Momentum and charge transport in non-relativistic holographic fluids from Hořava gravity

Abstract

We study the linearized transport of transverse momentum and charge in a conjectured field theory dual to a black brane solution of Hořava gravity with Lifshitz exponent z = 1. As expected from general hydrodynamic reasoning, we find that both of these quantities are diffusive over distance and time scales larger than the inverse temperature. We compute the diffusion constants and conductivities of transverse momentum and charge, as well the ratio of shear viscosity to entropy density, and find that they differ from their relativistic counterparts. To derive these results, we propose how the holographic dictionary should be modified to deal with the multiple horizons and differing propagation speeds of bulk excitations in Hořava gravity. When possible, as a check on our methods and results, we use the covariant Einstein-Aether formulation of Hořava gravity, along with field redefinitions, to re-derive our results from a relativistic bulk theory.

Dispersion relations in non-relativistic two-dimensional materials from quasinormal modes in Hǒrava Gravity

“…We close this section with a review of the (numerical) shooting method with which then the Hořava QNMs of the axial sector are computed. In the hydrodynamic limit, axial and polar 1 transport quantities have been found analytically in [9] 2 , which will serve as a check of our numerical solutions.…”

“…In this work, we lift this severe restriction and analyze QNMs for nonzero λ. 2 In [9], our axial modes are there called vector modes, and our polar modes are there called scalar modes. 3 Capitalized roman letter indices I, J, K, .…”

“…Since Hořava Gravity is non-relativistic, there exists another horizon: the spin-2 sound horizon at r = r h /2 1 3 , which is a trapping surface for the spin-2 graviton. There is also the Killing horizon located at r = r k [9]. The temperature is determined by the universal horizon [8] and is given by…”

“…After a radial diffeomorphism,h xr (r; ω, k) can be set to vanish. A linear combination of these fields turns out to be a gauge invariant master field, ψ(r; ω, k) = (ωh xy + kh tx ), and obeys the following single equation of motion 8 found in [9]…”

“…last points of return, in the presence of a black brane. In [9] it was conjectured that the relevant horizon for each set of fields is the sound horizon, which is identified as a regular singular point of the set of equations of motion of those fields. For the axial sector the relevant horizon was shown to be the horizon of the spin-2 graviton.…”