Fracton Magnetohydrodynamics with Momentum Conservation

The hydrodynamics of systems with multipolar symmetries (known as fracton hydrodynamics) can exhibit exotic behavior, such as emergent subdiffusion. We develop a hydrodynamic theory of systems with gauged charge and dipole symmetries and globally conserved momentum using the Martin-Siggia-Rose (MSR) effective field theory (EFT) formalism. We explicitly construct the entropy current and derive first-order dissipative corrections to hydrodynamics. Because we construct our theory from the level of symmetries, it is robust to microscopic details. Our approach also generalizes the EFT for magnetohydrodynamics (MHD) with momentum conservation developed in https://arxiv.org/pdf/1610.07392 to non-relativistic fluids.