Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

Abstract

We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the nonlinear sigma models of ferromagnets in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.

arXiv commentTypos are fixed. Comments are welcome!

References in corpus (46)

• Local stabilizer codes in three dimensions without string logical operators
• Quantum Glassiness
• Fractons
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Fracton Phases of Matter
• Hall Viscosity and Electromagnetic Response
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Fracton-Elasticity Duality
• Topological order in an exactly solvable 3D spin model
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• Infinite Symmetry in the Quantum Hall Effect
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Spacetime Symmetries of the Quantum Hall Effect
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Towards classification of Fracton phases: the multipole algebra
• Skyrmion dynamics in chiral ferromagnets
• Dual gauge field theory of quantum liquid crystals in two dimensions
• Field Theories With a Vector Global Symmetry
• Chiral Topological Elasticity and Fracton Order
• The Magnus Force on Skyrmions in Ferromagnets and the Quantum Hall Effect
• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Emergent Phases of Fractonic Matter
• Bimetric Theory of Fractional Quantum Hall States
• Conformal Symmetry and Universal Properties of Quantum Hall States
• Dual gauge field theory of quantum liquid crystals in three dimensions
• Symmetry Enriched Fracton Phases from Supersolid Duality
• Classification of Quantum Hall Universality Classes by $W_{1+\infty }$ symmetry
• Fractonic Chern-Simons and BF theories
• Fracton phases via exotic higher-form symmetry-breaking
• Large N Limit in the Quantum Hall Effect
• Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting
• Area-preserving diffeomorphisms, W_{\infty} and $U_{q}(sl(2)) in Chern-Simons theory and Quantum Hall system
• Topological kinematic constraints: quantum dislocations and the glide principle
• Quantum smectic gauge theory
• Particle-hole symmetry and composite fermions in fractional quantum Hall states
• Novel Algebraic Boson Liquid phase with soft Graviton excitations
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Multipole Expansion in the Quantum Hall Effect
• Field theories with higher-group symmetry from composite currents
• Higher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging
• Bosonic superfluid on lowest Landau level
• Fractonic gauge theory of smectics
• Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices
• Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon
• Lowest Landau Level Stress Tensor and Structure Factor of Trial Quantum Hall Wave Functions

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