On gauging finite subgroups

Abstract

We study in general spacetime dimension the symmetry of the theory obtained by gauging a non-anomalous finite normal Abelian subgroup $A$ of a $\Gamma$-symmetric theory. Depending on how anomalous $\Gamma$ is, we find that the symmetry of the gauged theory can be i) a direct product of $G=\Gamma /A$ and a higher-form symmetry $\hat{A}$ with a mixed anomaly, where $\hat{A}$ is the Pontryagin dual of $A$; ii) an extension of the ordinary symmetry group $G$ by the higher-form symmetry $\hat{A}$; iii) or even more esoteric types of symmetries which are no longer groups. We also discuss the relations to the effect called the $H^3(G,\hat{A})$ symmetry localization obstruction in the condensed-matter theory and to some of the constructions in the works of Kapustin-Thorngren and Wang-Wen-Witten.

26 pages; v3: numerous minor improvements suggested by an anonymous referee; v2: minor improvement in Sec. 2.6.1

References in corpus (7)

• Generalized Global Symmetries
• Exploring 2-Group Global Symmetries
• On 2-Group Global Symmetries and Their Anomalies
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Anomalies of discrete symmetries in various dimensions and group cohomology
• Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions

Cited by in corpus (184)

• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Exploring 2-Group Global Symmetries
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Non-Invertible Duality Defects in 3+1 Dimensions
• Symmetries and Strings of Adjoint QCD${}_2$
• Higher Gauging and Non-invertible Condensation Defects
• Orbifold groupoids
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Non-Invertible Higher-Categorical Symmetries
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Universal Non-Invertible Symmetries
• Intrinsically Gapless Topological Phases
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Generalized Global Symmetries of $T[M]$ Theories. I
• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• The Branes Behind Generalized Symmetry Operators
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Non-invertible Time-reversal Symmetry
• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
• Branes and Non-Invertible Symmetries
• 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories
• Anomalies and Bounds on Charged Operators
• Cobordism Conjecture, Anomalies, and the String Lamppost Principle
• Modified instanton sum in QCD and higher-groups
• On Continuous 2-Category Symmetries and Yang-Mills Theory
• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• Non-Invertible Symmetry Webs
• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Symmetry as a shadow of topological order and a derivation of topological holographic principle
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Remarks on Boundaries, Anomalies, and Noninvertible Symmetries
• Non-invertible Symmetries and Higher Representation Theory I
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• 2-Group Symmetries in Class S
• Discrete Theta Angles, Symmetries and Anomalies
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• Symmetric Mass Generation
• Symmetry TFTs for 3d QFTs from M-theory
• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
• 2-Group Symmetries and M-Theory
• Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond
• Dualities in one-dimensional quantum lattice models: topological sectors
• Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
• Continuous Generalized Symmetries in Three Dimensions
• Anomalies and Symmetry Fractionalization
• Cluster state as a non-invertible symmetry protected topological phase
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Generalized symmetries and holography in ABJM-type theories
• Classification of (2+1)D invertible fermionic topological phases with symmetry
• Higher categorical symmetries and gauging in two-dimensional spin systems
• Non-Invertible Symmetries from Discrete Gauging and Completeness of the Spectrum
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Bootstrapping Non-Invertible Symmetries
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Subsystem Non-Invertible Symmetry Operators and Defects
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Instantons, Symmetries and Anomalies in Five Dimensions
• Gauging the Kitaev chain
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics
• Anomalies and gauging of U(1) symmetries
• Duality Defects in $E_8$
• Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Revisiting Wess-Zumino-Witten terms
• Topological Field Theory with Haagerup Symmetry
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Lifetimes of (near) eternal false vacua
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• Anomalies of Generalized Symmetries from Solitonic Defects
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Zero-form and one-form symmetries of the ABJ and related theories
• Anomaly resolution via decomposition
• Line Operators of Gauge Theories on Non-Spin Manifolds
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• TQFT, Symmetry Breaking, and Finite Gauge Theory in 3+1D
• Non-invertible symmetries along 4d RG flows
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Generating Lattice Non-invertible Symmetries
• Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations
• Quantum symmetries in orbifolds and decomposition
• Disconnected 0-Form and 2-Group Symmetries
• Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains
• 2-group global symmetries, hydrodynamics and holography
• Field theories with higher-group symmetry from composite currents
• 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
• Non-invertible symmetry-protected topological order in a group-based cluster state
• New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories
• Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter
• Non-Invertible Symmetries in Supergravity
• Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• A study of time reversal symmetry of abelian anyons
• Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
• Unwinding Short-Range Entanglement
• Holographic duals of symmetry broken phases
• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems
• Ultra Unification
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
• A generalization of decomposition in orbifolds
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Fermi Surface Symmetric Mass Generation
• (SPT-)LSM theorems from projective non-invertible symmetries
• Topological defects
• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• When the moduli space is an orbifold: Spontaneous breaking of continuous non-invertible symmetries
• Anomaly inflow and $p$-form gauge theories
• A fresh view on string orbifolds
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• Anomalies, Extensions and Orbifolds
• Orbifolds from Modular Orbits
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Symmetry-preserving boundary of (2+1)D fractional quantum Hall states
• Non-Invertible T-duality at Any Radius via Non-Compact SymTFT
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• Bootstrapping Lieb-Schultz-Mattis anomalies
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Higher-group structure in lattice Abelian gauge theory under instanton-sum modification
• Galois Orbits of TQFTs: Symmetries and Unitarity
• Average-exact mixed anomalies and compatible phases
• Comments on Global Symmetries and Anomalies of $5d$ SCFTs
• Study of gapped phases of 4d gauge theories using temporal gauging of the ${\mathbb{Z}}_N$ 1-form symmetry
• Fiber 2-Functors and Tambara-Yamagami Fusion 2-Categories
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Symmetry Transmutation and Anomaly Matching
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Exotic Invertible Phases with Higher-Group Symmetries
• Notes on gauging noninvertible symmetries, part 2: higher multiplicity cases
• BCF anomaly and higher-group structure in the low energy effective theories of mesons
• Symmetry fractionalization and duality defects in Maxwell theory
• Global symmetries of quantum lattice models under non-invertible dualities
• Matching higher symmetries across Intriligator-Seiberg duality
• Lattice construction of exotic invertible topological phases
• Gauge theory and mixed state criticality
• Self-$G$-ality in 1+1 dimensions
• A Note on Proton Stability in the Standard Model
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Spin Structures and AdS${}_4$ Holography
• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Disconnected gauge groups in the infrared
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• The Free Fermion Anomaly and Representations of the Pin Groups
• The $F$-Symbols for Transparent Haagerup-Izumi Categories with $G={\mathbb{Z}}_{2n+1}$
• WZW terms without anomalies: generalised symmetries in chiral Lagrangians
• Non-Invertible Gauss Law and Axions
• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
• Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Vacuum Structures Revisited
• Anomaly resolution by non-invertible symmetries
• Cancelling mod-2 anomalies by Green-Schwarz mechanism with $B_{\mu \nu }$
• B-brane transport in anomalous (2,2) models and localization
• $N$-ality symmetry and SPT phases in (1+1)d
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• From gauging to duality in one-dimensional quantum lattice models
• Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d
• Genus-One data and Anomaly Detection
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Shift orbifolds, decompactification limits, and lattices
• Non-invertible translation from Lieb-Schultz-Mattis anomaly
• Perspectives on Anomaly Resolution
• Aspects of 4d supersymmetric dynamics and geometry
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory
• Generalization of anomaly formula for time reversal symmetry in (2+1)D abelian bosonic TQFTs
• Symmetry TFTs from String Theory