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 [1]. 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.
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Gentle, S.A., Keeler, C. On the reconstruction of Lifshitz spacetimes. J. High Energ. Phys. 2016, 195 (2016). https://doi.org/10.1007/JHEP03(2016)195
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DOI: https://doi.org/10.1007/JHEP03(2016)195