z=3 Lifshitz-Horava model and Fermi-point scenario of emergent gravity

TL;DR

This paper explores a high-energy gravity model with anisotropic scaling proposed by Horava, using condensed matter analogs like acoustic and fermionic emergent gravity to analyze its implications and consistency.

Contribution

It demonstrates how emergent gravity in condensed matter systems supports Horava's anisotropic scaling proposal and discusses conditions for the infrared Einstein action to be distorted.

Findings

Quantum hydrodynamics may exhibit anisotropic scaling consistent with Horava's model.

The Fermi point scenario shows the Einstein action can be distorted at low energies.

A hierarchy of energy scales and fine-tuning are necessary for a consistent theory.

Abstract

Recently Horava proposed a model for gravity which is described by the Einstein action in the infrared, but lacks the Lorentz invariance in the high-energy region where it experiences the anisotropic scaling. We test this proposal using two condensed matter examples of emergent gravity: acoustic gravity and gravity emerging in the fermionic systems with Fermi points. We suggest that quantum hydrodynamics, which together with the quantum gravity is the non-renormalizable theory, may exhibit the anisotropic scaling in agreement with the proposal. The Fermi point scenario of emergent general relativity demonstrates that under general conditions, the infrared Einstein action may be distorted, i.e. the Horava parameter $\lambda$ is not necessarily equal 1 even in the low energy limit. The consistent theory requires special hierarchy of the ultra-violet energy scales and the fine-tuning mechanism for the Newton constant.