Constructing entanglement wedges for Lifshitz spacetimes with Lifshitz gravity

TL;DR

This paper develops a method to construct entanglement and causal wedges in Lifshitz spacetimes using Lifshitz modes from Hořava-Lifshitz gravity, aligning geometric entanglement entropy with field theory calculations.

Contribution

It introduces a novel approach to build entanglement wedges in Lifshitz spacetimes by leveraging Lifshitz modes in Hořava-Lifshitz gravity, addressing previous challenges in non-AdS geometries.

Findings

Constructed causal and entanglement wedges in Lifshitz spacetimes.

Geometric entanglement entropy matches field theory results.

Demonstrated the utility of Lifshitz modes for holographic entanglement.

Abstract

Holographic relationships between entanglement entropy on the boundary of a spacetime and the area of minimal surfaces in the bulk provide an important entry in the bulk/boundary dictionary. While constructing the necessary causal and entanglement wedges is well understood in asymptotically AdS spacetimes, less is known about the equivalent constructions in spacetimes with different asymptotics. In particular, recent attempts to construct entanglement and causal wedges for asymptotically Lifshitz solutions in relativistic gravitational theories have proven problematic. We note a simple observation, that a Lifshitz bulk theory, specifically a covariant formulation of Ho\v{r}ava-Lifshitz gravity coupled to matter, has causal propagation defined by Lifshitz modes. We use these modes to construct causal and entanglement wedges and compute the geometric entanglement entropy, which in such a construction matches the field theory prescription.