First order Galilean superfluid dynamics

Abstract

We study dynamics of an (anomalous) Galilean superfluid up to first order in derivative expansion, both in parity-even and parity-odd sectors. We construct a relativistic system—null superfluid, which is a null fluid (introduced in N. Banerjee, S. Dutta, and A. Jain Akash, [Phys. Rev. D 93, 105020 (2016).]) with a spontaneously broken global U(1) symmetry. A null superfluid is in one-to-one correspondence with a Galilean superfluid in one lower dimension; i.e., they have the same symmetries, thermodynamics, constitutive relations and are related to each other by a mere choice of basis. The correspondence is based on null reduction, which is known to reduce the Poincaré symmetry of a theory to Galilean symmetry in one lower dimension. To perform this analysis, we use off-shell formalism of (super)fluid dynamics, adopting it appropriately to null (super)fluids. We also verify these results via c→∞ limit of a parent relativistic system.