Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory

Abstract

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

62 pages. v4: additions about robustness

References in corpus (13)

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• Symmetries and Strings in Field Theory and Gravity
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Phases of Matter
• Fracton hydrodynamics
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• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Exotic ${\mathbb{Z}}_N$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Resonating plaquette phases in large spin cold atom systems
• More Exotic Field Theories in 3+1 Dimensions
• Fractons with Twisted Boundary Conditions and Their Symmetries
• $(k,n)$-fractonic Maxwell theory
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Cited by in corpus (115)

• Generalized Symmetries in Condensed Matter
• The Branes Behind Generalized Symmetry Operators
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• A Modified Villain Formulation of Fractons and Other Exotic Theories
• The low-energy limit of some exotic lattice theories and UV/IR mixing
• Breakdown of hydrodynamics below four dimensions in a fracton fluid
• Hydrodynamics of ideal fracton fluids
• Spontaneous breaking of multipole symmetries
• Anomaly Inflow for Subsystem Symmetries
• An Introduction to Higher-Form Symmetries
• Bootstrapping Non-Invertible Symmetries
• Subsystem Non-Invertible Symmetry Operators and Defects
• Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• On completeness and generalized symmetries in quantum field theory
• Fractons with Twisted Boundary Conditions and Their Symmetries
• Gravity as a gapless phase and biform symmetries
• Exact emergent higher-form symmetries in bosonic lattice models
• Fracton hydrodynamics without time-reversal symmetry
• Comments on Foliated Gauge Theories and Dualities in 3+1d
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• FCC, Checkerboards, Fractons, and QFT
• Generalized Symmetries of the Graviton
• Hydrodynamics of dipole-conserving fluids
• Bose-Luttinger Liquids
• World-Line Description of Fractons
• Spontaneously Broken Subsystem Symmetries
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Generating Lattice Non-invertible Symmetries
• Foliated BF theories and Multipole symmetries
• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Fractons and exotic symmetries from branes
• Boson-fermion duality with subsystem symmetry
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Boundary theory of the X-cube model in the continuum
• Fracton Topological Order at Finite Temperature
• Foliated-Exotic Duality in Fractonic BF Theories
• A Chern-Simons theory for dipole symmetry
• Quantizing Carrollian field theories
• Ideal fracton superfluids
• A symmetry principle for gauge theories with fractons
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries
• Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions
• Gapped Lineon and Fracton Models on Graphs
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Five-Dimensional Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions
• Multipole and fracton topological order via gauging foliated SPT phases
• Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory
• Gapped boundaries of (3+1)d topological orders
• Reduced Conformal Symmetry
• Lattice Clifford fractons and their Chern-Simons-like theory
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Fractons on Graphs and Complexity
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
• Fractionalization of subsystem symmetries in two dimensions
• Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate
• Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions
• Boundary Modes in the Chamon Model
• Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions
• Comments on Quivers and Fractons
• Holographic subdiffusion
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Non-Fermi liquid induced by Bose metal with protected subsystem symmetries
• Topological order and Fractons from Gauging Exponential Symmetries
• Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models
• Asymptotic symmetries and soft charges of fractons
• Hall-like behaviour of higher rank Chern-Simons theory of fractons
• Covariant Interacting Fractons
• Anomalies in Covariant Fracton Theories
• Noninvertible operators in one, two, and three dimensions via gauging spatially modulated symmetry
• Fractons in effective field theories for spontaneously broken translations
• Anomalous diffusion and Noether's second theorem
• Interacting Fractons in 2+1-Dimensional Quantum Field Theory
• $U(1)$ symmetry-enriched toric code
• Hamiltonian Formulation of Higher Rank Symmetric Gauge Theories
• Quasi-topological fractons: a 3D dipolar gauge theory
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• A post-Gaussian approach to dipole symmetries and interacting fractons
• $\mathcal{N}=1$ Curves on Generalized Coulomb Branches
• Non-equilibrium dynamics of bosons with dipole symmetry: Large-$N$ Keldysh approach
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• A Multicritical Point with Infinite Fractal Symmetries
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Fractons in curved space
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Nonlinear Lifshitz Photon Theory in Condensed Matter Systems
• Fractonic criticality in Rydberg atom arrays
• Field Theories for type-II fractons
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Fractonic Coset Construction for Spontaneously Broken Translations
• Strings as Hyper-Fractons
• Electric-Magnetic Duality for Symmetric Tensor Gauge Theories and Immobile $p$-branes
• Quadrupole gauge theory: anti-Higgs mechanism and elastic dual
• Covariant Fractons and Weitzenböck Torsion
• Dual Description of Gauge Theories from an Iterative Noether Approach
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Covariant field theory of 3D massive fractons
• Fractons on the edge
• Hybrid Symmetry Breaking in Classical Spin Models With Subsystem Symmetries
• Entanglement renormalization of fractonic anisotropic ${\mathbb{Z}}_N$ Laplacian models
• Non-Fermi Liquids from Subsystem Symmetry Breaking in van der Waals Multilayers
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• A stabilizer code model with non-invertible symmetries: Strange fractons, confinement, and non-commutative and non-Abelian fusion rules
• Subsystem symmetries, critical Bose surface, and immobile excitations in an extended compass model
• Spontaneous Symmetry Breaking and Frustrated Phases
• Exotic theta terms in 2+1d fractonic field theory
• Covariant Fracton Electrodynamics in Six Dimensions
• Fracton models from product codes