On the reconstruction of Lifshitz spacetimes

TL;DR

This paper investigates how Lifshitz spacetimes can be reconstructed from boundary data using various holographic methods, revealing limitations and necessary modifications for Lifshitz geometries compared to AdS.

Contribution

It demonstrates that standard holographic reconstruction techniques face challenges in Lifshitz spacetimes, highlighting the need for additional considerations like boundary-emanating light-sheets.

Findings

Differential entropy cannot reconstruct all Lifshitz bulk curves.

Causal wedges degenerate in Lifshitz spacetimes.

Entanglement wedges require boundary-emanating light-sheets.

Abstract

We consider the reconstruction of a Lifshitz spacetime from three perspectives: differential entropy (or "hole-ography"), causal wedges and entanglement wedges. We find that not all time-varying bulk curves in vacuum Lifshitz can be reconstructed via the differential entropy approach, adding a caveat to the general analysis of \cite{Headrick:2014eia}. We show that the causal wedge for Lifshitz spacetimes degenerates, while the entanglement wedge requires the additional consideration of a set of boundary-emanating light-sheets. The need to include bulk surfaces with no clear field theory interpretation in the differential entropy construction and the change in the entanglement wedge formation both serve as warnings against a naive application of holographic entanglement entropy proposals in Lifshitz spacetimes.