Lifshitz Gravity for Lifshitz Holography

TL;DR

This paper demonstrates that Horava-Lifshitz gravity naturally provides a minimal holographic dual for Lifshitz field theories with anisotropic scaling, reproducing key features of their anomalies without extra matter fields.

Contribution

It shows Lifshitz spacetimes are solutions of HL gravity and performs holographic renormalization to match the anisotropic Weyl anomaly structure.

Findings

Lifshitz spacetimes are vacuum solutions of HL gravity

Holographic renormalization reproduces the z=2 Weyl anomaly

Minimal relativistic gravity captures only part of the anomaly

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.