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

TL;DR

This work establishes a framework for holography in a non-relativistic gravity theory (Horava gravity) by analyzing linear response on a black brane with Lifshitz scaling $z=1$. It develops a modified holographic dictionary to accommodate multiple bulk horizons and distinct bulk speeds, and computes diffusion constants and conductivities for transverse momentum and $U(1)$ charge, obtaining $\,\eta/s=2^{2/3}/(4\pi)$ and diffusion constants tied to the appropriate spin-2 horizon and bulk speeds. Using a covariant Einstein-Aether reformulation and field redefinitions, the authors relate Horava-gravity results to familiar GR results in a special limit ($\lambda=0$) and provide justification for their boundary conditions and counterterms. The analysis demonstrates that non-relativistic holography can yield well-defined hydrodynamics, highlights the role of horizons in transport, and paves the way for broader exploration of non-Lorentz-invariant duals and horizon-based transport phenomena.

Abstract

We study the linearized transport of transverse momentum and charge in a conjectured field theory dual to a black brane solution of Horava 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 Horava gravity. When possible, as a check on our methods and results, we use the covariant Einstein-Aether formulation of Horava gravity, along with field redefinitions, to re-derive our results from a relativistic bulk theory.

Figures (1)

• Figure 1: An illustration of the horizons of the Hořava black brane. The Killing horizon $r_k$, sound horizon of the spin-2 graviton $r_s$, and the universal horizon $r_h$, are trapped surfaces for waves with speed $s=1$, $s_2=\sqrt{1+\beta}$ and $s_0\rightarrow\infty$, respectively. Depending on the value of $\beta$, the spin-2 sound horizon $r_s$ can be inside or outside of the Killing horizon $r_k$.