Lifshitz Gravity for Lifshitz Holography

TL;DR

It is argued that Hořava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and a dynamical exponent z, and it is shown that Lifshitzer spacetimes are vacuum solutions of HL gravity, without need for additional matter.

Abstract

We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization of HL gravity, and show how it reproduces the full structure of the z=2 anisotropic Weyl anomaly in dual field theories in 2+1 dimensions, while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.