Breakdown and Restoration of Hydrodynamics in Dipole-conserving Active Fluids

We present a general hydrodynamic theory for active fluids, capable of describing living matter, that conserve center of mass or dipole moment. Imposition of dipole or center-of-mass conservation has been reported to yield peculiar behavior: breaking Galilean invariance in classical systems and potentially enabling exotic immobile excitations in quantum settings. In passive fluids, dipole conservation has been shown to cause a breakdown of linear hydrodynamics in all experimentally relevant dimensions. We show that introducing activity changes this picture: it can either restore or break linear hydrodynamics depending on spatial dimensions. Using our formulation, we predict universal dynamical scaling exponents for single-component active fluids in $d=1,2,3$ dimensions and find agreement with microscopic lattice-field simulations. Strikingly, for $d\geq 2$, activity revives linear hydrodynamics, while for $d<2$ it leads to a breakdown; both cases flow to previously unexplored universality classes. Our results suggest that dipole-conserving active fluids are far more experimentally accessible than their passive counterparts.