Abstract
A Lifshitz black brane at generic dynamical critical exponent z > 1, with non-zero linear momentum along the boundary, provides a holographic dual description of a non-equilibrium steady state in a quantum critical fluid, with Lifshitz scale invariance but without boost symmetry. We consider moving Lifshitz branes in Einstein-Maxwell-Dilaton gravity and obtain the non-relativistic stress tensor complex of the dual field theory via a suitable holographic renormalisation procedure. The resulting black brane hydrodynamics and thermodynamics are a concrete holographic realization of a Lifshitz perfect fluid with a generic dynamical critical exponent.
Highlights
Gravitational bulk theories with asymptotic geometries that are not AdS [8,9,10]
In previous work [24], we have studied out-of-equilibrium energy transport in a quantum critical fluid with Lifshitz scaling symmetry following a local quench between two semi-infinite fluid reservoirs
This can be remedied by taking advantage of a built-in symmetry of the model and a more or less standard holographic renormalisation is achieved by suitably adapting the formalism developed for a holographic model involving a massive vector field in [12]
Summary
We restrict our attention to a holographic theory with Lifshitz scaling defined in 4 bulk space-time dimensions but our results can be generalised to an arbitrary number of dimensions. Space-time geometries that are asymptotic to this metric provide a holographic dual description of a scale-invariant non-relativistic field theory formulated on a Rt × R2 boundary. While this model has the advantage of analytic control, it has the disadvantage of a logarithmically running dilaton and diverging vector field at the boundary This is not a very serious disadvantage because the vector field only serves to provide the background to support a Lifshitz geometry at the boundary and does not couple to any non-gravitational fields. Aμ should not be viewed as a gauge field but as a massless vector field that only interacts gravitationally (with a coupling that depends on the dilaton) With this in mind, we do not have to respect the U(1) gauge symmetry of the bulk action in (2.1) when we construct boundary counterterms for holographic renormalisation of the model. The shift symmetry is helpful in analysing the asymptotic behaviour of bulk fields
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