Abstract
The derivation of Lifshitz-invariant hydrodynamics from holography, presented in [1] is generalized to arbitrary hyperscaling violating Lifshitz scaling theories with an unbroken U(1) symmetry. The hydrodynamics emerging is non-relativistic with scalar “forcing”. By a redefinition of the pressure it becomes standard non-relativistic hydrodynamics in the presence of specific chemical potential for the mass current. The hydrodynamics is compatible with the scaling theory of Lifshitz invariance with hyperscaling violation. The bulk viscosity vanishes while the shear viscosity to entropy ratio is the same as in the relativistic case. We also consider the dimensional reduction ansatz for the hydrodynamics and clarify the difference with previous results suggesting a non-vanishing bulk viscosity.
Highlights
The derivation of Lifshitz-invariant hydrodynamics from holography, presented in [1] is generalized to arbitrary hyperscaling violating Lifshitz scaling theories with an unbroken U(1) symmetry
The hydrodynamics is compatible with the scaling theory of Lifshitz invariance with hyperscaling violation
We present the hydrodynamic ansatz which describes a Lifshitz-invariant fluid with hyperscaling violation on a non-trivial boundary metric
Summary
We consider a holographic model with Lifshitz scaling symmetry and hyperscalingviolation. The gravity dual is (d + 1)-dimensional Einstein gravity with a Maxwell field Aμ. Where F = dA is the field strength of the gauge field, Λ is a negative cosmological constant with coupling to dilaton, and λ and ν are dimensionless coupling constants. The equations of motion are given by
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