Holographic Reconstruction of General Bulk Surfaces

TL;DR

This paper develops a method to reconstruct arbitrary bulk surfaces in any dimension using differential entropy in boundary field theories, extending previous proofs to more general surfaces with potential implications for entanglement entropy.

Contribution

It extends the proof of holographic surface reconstruction to general surfaces with a 1-parameter foliation, broadening the scope of holographic entanglement methods.

Findings

Reconstruction of general bulk surfaces via differential entropy.

Extension of Headrick et al.'s proof to new classes of surfaces.

Discussion on covariant and entanglement entropy aspects.

Abstract

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.