Moving black branes and Lifshitz hydrodynamics at generic z

Quantum critical fluids with Lifshitz symmetry, or Lifshitz fluids for short, have interesting properties that set them aside from more conventional fluid systems. In particular, a Lifshitz fluid with a generic dynamical critical exponent z > 1 does not have boost symmetry meaning that a moving fluid is physically distinct from a fluid at rest in a moving coordinate frame. We show how a relatively simple Einstein-Maxwell-Dilaton model provides a concrete holographic realisation of Lifshitz fluids. In this setting, a black brane at generic z carrying linear momentum along the boundary corresponds to a non-equilibrium steady state of the fluid. We obtain the stress tensor complex for the dual field theory via a suitably defined holographic renormalisation procedure and demonstrate that the expected hydrodynamic relations for a Lifshitz perfect fluid are satisfied.