Comments on Global Symmetries, Anomalies, and Duality in (2+1)d

Abstract

We analyze in detail the global symmetries of various (2+1)d quantum field theories and couple them to classical background gauge fields. A proper identification of the global symmetries allows us to consider all non-trivial bundles of those background fields, thus finding more subtle observables. The global symmetries exhibit interesting 't Hooft anomalies. These allow us to constrain the IR behavior of the theories and provide powerful constraints on conjectured dualities.

45 pages, 2 figures; v2: minor improvements and refs added

References in corpus (11)

• Generalized Global Symmetries
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Level/rank Duality and Chern-Simons-Matter Theories
• Seiberg Duality in Chern-Simons Theory
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Nonsupersymmetric dualities from mirror symmetry
• More Abelian Dualities in 2+1 Dimensions
• Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter
• Non-Abelian 3d Bosonization and Quantum Hall States
• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories

Cited by in corpus (107)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Theta, Time Reversal, and Temperature
• Deconfined quantum critical points: symmetries and dualities
• Entanglement entropy: holography and renormalization group
• On 2-Group Global Symmetries and Their Anomalies
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Comments on Abelian Higgs Models and Persistent Order
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Generalized Global Symmetries of $T[M]$ Theories. I
• Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets
• Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
• Anomaly constraints on deconfinement and chiral phase transition
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• Dual Boundary Conditions in 3d SCFT's
• Phases Of Adjoint QCD${}_3$ And Dualities
• A Symmetry Breaking Scenario for QCD${}_3$
• Discrete Theta Angles, Symmetries and Anomalies
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• Three-dimensional dualities with bosons and fermions
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$
• Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D
• Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena
• Anomalies and Symmetry Fractionalization
• Continuous Generalized Symmetries in Three Dimensions
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Higher Form Symmetries TFT in 6d
• Monopole Operators in $U(1)$ Chern-Simons-Matter Theories
• Exact Boson-Fermion Duality on a 3D Euclidean Lattice
• Anomaly matching and symmetry-protected critical phases in $SU(N)$ spin systems in 1+1 dimensions
• Subsystem Non-Invertible Symmetry Operators and Defects
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• Instantons, Symmetries and Anomalies in Five Dimensions
• Enhanced thermal Hall effect in the square-lattice Néel state
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• On the baryon-color-flavor (BCF) anomaly in vector-like theories
• The Bi-Fundamental Gauge Theory in 3+1 Dimensions: The Vacuum Structure and a Cascade
• Embedding three-dimensional bosonization dualities into string theory
• Comments on Foliated Gauge Theories and Dualities in 3+1d
• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• A master bosonization duality
• Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• Anomalies of Generalized Symmetries from Solitonic Defects
• Dualities and Phases of 3D N=1 SQCD
• Bosonizing three-dimensional quiver gauge theories
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• $\mathcal{N}=1$ dualities in 2+1 dimensions
• Living on the walls of super-QCD
• Parity and the modular bootstrap
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• All tree level scattering amplitudes in Chern-Simons theories with fundamental matter
• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• From 3d dualities to hadron physics
• Novel 3d bosonic dualities from bosonization and holography
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Metastable Vacua in Large-$N$ QCD${}_3$
• Bose-Fermi Chern-Simons Dualities in the Higgsed Phase
• Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Covariant fracton gauge theory with boundary
• N=1 QED in 2+1 dimensions: Dualities and enhanced symmetries
• Gauging Lie group symmetry in (2+1)d topological phases
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• Dual Superconformal Symmetry of $\mathcal{N}=2$ Chern-Simons theory with Fundamental Matter at Large $N$
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Twisted indices, Bethe ideals and 3d $\mathcal{N}=2$ infrared dualities
• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• Charting the phase diagram of QCD${}_3$
• Conformality and self-duality of $N_f=2$ QED${}_3$
• Two-dimensional conductors with interactions and disorder from particle-vortex duality
• Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry
• Comments on Global Symmetries and Anomalies of $5d$ SCFTs
• Chern-Simons dualities with multiple flavors at large $N$
• Anomalous dimensions of monopole operators in scalar QED${}_3$ with Chern-Simons term
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• $QC{D}_3$ Dualities and the F-Theorem
• Duality Web on a 3D Euclidean Lattice and Manifestation of Hidden Symmetries
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• The Hilbert Space of large $N$ Chern-Simons matter theories
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter
• Boson-fermion duality in a gravitational background
• Spontaneous symmetry breaking in pure 2D Yang-Mills theory
• Continuous transition between Ising magnetic order and a chiral spin liquid
• Induced Maxwell-Chern-Simons Effective Action in Very Special Relativity
• Phases of Flavor Broken QCD${}_3$
• New and Old Fermionic Dualities from 3d Bosonization
• Global Aspects of Spaces of Vacua
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• Generalization of QCD${}_3$ Symmetry-Breaking and Flavored Quiver Dualities
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
• On S-duality for holographic p-wave superconductors
• One-loop Photon's Effective Action in the Noncommutative Scalar QED${}_3$
• Interface Junctions in QCD${}_4$
• Time-Reversal Anomalies of QCD${}_3$ and QED${}_3$
• Self-duality protected multi-criticality in deconfined quantum phase transitions
• Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases
• Phases of QCD${}_3$ with three families of fundamental flavors