SciPost Physics

Field theories with a vector global symmetry

Nathan Seiberg

SciPost Phys. 8, 050 (2020) · published 3 April 2020

• doi: 10.21468/SciPostPhys.8.4.050
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They differ by the equations their Noether currents satisfy. Simple cases, other than the translation symmetry, are an ordinary (relativistic) one-form global symmetry and its nonrelativistic generalization. In the latter case the conserved charge is associated with a codimension-one spatial manifold, but it is not topological. More general examples involve charges that are integrated over the entire space. We also discuss the coupling of these systems to gauge fields for these symmetries. We relate our examples to known continuum and lattice constructions.

• Manoj et al., Fractonic View of Folding and Tearing Paper: Elasticity of Plates Is Dual to a Gauge Theory with Vector Charges
  Phys. Rev. Lett. 127, 067601 (2021) [Crossref]
• Figueroa-O’Farrill et al., Quantum Carroll/fracton particles
  J. High Energ. Phys. 2023, 41 (2023) [Crossref]
• Han et al., Realization of fractonic quantum phases in the breathing pyrochlore lattice
  Phys. Rev. B 105, 235120 (2022) [Crossref]
• Brauner, Field theories with higher-group symmetry from composite currents
  J. High Energ. Phys. 2021, 45 (2021) [Crossref]
• Honda et al., Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d + 1 dimensions
  J. High Energ. Phys. 2023, 188 (2023) [Crossref]
• Yamaguchi, Supersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases
  2021, 063B04 (2021) [Crossref]
• Phillips et al.,
  335, 135 (2020) [Crossref]
• Du et al., Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry
  SciPost Phys. 12, 050 (2022) [Crossref]
• Gorantla et al., fcc lattice, checkerboards, fractons, and quantum field theory
  Phys. Rev. B 103, 205116 (2021) [Crossref]
• Razamat, Quivers and Fractons
  Phys. Rev. Lett. 127, 141603 (2021) [Crossref]
• Choi et al., Noninvertible duality defects in 3+1 dimensions
  Phys. Rev. D 105, 125016 (2022) [Crossref]
• Ning et al., Fractionalizing global symmetry on looplike topological excitations
  Phys. Rev. B 105, 205137 (2022) [Crossref]
• Bidussi et al., Fractons, dipole symmetries and curved spacetime
  SciPost Phys. 12, 205 (2022) [Crossref]
• Zhou et al., Detecting subsystem symmetry protected topological order through strange correlators
  Phys. Rev. B 106, 214428 (2022) [Crossref]
• Ohmori et al., Foliated-exotic duality in fractonic BF theories
  SciPost Phys. 14, 164 (2023) [Crossref]
• Gorantla et al., Gapped lineon and fracton models on graphs
  Phys. Rev. B 107, 125121 (2023) [Crossref]
• Gromov et al., Fracton hydrodynamics
  Phys. Rev. Research 2, 033124 (2020) [Crossref]
• Grosvenor et al., Hydrodynamics of ideal fracton fluids
  Phys. Rev. Research 3, 043186 (2021) [Crossref]
• Fontana et al., Field Theories for type-II fractons
  SciPost Phys. 12, 064 (2022) [Crossref]
• Pérez et al., Asymptotic symmetries and soft charges of fractons
  Phys. Rev. D 106, 044017 (2022) [Crossref]
• Lake et al., Dipolar Bose-Hubbard model
  Phys. Rev. B 106, 064511 (2022) [Crossref]
• Zhu et al., Topological Fracton Quantum Phase Transitions by Tuning Exact Tensor Network States
  Phys. Rev. Lett. 130, 216704 (2023) [Crossref]
• Yuan et al., Quantum Hydrodynamics of Fractonic Superfluids with Lineon Condensate: From Navier–Stokes-Like Equations to Landau-Like Criterion
  Chinese Phys. Lett. 39, 057101 (2022) [Crossref]
• Cremonini et al., Surface operators in superspace
  J. High Energ. Phys. 2020, 50 (2020) [Crossref]
• Seiberg et al., Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory
  SciPost Phys. 10, 027 (2021) [Crossref]
• Biswas et al., Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models
  SciPost Phys. 12, 148 (2022) [Crossref]
• Stahl et al., Spontaneous breaking of multipole symmetries
  Phys. Rev. B 105, 155107 (2022) [Crossref]
• Luo et al., Boundary theory of the X-cube model in the continuum
  Phys. Rev. B 106, 195102 (2022) [Crossref]
• Luo, Gapped boundaries of (3+1) -dimensional topological order
  Phys. Rev. B 107, 125425 (2023) [Crossref]
• Dubinkin et al., Higher-form gauge symmetries in multipole topological phases
  Annals of Physics 422, 168297 168297 (2020) [Crossref]
• Gorantla et al., More exotic field theories in 3+1 dimensions
  SciPost Phys. 9, 073 (2020) [Crossref]
• Yuan et al., Fractonic superfluids
  Phys. Rev. Research 2, 023267 (2020) [Crossref]
• Jian et al., Physics of symmetry protected topological phases involving higher symmetries and its applications
  Phys. Rev. B 103, 064426 (2021) [Crossref]
• Rudelius et al., Fractons with twisted boundary conditions and their symmetries
  Phys. Rev. B 103, 195113 (2021) [Crossref]
• Slagle, Foliated Quantum Field Theory of Fracton Order
  Phys. Rev. Lett. 126, 101603 (2021) [Crossref]
• May-Mann et al., Topological dipole conserving insulators and multipolar responses
  Phys. Rev. B 104, 085136 (2021) [Crossref]
• Cao et al., Boson-fermion duality with subsystem symmetry
  Phys. Rev. B 106, 075150 (2022) [Crossref]
• Banerjee et al., Shift symmetries and duality web in gauge theories
  Nuclear Physics B 996, 116354 116354 (2023) [Crossref]
• Wang et al., Higher-rank tensor non-Abelian field theory: Higher-moment or subdimensional polynomial global symmetry, algebraic variety, Noether's theorem, and gauging
  Phys. Rev. Research 3, 013185 (2021) [Crossref]
• Banerjee, Hamiltonian formulation of higher rank symmetric gauge theories
  Eur. Phys. J. C 82, 22 (2022) [Crossref]
• Burnell et al., Anomaly inflow for subsystem symmetries
  Phys. Rev. B 106, 085113 (2022) [Crossref]
• Seiberg et al., Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory
  SciPost Phys. 9, 046 (2020) [Crossref]
• Stahl, Self-Correction from Higher-Form Symmetry Protection on a Boundary
  PRX Quantum 4, 030341 (2023) [Crossref]
• Angus et al., Fractons, non-Riemannian geometry, and double field theory
  Phys. Rev. Research 4, 033186 (2022) [Crossref]
• Rayhaun et al., Higher-form subsystem symmetry breaking: Subdimensional criticality and fracton phase transitions
  SciPost Phys. 15, 017 (2023) [Crossref]
• Qi et al., Anomalous hydrodynamics with triangular point group in 2+1 dimensions
  Phys. Rev. B 107, 144305 (2023) [Crossref]
• McGreevy, Generalized Symmetries in Condensed Matter
  Annu. Rev. Condens. Matter Phys. 14, 57 (2023) [Crossref]
• Yamaguchi, Gapless edge modes in (4+1)-dimensional topologically massive tensor gauge theory and anomaly inflow for subsystem symmetry
  2022, 033B08 (2022) [Crossref]
• Dedushenko, Snowmass white paper: The quest to define QFT
  Int. J. Mod. Phys. A 38, 2330002 (2023) [Crossref]
• Kaya et al., Higher-group symmetries and weak gravity conjecture mixing
  J. High Energ. Phys. 2022, 40 (2022) [Crossref]
• Myerson-Jain et al., Multicritical point with infinite fractal symmetries
  Phys. Rev. B 106, 115130 (2022) [Crossref]
• Craig, Naturalness: past, present, and future
  Eur. Phys. J. C 83, 825 (2023) [Crossref]
• Gliozzi et al., Hierarchical hydrodynamics in long-range multipole-conserving systems
  Phys. Rev. B 108, 195106 (2023) [Crossref]
• Duan et al., ℤN duality and parafermions revisited
  J. High Energ. Phys. 2023, 206 (2023) [Crossref]
• Devakul et al., Fractalizing quantum codes
  Quantum 5, 438 438 (2021) [Crossref]
• Seiberg et al., Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory
  SciPost Phys. 10, 003 (2021) [Crossref]
• Gorantla et al., Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons
  Phys. Rev. B 106, 045112 (2022) [Crossref]
• Geng et al., Fractons and Exotic Symmetries from Branes
  Fortschritte der Physik 69, 2100133 (2021) [Crossref]
• Grosvenor et al., Space-Dependent Symmetries and Fractons
  Front. Phys. 9, 792621 (2022) [Crossref]
• Zhou et al., Evolution of dynamical signature in the X-cube fracton topological order
  Phys. Rev. Research 4, 033111 (2022) [Crossref]
• Fuji et al., Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
  Phys. Rev. Research 5, 043108 (2023) [Crossref]
• Gorantla et al., (2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons
  Phys. Rev. B 108, 075106 (2023) [Crossref]
• Gorantla et al., Fractons on graphs and complexity
  Phys. Rev. B 106, 195139 (2022) [Crossref]
• Tantivasadakarn, Jordan-Wigner dualities for translation-invariant Hamiltonians in any dimension: Emergent fermions in fracton topological order
  Phys. Rev. Research 2, 023353 (2020) [Crossref]
• Osborne et al., Infinite families of fracton fluids with momentum conservation
  Phys. Rev. B 105, 024311 (2022) [Crossref]
• Chen et al., Fractonic superfluids. II. Condensing subdimensional particles
  Phys. Rev. Research 3, 013226 (2021) [Crossref]
• Jian et al., Note on generalized symmetries, gapless excitations, generalized symmetry protected topological states, and anomaly
  J. Stat. Mech. 2021, 033102 (2021) [Crossref]
• Distler et al., Spontaneously broken subsystem symmetries
  J. High Energ. Phys. 2022, 16 (2022) [Crossref]
• Wu et al., Categorical symmetries at criticality
  J. Stat. Mech. 2021, 073101 (2021) [Crossref]
• Gorantla et al., A modified Villain formulation of fractons and other exotic theories
  62, 102301 (2021) [Crossref]
• Marsot et al., Hall motions in Carroll dynamics
  Physics Reports 1028, 1 (2023) [Crossref]
• Qi et al., Fracton phases via exotic higher-form symmetry-breaking
  Annals of Physics 424, 168360 168360 (2021) [Crossref]
• Manoj et al., Arboreal topological and fracton phases
  Phys. Rev. B 107, 165136 (2023) [Crossref]
• Wang et al., Non-Abelian gauged fracton matter field theory: Sigma models, superfluids, and vortices
  Phys. Rev. Research 2, 043219 (2020) [Crossref]
• Distler et al., Interacting fractons in 2+1-dimensional quantum field theory
  J. High Energ. Phys. 2022, 70 (2022) [Crossref]
• Gomes, An introduction to higher-form symmetries
  SciPost Phys. Lect. Notes, 74 (2023) [Crossref]
• Gorantla et al., Low-energy limit of some exotic lattice theories and UV/IR mixing
  Phys. Rev. B 104, 235116 (2021) [Crossref]
• Sullivan et al., Planar p-string condensation: Chiral fracton phases from fractional quantum Hall layers and beyond
  Phys. Rev. B 103, 205301 (2021) [Crossref]
• Song et al., Topological Defect Network Representations of Fracton Stabilizer Codes
  PRX Quantum 4, 010304 (2023) [Crossref]
• Xu et al., Deconfined quantum critical point with nonlocality
  Phys. Rev. B 106, 155131 (2022) [Crossref]
• Aasen et al., Topological defect networks for fractons of all types
  Phys. Rev. Research 2, 043165 (2020) [Crossref]
• Sullivan et al., Fractonic topological phases from coupled wires
  Phys. Rev. Research 3, 023123 (2021) [Crossref]
• Banerjee, Dual description of gauge theories from an iterative Noether approach
  Nuclear Physics B 981, 115875 115875 (2022) [Crossref]
• Fontana et al., Lattice Clifford fractons and their Chern-Simons-like theory
  SciPost Phys. Core 4, 012 (2021) [Crossref]
• Gerhardinger et al., Well-posed UV completion for simulating scalar Galileons
  Phys. Rev. D 106, 043522 (2022) [Crossref]
• Cao et al., Subsystem non-invertible symmetry operators and defects
  SciPost Phys. 15, 155 (2023) [Crossref]