Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

Higher-rank gauge theories have been drawing attention in condensed matter physics in recent years. The physical motivation of such theories is thought to be associated with a new class of topological matter so-called "fractons," quasiparticles with restricted mobility. We demonstrate a nonlinear version of the higher rank gauge symmetry in 2+1D and 3+1D with volume-preserving diffeomorphism as the symmetry group. We show that various condensed matter systems, including fractional quantum Hall effect and ferromagnetism, possess this symmetry, which exhibits fractonic behavior of the excitations in these systems.