Nuts and Bolts for Creating Space
Bartlomiej Czech, Lampros Lamprou

TL;DR
This paper explores how entanglement entropies in boundary field theories encode the geometry of AdS3 space, proposing a new distance function consistent with holographic principles and extending to quotient geometries.
Contribution
It introduces a novel method to reconstruct AdS3 geometry from boundary entanglement entropies and proposes a distance function satisfying the triangle inequality.
Findings
Reproduces static AdS3 slice from entanglement data
Proposes a distance function obeying triangle inequality
Extends framework to conical defect and BTZ geometries
Abstract
We discuss the way in which field theory quantities assemble the spatial geometry of three-dimensional anti-de Sitter space (AdS3). The field theory ingredients are the entanglement entropies of boundary intervals. A point in AdS3 corresponds to a collection of boundary intervals, which is selected by a variational principle we discuss. Coordinates in AdS3 are integration constants of the resulting equation of motion. We propose a distance function for this collection of points, which obeys the triangle inequality as a consequence of the strong subadditivity of entropy. Our construction correctly reproduces the static slice of AdS3 and the Ryu-Takayanagi relation between geodesics and entanglement entropies. We discuss how these results extend to quotients of AdS3 -- the conical defect and the BTZ geometries. In these cases, the set of entanglement entropies must be supplemented by…
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