Hydrodynamics with exotic charges and currents: multipole conservation, higher form symmetry, and beyond

We explore the landscape of possible hydrodynamic universality classes that can arise out of: conserved quantities that transform non-trivially under spatial point group symmetries, currentsin non-standard representations of the point group, and/or higher-deriative generalizations of thecharge conservation Ward identity. Our framework links together numerous existing theories, including magnetohydrodynamics and fracton hydrodynamics; moreover, it can easily be extended to generate infinite families of new universality classes. As an application, we introduce a new class of hydrodynamics exhibiting almost-conserved quantities and dangerously irrelevant operators and fluctuations; as another, we derive the analogue of magnetohydrodynamics for higher rank gauge fields.