Null Fluids - A New Viewpoint of Galilean Fluids

Abstract

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.

50+1 pages, extended version of [arXiv:1505.05677]

References in corpus (14)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Revisiting non-relativistic limits
• The eightfold way to dissipation
• Fields and fluids on curved non-relativistic spacetimes
• Conformal non-relativistic hydrodynamics from gravity
• A new formulation of non-relativistic diffeomorphism invariance
• Aspects of hot Galilean field theory
• Anomalies for Galilean fields
• General algorithm for non-relativistic diffeomorphism invariance
• Galilean Anomalies and Their Effect on Hydrodynamics
• Equilibrium partition function for nonrelativistic fluids
• Localisation of the Galilean symmetry and dynamical realisation of Newton-Cartan geometry
• Entropy current for non-relativistic fluid
• Higher Derivative Corrections to Charged Fluids in 2n Dimensions

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• Lifshitz Hydrodynamics from Lifshitz Black Branes with Linear Momentum
• Equilibrium partition function for nonrelativistic fluids
• Surface transport in plasma-balls
• A theory for non-Abelian superfluid dynamics
• Effective field theory for non-relativistic hydrodynamics
• Existence and Construction of Galilean invariant $z\ne 2$ Theories
• Hydrodynamics of plastic deformations in electronic crystals
• First Order Galilean Superfluid Dynamics
• Gravitational anomalies on the Newton-Cartan background
• Nonrelativistic hydrodynamics from quantum field theory: (I) Normal fluid composed of spinless Schrödinger fields
• Chiral Torsional Effects in Anomalous Fluids in Thermal Equilibrium
• Non-relativistic transport from frame-indifferent kinetic theory
• Holographic Constraints on Generalised Rivlin-Ericksen Fluid
• Second order Galilean fluids & Stokes' law