Notes on generalized global symmetries in QFT

Abstract

It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as special cases of more general 2-groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one-form and higher-form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli `space' (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2-group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization.

47 pages, LaTeX; v2: references added; v3: more references added; v4: added pub info; v5: added reference

References in corpus (58)

• Generalized Global Symmetries
• A Strong Coupling Test of S-Duality
• Reading between the lines of four-dimensional gauge theories
• Notes on the K3 Surface and the Mathieu group M_24
• Topological boundary conditions in abelian Chern-Simons theory
• Higher-Dimensional Algebra V: 2-Groups
• An Invitation to Higher Gauge Theory
• 2D Kac-Moody Symmetry of 4D Yang-Mills Theory
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Higher Algebraic Structures and Quantization
• Defect lines, dualities, and generalised orbifolds
• D-branes and Discrete Torsion II
• Cluster decomposition, T-duality, and gerby CFT's
• GLSM's for gerbes (and other toric stacks)
• Twisted differential String and Fivebrane structures
• String compactifications on Calabi-Yau stacks
• Orbifold completion of defect bicategories
• Non-birational twisted derived equivalences in abelian GLSMs
• Torsion-free generalized connections and Heterotic Supergravity
• On the Classification of Topological Field Theories
• Principal infinity-bundles -- General theory
• Notes on gauging noneffective group actions
• Higher gauge theory and a non-Abelian generalization of 2-form electrodynamics
• Sums over topological sectors and quantization of Fayet-Iliopoulos parameters
• Central Extensions of Smooth 2-Groups and a Finite-Dimensional String 2-Group
• Perturbative gauge theory at null infinity
• D-branes and Discrete Torsion
• Higher gauge theory I: 2-Bundles
• Topological Approach to Alice Electrodynamics
• Magnetic Z(N) symmetry in hot QCD and the spatial Wilson loop
• A higher stacky perspective on Chern-Simons theory
• New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories
• Discrete torsion defects
• A higher Chern-Weil derivation of AKSZ sigma-models
• Decomposition in diverse dimensions
• Orbifold equivalent potentials
• The overarching finite symmetry group of Kummer surfaces in the Mathieu group M_24
• AQFT from n-functorial QFT
• Analogues of Discrete Torsion for the M-Theory Three-Form
• Antisymmetric tensor Z_p gauge symmetries in field theory and string theory
• A Note on the Equivalence of Vafa's and Douglas's Picture of Discrete Torsion
• New Look at QED${}_4$: the Photon as a Goldstone Boson and the Topological Interpretation of Electric Charge
• A Construction of String 2-Group Models using a Transgression-Regression Technique
• Heterotic compactifications with principal bundles for general groups and general levels
• On Gromov-Witten theory of root gerbes
• Gromov-Witten theory of banded gerbes over schemes
• General aspects of heterotic string compactifications on stacks and gerbes
• Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors
• The symmetries of the tetrahedral Kummer surface in the Mathieu group M_24
• A Smooth Model for the String Group
• Confinement, magnetic Z(N) symmetry and low energy effective theory of gluodynamics
• A few recent developments in 2d (2,2) and (0,2) theories
• N=2 Moonshine
• Higher abelian Dijkgraaf-Witten theory
• Calabi-Yau completions and orbifold equivalences
• Two-dimensional topological field theories as taffy
• Anomalies and Invertible Field Theories
• Kac-Moody and Borcherds Symmetries of Six-Dimensional Chiral Supergravity

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• Exploring 2-Group Global Symmetries
• On finite symmetries and their gauging in two dimensions
• On gauging finite subgroups
• On 2-Group Global Symmetries and Their Anomalies
• Non-Invertible Higher-Categorical Symmetries
• Universal Non-Invertible Symmetries
• The Weak Gravity Conjecture: A Review
• Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
• Generalized Global Symmetries of $T[M]$ Theories. I
• The Branes Behind Generalized Symmetry Operators
• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• Branes and Non-Invertible Symmetries
• Modified instanton sum in QCD and higher-groups
• Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory
• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• Symmetry as a shadow of topological order and a derivation of topological holographic principle
• Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality
• Higher-form symmetries and 3-group in axion electrodynamics
• 2-Group Symmetries in Class S
• 2-Group Symmetries of 6d Little String Theories and T-duality
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Symmetry TFTs for 3d QFTs from M-theory
• Noether's Second Theorem and Ward Identities for Gauge Symmetries
• 2-Group Symmetries and M-Theory
• Higher Symmetries of 5d Orbifold SCFTs
• Continuous Generalized Symmetries in Three Dimensions
• Anomalies and Symmetry Fractionalization
• An Introduction to Higher-Form Symmetries
• Non-Invertible Symmetries from Discrete Gauging and Completeness of the Spectrum
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• Topological axion electrodynamics and 4-group symmetry
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics
• Exact emergent higher-form symmetries in bosonic lattice models
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Lifetimes of (near) eternal false vacua
• Counting Nambu-Goldstone modes of higher-form global symmetries
• Anomalies of Generalized Symmetries from Solitonic Defects
• 2-group global symmetries, hydrodynamics and holography
• Disconnected 0-Form and 2-Group Symmetries
• Field theories with higher-group symmetry from composite currents
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Orbifolds by 2-groups and decomposition
• Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory
• 1-form symmetry versus large N QCD
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• A fresh view on string orbifolds
• A Lie based 4-dimensional higher Chern-Simons theory
• Toric 2-group anomalies via cobordism
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Fractionally Charged Particles at the Energy Frontier: The SM Gauge Group and One-Form Global Symmetry
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• Magnetic operators in 2D compact scalar field theories on the lattice
• 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
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Algebraic formulation of higher gauge theory
• Fiber 2-Functors and Tambara-Yamagami Fusion 2-Categories
• Two-dimensional algebra in lattice gauge theory
• Topological mass generation in gapless systems
• Topological aspects of brane fields: solitons and higher-form symmetries
• Higher Gauge Theory and Integrability
• Higher Gauge Theory
• Three-dimensional orbifolds by 2-groups
• Quantum Groups as Global Symmetries
• Matching higher symmetries across Intriligator-Seiberg duality
• Duality, generalized global symmetries and jet space isometries
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
• Bagger-Witten line bundles on moduli spaces of elliptic curves
• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Some remarks on representations up to homotopy
• WZW terms without anomalies: generalised symmetries in chiral Lagrangians
• B-brane transport in anomalous (2,2) models and localization
• Generalized symmetry constraints on deformed 4d (S)CFTs
• Vacuum Structures Revisited
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• Higher categorical groups and the classification of topological defects and textures
• Universal Deformations
• Instances of Higher Geometry in Field Theory
• A concrete construction of a topological operator in factorization algebras
• Symmetry TFTs from String Theory
• Non-invertible symmetries of two-dimensional Non-Linear Sigma Models
• Decomposition in 2d non-invertible gaugings
• Higher-form anomalies and state-operator correspondence beyond conformal invariance
• Current Groups and the Hamiltonian Anomaly