Exploring 2-Group Global Symmetries

Abstract

We analyze four-dimensional quantum field theories with continuous 2-group global symmetries. At the level of their charges such symmetries are identical to a product of continuous flavor or spacetime symmetries with a 1-form global symmetry $U(1{)}_B^{(1)}$, which arises from a conserved 2-form current $J_B^{(2)}$. Rather, 2-group symmetries are characterized by deformed current algebras, with quantized structure constants, which allow two flavor currents or stress tensors to fuse into $J_B^{(2)}$. This leads to unconventional Ward identities, which constrain the allowed patterns of spontaneous 2-group symmetry breaking and other aspects of the renormalization group flow. If $J_B^{(2)}$ is coupled to a 2-form background gauge field $B^{(2)}$, the 2-group current algebra modifies the behavior of $B^{(2)}$ under background gauge transformations. Its transformation rule takes the same form as in the Green-Schwarz mechanism, but only involves the background gauge or gravity fields that couple to the other 2-group currents. This makes it possible to partially cancel reducible 't Hooft anomalies using Green-Schwarz counterterms for the 2-group background gauge fields. The parts that cannot be cancelled are reinterpreted as mixed, global anomalies involving $U(1{)}_B^{(1)}$ and receive contributions from topological, as well as massless, degrees of freedom. Theories with 2-group symmetry are constructed by gauging an abelian flavor symmetry with suitable mixed 't Hooft anomalies, which leads to many simple and explicit examples. Some of them have dynamical string excitations that carry $U(1{)}_B^{(1)}$ charge, and 2-group symmetry determines certain 't Hooft anomalies on the world sheets of these strings. Finally, we point out that holographic theories with 2-group global symmetries have a bulk description in terms of dynamical gauge fields that participate in a conventional Green-Schwarz mechanism.

137 pages, 2 figures

References in corpus (15)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• On gauging finite subgroups
• Higher-Dimensional Algebra V: 2-Groups
• Anomaly polynomial of general 6d SCFTs
• Higher Gauge Theory: 2-Connections on 2-Bundles
• Anomalies of discrete symmetries in various dimensions and group cohomology
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• TASI 2003 Lectures on Anomalies
• Lectures on Anomalies
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• TASI Lectures on the Emergence of the Bulk in AdS/CFT
• Higher Derivative Terms, Toroidal Compactification, and Weyl Anomalies in Six-Dimensional (2,0) Theories
• Universal Bounds on Operator Dimensions from the Average Null Energy Condition

Cited by in corpus (173)

• Generalized Symmetries in Condensed Matter
• On gauging finite subgroups
• Non-Invertible Duality Defects in 3+1 Dimensions
• On 2-Group Global Symmetries and Their Anomalies
• Non-Invertible Higher-Categorical Symmetries
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Non-Invertible Global Symmetries and Completeness of the Spectrum
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
• 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
• 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories
• 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
• Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• 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
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Non-invertible Symmetries and Higher Representation Theory I
• Higher-form symmetries and 3-group in axion electrodynamics
• 2-Group Symmetries of 6d Little String Theories and T-duality
• Non-Invertible Defects in 5d, Boundaries and Holography
• 2-Group Symmetries in Class S
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Discrete Theta Angles, Symmetries and Anomalies
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Symmetry TFTs for 3d QFTs from M-theory
• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• Topological dualities in the Ising model
• 2-Group Symmetries and M-Theory
• Higher Symmetries of 5d Orbifold SCFTs
• Superfluids as Higher-form Anomalies
• Continuous Generalized Symmetries in Three Dimensions
• Anomalies and Symmetry Fractionalization
• Anomalies of Duality Groups and Extended Conformal Manifolds
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• Higher categorical symmetries and gauging in two-dimensional spin systems
• Classification of (2+1)D invertible fermionic topological phases with symmetry
• Non-Invertible Symmetries from Discrete Gauging and Completeness of the Spectrum
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT
• Higher Form Symmetries TFT in 6d
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• Universal Features of Higher-Form Symmetries at Phase Transitions
• 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
• Non-Abelian Hybrid Fracton Orders
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics
• Anomalies and gauging of U(1) symmetries
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• Gravity as a gapless phase and biform symmetries
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Exact emergent higher-form symmetries in bosonic lattice models
• Anomalies of QFTs from M-theory and Holography
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Symmetries and Anomalies of (1+1)d Theories: 2-groups and Symmetry Fractionalization
• On 2-form gauge models of topological phases
• Revisiting Wess-Zumino-Witten terms
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Quantization of Axion-Gauge Couplings and Non-Invertible Higher Symmetries
• Lifetimes of (near) eternal false vacua
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• General Prescription for Global U(1)'s in 6D SCFTs
• T-Branes, String Junctions, and 6D SCFTs
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Anomalies of Generalized Symmetries from Solitonic Defects
• Exceptional Chern-Simons-Matter Dualities
• On Triality Defects in 2d CFT
• Categorical Symmetries at Criticality
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Foliated BF theories and Multipole symmetries
• 2-group global symmetries, hydrodynamics and holography
• Disconnected 0-Form and 2-Group Symmetries
• Field theories with higher-group symmetry from composite currents
• Surface defects in holographic 5d SCFTs
• Gauging 1-form center symmetries in simple $SU(N)$ gauge theories
• 't Hooft anomalies and the holomorphy of supersymmetric partition functions
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• A study of time reversal symmetry of abelian anyons
• Effective Field Theory of Force-Free Electrodynamics
• A symmetry principle for gauge theories with fractons
• Comments on compatibility between Conformal symmetry and Continuous higher-form symmetries
• Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications
• Holographic duals of symmetry broken phases
• Modified Villain formulation of abelian Chern-Simons theory
• Orbifolds by 2-groups and decomposition
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Topological defects
• Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory
• Multipole and fracton topological order via gauging foliated SPT phases
• (SPT-)LSM theorems from projective non-invertible symmetries
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Dihedral symmetry in $SU(N)$ Yang-Mills theory
• 1-form symmetry versus large N QCD
• Excitations in strict 2-group higher gauge models of topological phases
• When the moduli space is an orbifold: Spontaneous breaking of continuous non-invertible symmetries
• Gravitational Solitons and Completeness
• High-temperature domain walls of QCD with imaginary chemical potentials
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• Flowing from 16 to 32 Supercharges
• A fresh view on string orbifolds
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Revisiting relativistic magnetohydrodynamics from quantum electrodynamics
• Toric 2-group anomalies via cobordism
• Pascal's Triangle Fractal Symmetries
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Infinitely many 4d N=1 SCFTs with a=c
• Courant sigma model and $L_{\infty }$-algebras
• Supersymmetry anomalies in new minimal supergravity
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Bootstrapping Lieb-Schultz-Mattis anomalies
• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions
• Super-Spin Chains for 6D SCFTs
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Kac-Moody symmetry in the light front of gauge theories
• Magnetic operators in 2D compact scalar field theories on the lattice
• Comments on Global Symmetries and Anomalies of $5d$ SCFTs
• The Fate of Discrete 1-Form Symmetries in 6d
• Generalized chiral instabilities, linking numbers, and non-invertible symmetries
• Higher-group structure in lattice Abelian gauge theory under instanton-sum modification
• Hypercharge Quantisation and Fermat's Last Theorem
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Study of gapped phases of 4d gauge theories using temporal gauging of the ${\mathbb{Z}}_N$ 1-form symmetry
• Non-Invertible Peccei-Quinn Symmetry, Natural 2HDM Alignment, and the Visible Axion
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Two-dimensional Anomaly, Orbifolding, and Boundary States
• Exotic Invertible Phases with Higher-Group Symmetries
• Duality and higher Buscher rules in p-form gauge theory and linearized gravity
• Topological aspects of brane fields: solitons and higher-form symmetries
• $3d$ One-form Mixed Anomaly and Entanglement Entropy
• BCF anomaly and higher-group structure in the low energy effective theories of mesons
• Higher Gauge Theory and Integrability
• (2-)Drinfel'd Double and (2-)BF Theory
• Matching higher symmetries across Intriligator-Seiberg duality
• Lattice construction of exotic invertible topological phases
• Impossible Symmetries and Conformal Gravity
• Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries
• Duality, generalized global symmetries and jet space isometries
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Topological terms and anomaly matching in effective field theories on ${\mathbb{R}}^3\times S^1$: I. Abelian symmetries and intermediate scales
• WZW terms without anomalies: generalised symmetries in chiral Lagrangians
• Higher-group global symmetry and the bosonic M5 brane
• Higher-form symmetry breaking and holographic flavour
• Surface Operators in Superspace
• Non-Invertible Gauss Law and Axions
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• B-brane transport in anomalous (2,2) models and localization
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• CFTs on curved spaces
• Notes on anomalies, elliptic curves and the BS-D conjecture
• Generalized symmetries as homotopy Lie algebras
• Intertwined order of generalized global symmetries
• Symmetry TFTs from String Theory
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Instances of Higher Geometry in Field Theory