Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

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