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Title: Equivalence of emergent de Sitter spaces from conformal field theory

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 (dS 2), 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 dS 2. As a result, we offer a general method for relating kinematic space and the auxiliary de Sitter space that is validmore » in the vacuum and thermal cases.« less

Authors:
 [1];  [2];  [1]
  1. Columbia Univ., New York, NY (United States)
  2. Columbia Univ., New York, NY (United States); Instituut voor Theoretische Fysica, Leuven (Belgium)
Publication Date:
Research Org.:
Columbia Univ., New York, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1360131
Grant/Contract Number:
SC0011941
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; AdS-CFT correspondence; conformal field theory; spacetime singularities

Citation Formats

Asplund, Curtis T., Callebaut, Nele, and Zukowski, Claire. Equivalence of emergent de Sitter spaces from conformal field theory. United States: N. p., 2016. Web. doi:10.1007/JHEP09(2016)154.
Asplund, Curtis T., Callebaut, Nele, & Zukowski, Claire. Equivalence of emergent de Sitter spaces from conformal field theory. United States. doi:10.1007/JHEP09(2016)154.
Asplund, Curtis T., Callebaut, Nele, and Zukowski, Claire. 2016. "Equivalence of emergent de Sitter spaces from conformal field theory". United States. doi:10.1007/JHEP09(2016)154. https://www.osti.gov/servlets/purl/1360131.
@article{osti_1360131,
title = {Equivalence of emergent de Sitter spaces from conformal field theory},
author = {Asplund, Curtis T. and Callebaut, Nele and Zukowski, Claire},
abstractNote = {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. As a result, we offer a general method for relating kinematic space and the auxiliary de Sitter space that is valid in the vacuum and thermal cases.},
doi = {10.1007/JHEP09(2016)154},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2016,
place = {United States},
year = 2016,
month = 9
}

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  • A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d+1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS{sub d+2}, analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS{sub 3}. We also compare the entropy computed in AdS{sub 5}xS{sup 5} with that of the free N=4 super Yang-Mills theory.
  • We analyze the anti-de Sitter/conformal-field-theory dual geometry of an expanding boost-invariant plasma. We show that the requirement of nonsingularity of the dual geometry for leading and subasymptotic times predicts, without any further assumptions about gauge theory dynamics, hydrodynamic expansion of the plasma with viscosity coefficient exactly matching the one obtained earlier in the static case by Policastro, Son, and Starinets.
  • An S matrix analog is defined for anti{endash}de Sitter (Ads) space by constructing {open_quotes}in{close_quotes} and {open_quotes}out{close_quotes} states that asymptote to the timelike boundary. A derivation parallel to that of the Lehmann-Symanzik-Zimmermann formula shows that this {open_quotes}boundary S matrix{close_quotes} is given directly by correlation functions in the boundary conformal theory. This provides a key entry in the AdS to conformal field theory dictionary. {copyright} {ital 1999} {ital The American Physical Society }
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