Generalized Global Symmetries

Abstract

A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.

49 pages plus appendices. v2: references added

References in corpus (11)

• Symmetries and Strings in Field Theory and Gravity
• Duality and defects in rational conformal field theory
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• The Uncertainty of Fluxes
• Heisenberg Groups and Noncommutative Fluxes
• Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity
• Anomalies of discrete symmetries in various dimensions and group cohomology
• Short-range entanglement and invertible field theories
• Discrete torsion defects
• Topological Model for Domain Walls in (Super-)Yang-Mills Theories
• On Orbits of the Ring $Z_n^m$ under the Action of the Group $SL(m,Z_n)$

Cited by in corpus (45)

• The Swampland: Introduction and Review
• Level/rank Duality and Chern-Simons-Matter Theories
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Abelian gauge theories on the lattice: $\theta$-terms and compact gauge theory with(out) monopoles
• Higher-form symmetries and 3-group in axion electrodynamics
• Thermal Order in Conformal Theories
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Generalized symmetries and holography in ABJM-type theories
• Cobordism Classes and the Swampland
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• On Irregular Singularity Wave Functions and Superconformal Indices
• 3d Abelian Gauge Theories at the Boundary
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade
• Anomalies of QFTs from M-theory and Holography
• On 2-form gauge models of topological phases
• Lorentz Symmetry Fractionalization and Dualities in (2+1)d
• Higher Derivative Terms, Toroidal Compactification, and Weyl Anomalies in Six-Dimensional (2,0) Theories
• $\theta =\pi$ in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• Yang--Mills Glueballs as Closed Bosonic Strings
• 't Hooft anomaly matching condition and chiral symmetry breaking without bilinear condensate
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
• Weakly coupled conformal manifolds in 4d
• Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms
• High-temperature domain walls of QCD with imaginary chemical potentials
• Geometrical tools for embedding fields, submanifolds, and foliations
• Magnetic discrete gauge field in the confining vacua and the supersymmetric index
• Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy
• Dynamical Casimir Effect in a small compact manifold for the Maxwell vacuum
• Ramond-Ramond couplings of D-branes
• $3d$ One-form Mixed Anomaly and Entanglement Entropy
• 't Hooft surface in lattice gauge theory
• Notes on $\mathcal{N}=1$ QCD${}_3$ with baryon superpotential
• OPE of the stress tensors and surface operators
• From $\mathcal{N}=4$ Super-Yang-Mills on ${\mathbb{RP}}^4$ to bosonic Yang-Mills on ${\mathbb{RP}}^2$
• Swampland conjectures for type IIB orientifolds with closed-string U(1)s
• Current Groups and the Hamiltonian Anomaly