unifying Constructions of Non-Invertible Symmetries
• Non-Invertible Symmetry Webs
• Lecture Notes on Generalized Symmetries and Applications
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Generalized Charges, Part I: Invertible Symmetries and Higher Representations
• Non-invertible Symmetries and Higher Representation Theory II
• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Subsystem Non-Invertible Symmetry Operators and Defects
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
• Fusion 3-Categories for Duality Defects
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Local Modules in Braided Monoidal 2-Categories
• The Smith Fiber Sequence and Invertible Field Theories
• Non-Invertible Gauss Law and Axions