Horava-Lifshitz Holography

TL;DR

This paper explores the holographic relationship between Horava-Lifshitz gravity and boundary quantum field theories, deriving key conditions and flow equations that connect bulk gravity to boundary dynamics.

Contribution

It derives the detailed balance condition from the Hamilton-Jacobi equation and proposes a holographic duality with a boundary quantum field theory in Horava-Lifshitz gravity.

Findings

Derived the detailed balance condition as a solution to the Hamilton-Jacobi equation.

Proposed the existence of a boundary quantum field theory in the holographic framework.

Obtained a Ricci flow equation as the holographic RG flow in this setting.

Abstract

We derive the detailed balance condition as a solution to the Hamilton-Jacobi equation in the Horava-Lifshitz gravity. This result leads us to propose the existence of the d-dimensional quantum field theory on the future boundary of the (d+1)-dimensional Horava-Lifshitz gravity from the viewpoint of the holographic renormalization group. We also obtain a Ricci flow equation of the boundary theory as the holographic RG flow, which is the Hamilton equation in the bulk gravity, by tuning parameters in the theory.