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Holographic Reconstruction of General Bulk Surfaces
We propose a reconstruction of general bulk surfaces in any dimension in
terms of the differential entropy in the boundary field theory. In particular,
we extend the proof of Headrick et al. to calculate the area of a general class
of surfaces, which have a 1-parameter foliation over a closed manifold. The
area can be written in terms of extremal surfaces whose boundaries lie on
ring-like regions in the field theory. We discuss when this construction has a
description in terms of spatial entanglement entropy and suggest lessons for a
more complete and covariant approach.Comment: 21 pages, 10 figures; v2: minor clarifications, references added,
published versio
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