Equivalence of emergent de Sitter spaces from conformal field theory

Curtis T. Asplund, Nele Callebaut, Claire Zukowski

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

Recently, two groups have made distinct proposals for a de Sitter space that is emergent from conformal field theory (CFT). The first proposal is that, for two-dimensional holographic CFTs, the kinematic space of geodesics on a space-like slice of the asymptotically anti-de Sitter bulk is two-dimensional de Sitter space (dS2), with a metric that can be derived from the entanglement entropy of intervals in the CFT. In the second proposal, de Sitter dynamics emerges naturally from the first law of entanglement entropy for perturbations around the vacuum state of CFTs. We provide support for the equivalence of these two emergent spacetimes in the vacuum case and beyond. In particular, we study the kinematic spaces of nontrivial solutions of 3d gravity, including the BTZ black string, BTZ black hole, and conical singularities. We argue that the resulting spaces are generically globally hyperbolic spacetimes that support dynamics given boundary conditions at future infinity. For the BTZ black string, corresponding to a thermal state of the CFT, we show that both prescriptions lead to an emergent hyperbolic patch of dS2. We offer a general method for relating kinematic space and the auxiliary de Sitter space that is valid in the vacuum and thermal cases.

Original languageEnglish (US)
Article number154
JournalJournal of High Energy Physics
Volume2016
Issue number9
DOIs
StatePublished - Sep 1 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016, The Author(s).

Keywords

  • AdS-CFT Correspondence
  • Conformal Field Theory
  • Spacetime Singularities

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