Null Fluids - A New Viewpoint of Galilean Fluids

This article is a detailed version of our short letter `On equilibrium partition function for non-relativistic fluid' [arXiv:1505.05677] extended to include an anomalous $U(1)$ symmetry. We construct a relativistic system, which we call null fluid and show that it is in one-to-one correspondence with a Galilean fluid living in one lower dimension. The correspondence is based on light cone reduction, which is known to reduce the Poincare symmetry of a theory to Galilean in one lower dimension. We show that the proposed null fluid and the corresponding Galilean fluid have exactly same symmetries, thermodynamics, constitutive relations, and equilibrium partition to all orders in derivative expansion. We also devise a mechanism to introduce $U(1)$ anomaly in even dimensional Galilean theories using light cone reduction, and study its effect on the constitutive relations of a Galilean Fluid.