Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory

Abstract

We extend our exploration of nonstandard continuum quantum field theories in 2+1 dimensions to 3+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global $U(1)$ symmetry and in a followup paper we will study models with a global ${\mathbb{Z}}_N$ symmetry.

74 pages. v3: significant changes

References in corpus (15)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Phases of Matter
• Fracton hydrodynamics
• Field Theories With a Vector Global Symmetry
• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Resonating plaquette phases in large spin cold atom systems
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Emergent fractons and algebraic quantum liquid from plaquette melting transitions
• Fractons with Twisted Boundary Conditions and Their Symmetries
• $(k,n)$-fractonic Maxwell theory
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Systematic Constructions of Fracton Theories

Cited by in corpus (110)

• Generalized Symmetries in Condensed Matter
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Foliated Quantum Field Theory of Fracton Order
• 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
• Exotic ${\mathbb{Z}}_N$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Spontaneous breaking of multipole symmetries
• Anomaly Inflow for Subsystem Symmetries
• More Exotic Field Theories in 3+1 Dimensions
• Subsystem Non-Invertible Symmetry Operators and Defects
• On completeness and generalized symmetries in quantum field theory
• Fractons with Twisted Boundary Conditions and Their Symmetries
• Fracton hydrodynamics without time-reversal symmetry
• Fractonic superfluids. (II). Condensing subdimensional particles
• 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
• Generalized Symmetries of the Graviton
• FCC, Checkerboards, Fractons, and QFT
• Quantum effects on unconventional pinch point singularities
• Bose-Luttinger Liquids
• Spontaneously Broken Subsystem Symmetries
• World-Line Description of Fractons
• 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
• Generating Lattice Non-invertible Symmetries
• Foliated BF theories and Multipole symmetries
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Maxwell theory of fractons
• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Fractonic order in infinite-component Chern-Simons gauge theories
• The theory of symmetric tensor field: from fractons to gravitons and back
• Boson-fermion duality with subsystem symmetry
• Fractons and exotic symmetries from branes
• Gauging fractons and linearized gravity
• Gapless edge modes in (4+1)-dimensional topologically massive tensor gauge theory and anomaly inflow for subsystem symmetry
• Emergent tracer dynamics in constrained quantum systems
• Fracton Topological Order at Finite Temperature
• Boundary theory of the X-cube model in the continuum
• Foliated-Exotic Duality in Fractonic BF Theories
• A Chern-Simons theory for dipole symmetry
• Quantizing Carrollian field theories
• A symmetry principle for gauge theories with fractons
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions
• Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries
• Fractonic plaquette-dimer liquid beyond renormalization
• Gapped Lineon and Fracton Models on Graphs
• Covariant fracton gauge theory with boundary
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Ultraviolet-Infrared Mixing in Marginal Fermi Liquids
• Gapped boundaries of (3+1)d topological orders
• Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries
• Lattice Clifford fractons and their Chern-Simons-like theory
• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Fractons on Graphs and Complexity
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
• Fractonic topological phases from coupled wires
• Fractionalization of subsystem symmetries in two dimensions
• Topological Dipole Conserving Insulators and Multipolar Responses
• Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions
• Anyon condensation web and multipartite entanglement in 2D modulated gauge theories
• Boundary Modes in the Chamon Model
• Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions
• Spectroscopic fingerprints of gapless type-II fracton phases
• Holographic subdiffusion
• Comments on Quivers and Fractons
• Screw dislocations in the X-cube fracton model
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Asymptotic symmetries and soft charges of fractons
• Snowmass White Paper: The Quest to Define QFT
• Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models
• Hall-like behaviour of higher rank Chern-Simons theory of fractons
• Covariant Interacting Fractons
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• $U(1)$ symmetry-enriched toric code
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Interacting Fractons in 2+1-Dimensional Quantum Field Theory
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• A post-Gaussian approach to dipole symmetries and interacting fractons
• Fractonic self-duality and covariant magnetic fractons
• Fractonic Berezinskii-Kosterlitz-Thouless transition from a renormalization group perspective
• Non-equilibrium dynamics of bosons with dipole symmetry: Large-$N$ Keldysh approach
• Fractons in curved space
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Surface Operators in Superspace
• Fractonic criticality in Rydberg atom arrays
• Nonlinear Lifshitz Photon Theory in Condensed Matter Systems
• Neural Quantum State Study of Fracton Models
• Strings as Hyper-Fractons
• Field Theories for type-II fractons
• Supersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases
• Dual Description of Gauge Theories from an Iterative Noether Approach
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• Electric-Magnetic Duality for Symmetric Tensor Gauge Theories and Immobile $p$-branes
• Shift symmetries and duality web in gauge theories
• Hybrid Symmetry Breaking in Classical Spin Models With Subsystem Symmetries
• A pedagogical review of gravity as a gauge theory
• A stabilizer code model with non-invertible symmetries: Strange fractons, confinement, and non-commutative and non-Abelian fusion rules
• Spontaneous Symmetry Breaking and Frustrated Phases
• Collective dynamics in holographic fractonic solids
• Hollow Lattice Tensor Gauge Theories with Bosonic Matter
• Exotic theta terms in 2+1d fractonic field theory
• Emergent fracton strings from covariant bi-form gauge field theory