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Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

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arxiv 2103.09826 v6 pith:UO7N34L6 submitted 2021-03-17 cond-mat.str-el cond-mat.mes-hallcond-mat.quant-gashep-th

Yi-Hsien Du , Umang Mehta , Dung Xuan Nguyen , Dam Thanh Son This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hallcond-mat.quant-gashep-th
keywords gaugehigher-ranksymmetrycrystalderiveferromagnetslandaulevel
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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.

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Cited by 3 Pith papers

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  1. Chiral Graviton Theory of Fractional Quantum Hall States

    cond-mat.str-el 2025-09 conditional novelty 6.0 of 10

    By gauging area-preserving diffeomorphisms and adding a Stueckelberg mass term, the paper constructs a nonlinear effective theory whose quadratic limit reproduces the bimetric description of the chiral spin-2 magnetoroton.

  2. Breakdown of hydrodynamics in a Galilean quantum Hall crystal

    cond-mat.mes-hall 2024-12 conditional novelty 6.0 of 10

    In a Galilean-invariant quantum Hall crystal, nonlinear fluctuations destabilize the linear-response magnetophonon and drive its dynamical exponent from z=4 to z≈3.

  3. Notes from the bulk

    hep-th 2025-07 conditional novelty 4.0 of 10

    A boundary-QFT analysis shows that curved bulk metrics create local edge velocities in topological models and that fracton and linearized-gravity theories carry Kac-Moody boundary algebras.

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