Galilean Anomalies and Their Effect on Hydrodynamics

Abstract

We extend the null background construction of [arXiv:1505.05677,arXiv:1509.04718] to include torsion and a conserved spin current, and use it to study gauge and gravitational anomalies in Galilean theories coupled to torsional Newton-Cartan backgrounds. We establish that the relativistic anomaly inflow mechanism with an appropriately modified anomaly polynomial, can be used to generate these anomalies. Similar to relativistic case, we find that Galilean anomalies also survive only in even dimensions. Further, these anomalies only effect the gauge and rotational symmetries of a Galilean theory; in particular the Milne boost symmetry remains non-anomalous. We also extend the transgression machinery used in relativistic fluids to fluids on null backgrounds, and use it to determine how these anomalies affect the constitutive relations of a Galilean fluid. Unrelated to Galilean fluids, we propose an analogue of the off-shell second law of thermodynamics for relativistic fluids introduced by [arXiv:1106.0277], to include torsion and a conserved spin current in Vielbein formalism. Interestingly, we find that even in absense of spin and torsion the entropy currents in two formalisms are different; while the usual entropy current gets a contribution from gravitational anomaly, the entropy current in Vielbein formalism does not have any anomaly induced part.

41+1 pages

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Cited by in corpus (25)

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• Null Fluids - A New Viewpoint of Galilean Fluids
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• Galilean Yang-Mills Theory
• Effective field theory for non-relativistic hydrodynamics
• Hydrodynamic effective field theories with discrete rotational symmetry
• Spinor fields in general Newton-Cartan backgrounds
• First Order Galilean Superfluid Dynamics
• Quantization of Interacting Galilean Field theories
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• Anomalous Currents and Constitutive Relations of a Chiral Hadronic Superfluid
• Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure
• Gravitational anomalies on the Newton-Cartan background
• Chiral Torsional Effects in Anomalous Fluids in Thermal Equilibrium
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• New formulation of Galilean relativistic Maxwell theory
• Sengupta Transformations and Carrollian Relativistic Theory
• Galilean fermions: Classical and quantum aspects
• Action principle of Galilean relativistic Proca theory
• Holographic Constraints on Generalised Rivlin-Ericksen Fluid
• Formulation of Galilean relativistic Born-Infeld theory
• Canonical Formulation for a Non-relativistic Spinning Particle Coupled to Gravity
• Second order Galilean fluids & Stokes' law