SciPost Physics

Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

Nathan Seiberg, Shu-Heng Shao

SciPost Phys. 9, 046 (2020) · published 5 October 2020

• doi: 10.21468/SciPostPhys.9.4.046
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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.

• Rudelius et al., Fractons with twisted boundary conditions and their symmetries
  Phys. Rev. B 103, 195113 (2021) [Crossref]
• Fazza et al., Lattice quantum Villain Hamiltonians: compact scalars, U(1) gauge theories, fracton models and quantum Ising model dualities
  J. High Energ. Phys. 2023, 17 (2023) [Crossref]
• Lake et al., Subdimensional criticality: Condensation of lineons and planons in the X-cube model
  Phys. Rev. B 104, 165121 (2021) [Crossref]
• Gorantla et al., (2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons
  Phys. Rev. B 108, 075106 (2023) [Crossref]
• Chen et al., Fractonic superfluids. II. Condensing subdimensional particles
  Phys. Rev. Research 3, 013226 (2021) [Crossref]
• Casini et al., On completeness and generalized symmetries in quantum field theory
  Mod. Phys. Lett. A 36, 2130025 (2021) [Crossref]
• Cremonini et al., Surface operators in superspace
  J. High Energ. Phys. 2020, 50 (2020) [Crossref]
• Feldmeier et al., Emergent tracer dynamics in constrained quantum systems
  Phys. Rev. B 106, 094303 (2022) [Crossref]
• Fontana et al., Boundary modes in the Chamon model
  SciPost Phys. 15, 010 (2023) [Crossref]
• Benedetti et al., Generalized symmetries of the graviton
  J. High Energ. Phys. 2022, 45 (2022) [Crossref]
• Lake et al., Bose-Luttinger liquids
  Phys. Rev. B 104, 014517 (2021) [Crossref]
• Stephen et al., Fractionalization of subsystem symmetries in two dimensions
  Phys. Rev. B 106, 085104 (2022) [Crossref]
• McGreevy, Generalized Symmetries in Condensed Matter
  Annu. Rev. Condens. Matter Phys. 14, 57 (2023) [Crossref]
• Casalbuoni et al., Worldline description of fractons
  Phys. Rev. D 104, 125013 (2021) [Crossref]
• Rayhaun et al., Higher-form subsystem symmetry breaking: Subdimensional criticality and fracton phase transitions
  SciPost Phys. 15, 017 (2023) [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]
• Pérez et al., Asymptotic symmetries and soft charges of fractons
  Phys. Rev. D 106, 044017 (2022) [Crossref]
• Fontana et al., Field Theories for type-II fractons
  SciPost Phys. 12, 064 (2022) [Crossref]
• Gorantla et al., Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons
  Phys. Rev. B 106, 045112 (2022) [Crossref]
• Hsin et al., Comments on foliated gauge theories and dualities in 3+1d
  SciPost Phys. 11, 032 (2021) [Crossref]
• Ganesan et al., Holographic subdiffusion
  J. High Energ. Phys. 2020, 149 (2020) [Crossref]
• Delfino et al., Effective fractonic behavior in a two-dimensional exactly solvable spin liquid
  SciPost Phys. 14, 002 (2023) [Crossref]
• Zhang et al., Dynamical signatures of rank-2 U(1) spin liquids
  Phys. Rev. B 105, L060408 (2022) [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]
• Ma et al., Fractonic order in infinite-component Chern-Simons gauge theories
  Phys. Rev. B 105, 195124 (2022) [Crossref]
• Gorantla et al., Low-energy limit of some exotic lattice theories and UV/IR mixing
  Phys. Rev. B 104, 235116 (2021) [Crossref]
• Li et al., Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
  Phys. Rev. B 104, 235127 (2021) [Crossref]
• Niggemann et al., Quantum Effects on Unconventional Pinch Point Singularities
  Phys. Rev. Lett. 130, 196601 (2023) [Crossref]
• Dedushenko, Snowmass white paper: The quest to define QFT
  Int. J. Mod. Phys. A 38, 2330002 (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]
• Jain et al., Fractons in curved space
  SciPost Phys. 12, 142 (2022) [Crossref]
• Oh et al., Effective field theory of dipolar braiding statistics in two dimensions
  Phys. Rev. B 106, 155150 (2022) [Crossref]
• You et al., Fracton critical point at a higher-order topological phase transition
  Phys. Rev. B 106, 235130 (2022) [Crossref]
• Hart et al., Spectroscopic fingerprints of gapless type-II fracton phases
  Phys. Rev. B 105, L180416 (2022) [Crossref]
• Lehmann et al., Fragmentation-induced localization and boundary charges in dimensions two and above
  SciPost Phys. 14, 140 (2023) [Crossref]
• Fontana et al., Lattice Clifford fractons and their Chern-Simons-like theory
  SciPost Phys. Core 4, 012 (2021) [Crossref]
• Molina-Vilaplana, A post-Gaussian approach to dipole symmetries and interacting fractons
  J. High Energ. Phys. 2023, 65 (2023) [Crossref]
• Sullivan et al., Fractonic topological phases from coupled wires
  Phys. Rev. Research 3, 023123 (2021) [Crossref]
• Distler et al., Spontaneously broken subsystem symmetries
  J. High Energ. Phys. 2022, 16 (2022) [Crossref]
• Jian et al., Note on generalized symmetries, gapless excitations, generalized symmetry protected topological states, and anomaly
  J. Stat. Mech. 2021, 033102 (2021) [Crossref]
• Geng et al., Fractons and Exotic Symmetries from Branes
  Fortschritte der Physik 69, 2100133 (2021) [Crossref]
• Gorantla et al., A modified Villain formulation of fractons and other exotic theories
  62, 102301 (2021) [Crossref]
• Distler et al., Interacting fractons in 2+1-dimensional quantum field theory
  J. High Energ. Phys. 2022, 70 (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]
• Gorantla et al., fcc lattice, checkerboards, fractons, and quantum field theory
  Phys. Rev. B 103, 205116 (2021) [Crossref]
• Glorioso et al., Breakdown of hydrodynamics below four dimensions in a fracton fluid
  Nat. Phys. 18, 912 (2022) [Crossref]
• Gorantla et al., Gapped lineon and fracton models on graphs
  Phys. Rev. B 107, 125121 (2023) [Crossref]
• Katsura et al., Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries
  J. High Energ. Phys. 2022, 72 (2022) [Crossref]
• Ohmori et al., Foliated-exotic duality in fractonic BF theories
  SciPost Phys. 14, 164 (2023) [Crossref]
• Guo et al., Fracton Hydrodynamics without Time-Reversal Symmetry
  Phys. Rev. Lett. 129, 150603 (2022) [Crossref]
• Sala et al., Dynamics in Systems with Modulated Symmetries
  Phys. Rev. Lett. 129, 170601 (2022) [Crossref]
• Fliss, Entanglement in the quantum Hall fluid of dipoles
  SciPost Phys. 11, 052 (2021) [Crossref]
• Grosvenor et al., Fractonic Berezinskii-Kosterlitz-Thouless transition from a renormalization group perspective
  Phys. Rev. B 107, 045139 (2023) [Crossref]
• You et al., Fractonic plaquette-dimer liquid beyond renormalization
  Phys. Rev. B 106, 115145 (2022) [Crossref]
• Gorantla et al., Fractons on graphs and complexity
  Phys. Rev. B 106, 195139 (2022) [Crossref]
• Manoj et al., Screw dislocations in the X-cube fracton model
  SciPost Phys. 10, 094 (2021) [Crossref]
• Angus et al., Fractons, non-Riemannian geometry, and double field theory
  Phys. Rev. Research 4, 033186 (2022) [Crossref]
• Shen et al., Fracton topological order at finite temperature
  Phys. Rev. Research 4, L032008 (2022) [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]
• Lake, Renormalization group and stability in the exciton Bose liquid
  Phys. Rev. B 105, 075115 (2022) [Crossref]
• Blasi et al., The theory of symmetric tensor field: From fractons to gravitons and back
  Physics Letters B 833, 137304 137304 (2022) [Crossref]
• Yamaguchi, Supersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases
  2021, 063B04 (2021) [Crossref]
• Casasola et al., Spontaneous symmetry breaking and frustrated phases
  Phys. Rev. E 104, 034131 (2021) [Crossref]
• Qi et al., Anomalous hydrodynamics with triangular point group in 2+1 dimensions
  Phys. Rev. B 107, 144305 (2023) [Crossref]
• Han et al., Realization of fractonic quantum phases in the breathing pyrochlore lattice
  Phys. Rev. B 105, 235120 (2022) [Crossref]
• Bertolini et al., Maxwell theory of fractons
  Phys. Rev. D 106, 125008 (2022) [Crossref]
• Canossa et al., Hybrid symmetry breaking in classical spin models with subsystem symmetries
  Phys. Rev. B 107, 054431 (2023) [Crossref]
• Stahl et al., Spontaneous breaking of multipole symmetries
  Phys. Rev. B 105, 155107 (2022) [Crossref]
• Razamat, Quivers and Fractons
  Phys. Rev. Lett. 127, 141603 (2021) [Crossref]
• Seiberg et al., Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory
  SciPost Phys. 10, 027 (2021) [Crossref]
• Ye et al., Ultraviolet-Infrared Mixing in Marginal Fermi Liquids
  Phys. Rev. Lett. 128, 106402 (2022) [Crossref]
• Cao et al., Boson-fermion duality with subsystem symmetry
  Phys. Rev. B 106, 075150 (2022) [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]
• Bertolini et al., Covariant fracton gauge theory with boundary
  Phys. Rev. D 108, 025009 (2023) [Crossref]
• Gorantla et al., More exotic field theories in 3+1 dimensions
  SciPost Phys. 9, 073 (2020) [Crossref]
• Bertolini et al., Gauging Fractons and Linearized Gravity
  Symmetry 15, 945 (2023) [Crossref]
• Burnell et al., Anomaly inflow for subsystem symmetries
  Phys. Rev. B 106, 085113 (2022) [Crossref]
• Li et al., Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
  Phys. Rev. Research 3, 043176 (2021) [Crossref]