2013/11/30 by Pavel Krtous, Pavel Krtouš, Andrei Zelnikov
Mathematics · Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Cosmology and Gravitation Theories #De Sitter space #De Sitter universe #Disjoint sets #Entropy (arrow of time) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Minimal surface #Noncommutative and Quantum Gravity Theories #Phase transition #Physics #Quantum entanglement #Quantum mechanics #Replica trick #Spacetime #Spin glass #Theoretical physics #Universe #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.89.104058
published as Phys. Rev. D 89, 104058 (2014) · 7 pages, 13 figures (v2: minor modifications, figures and references added)
arxiv created 2014/03/20 · openalex publication_date 2014/05/27 · arxiv updated 2014/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It was proposed by Ryu and Takayanagi that the entanglement entropy in conformal field theory (CFT) is related through the AdS/CFT correspondence to the area of a minimal surface in the bulk. We apply this holographic geometrical method of calculating the entanglement entropy to study the vacuum case of a CFT which is holographically dual to empty anti-de Sitter (AdS) spacetime. We present all possible minimal surfaces spanned on one or two spherical boundaries at AdS infinity. We give exact analytical expressions for the regularized areas of these surfaces and identify finite renormalized quantities. In the case of two disjoint boundaries the existence of two different phases of the entanglement entropy is confirmed. A trivial phase corresponds to two disconnected minimal surfaces, while the other one corresponds to a tube connecting the spherical boundaries. A transition between these phases is reminiscent of the finite temperature deconfinement transition in the CFT on the boundary. The exact analytical results are thus consistent with previous numerical and approximate computations. We also briefly discuss the character of a spacetime extension of the minimal surface spanned on two uniformly accelerated boundaries.