2014/09/16 by Bartłomiej Czech, Bartlomiej Czech, Lampros Lamprou · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Anti-de Sitter space #Black Holes and Theoretical Physics #Boundary (topology) #Combinatorics #Cosmology and Gravitation Theories #Geodesic #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum #Quantum entanglement #Quantum mechanics #Subadditivity #hep-th
paper · pdf · doi:10.1103/physrevd.90.106005
published as Phys. Rev. D 90, 106005 (2014) · 37 pages plus appendices, 15 figures
arxiv created 2014/09/16 · openalex publication_date 2014/11/19 · arxiv updated 2014/11/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 other field theory quantities, which can carry the information about lengths of nonminimal geodesics.