Null fluids: A new viewpoint of Galilean fluids

Abstract

In this article, we study a Galilean fluid with a conserved U ( 1 ) current up to anomalies. We construct a relativistic system, which we call a 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 Poincaré 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 the 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.