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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 (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 themore » 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)
OSTI Identifier:
1360131
Grant/Contract Number:  
SC0011941
Resource Type:
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. Tue . "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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Works referenced in this record:

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006


Aspects of holographic entanglement entropy
journal, August 2006


A covariant holographic entanglement entropy proposal
journal, July 2007

  • Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
  • Journal of High Energy Physics, Vol. 2007, Issue 07
  • DOI: 10.1088/1126-6708/2007/07/062

Covariant constraints on hole-ography
journal, September 2015


Eternal black holes in anti-de Sitter
journal, April 2003


Building up spacetime with quantum entanglement
journal, June 2010


Gravitational dynamics from entanglement “thermodynamics”
journal, April 2014

  • Lashkari, Nima; McDermott, Michael B.; Van Raamsdonk, Mark
  • Journal of High Energy Physics, Vol. 2014, Issue 4
  • DOI: 10.1007/JHEP04(2014)195

Gravitation from entanglement in holographic CFTs
journal, March 2014

  • Faulkner, Thomas; Guica, Monica; Hartman, Thomas
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)051

Holographic geometry of entanglement renormalization in quantum field theories
journal, October 2012

  • Nozaki, Masahiro; Ryu, Shinsei; Takayanagi, Tadashi
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)193

Integral geometry and holography
journal, October 2015

  • Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)175

Tensor networks from kinematic space
journal, July 2016

  • Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)100

Holographic holes in higher dimensions
journal, June 2014

  • Myers, Robert C.; Rao, Junjie; Sugishita, Sotaro
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)044

Holographic holes and differential entropy
journal, October 2014

  • Headrick, Matthew; Myers, Robert C.; Wien, Jason
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)149

Holographic de Sitter Geometry from Entanglement in Conformal Field Theory
journal, February 2016


Tensor network quotient takes the vacuum to the thermal state
journal, August 2016


A stereoscopic look into the bulk
journal, July 2016

  • Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)129

Entanglement, holography and causal diamonds
journal, August 2016

  • de Boer, Jan; Haehl, Felix M.; Heller, Michal P.
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)162

Entanglement entropy and quantum field theory
journal, June 2004


Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity
journal, June 1986

  • Brown, J. D.; Henneaux, Marc
  • Communications in Mathematical Physics, Vol. 104, Issue 2
  • DOI: 10.1007/BF01211590

Black hole in three-dimensional spacetime
journal, September 1992


Geometry of the 2+1 black hole
journal, August 1993

  • Bañados, Máximo; Henneaux, Marc; Teitelboim, Claudio
  • Physical Review D, Vol. 48, Issue 4
  • DOI: 10.1103/PhysRevD.48.1506

Holographic entanglement plateaux
journal, August 2013

  • Hubeny, Veronika E.; Maxfield, Henry; Rangamani, Mukund
  • Journal of High Energy Physics, Vol. 2013, Issue 8
  • DOI: 10.1007/JHEP08(2013)092

Thermodynamics of black holes in anti-de Sitter space
journal, December 1983

  • Hawking, S. W.; Page, Don N.
  • Communications in Mathematical Physics, Vol. 87, Issue 4
  • DOI: 10.1007/BF01208266

Entwinement and the emergence of spacetime
journal, January 2015

  • Balasubramanian, Vijay; Chowdhury, Borun D.; Czech, Bartłlomiej
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/JHEP01(2015)048

Massless black holes and black rings as effective geometries of the D1–D5 system
journal, October 2005

  • Balasubramanian, Vijay; Kraus, Per; Shigemori, Masaki
  • Classical and Quantum Gravity, Vol. 22, Issue 22
  • DOI: 10.1088/0264-9381/22/22/010

Holographic entanglement entropy from 2d CFT: heavy states and local quenches
journal, February 2015

  • Asplund, Curtis T.; Bernamonti, Alice; Galli, Federico
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)171

Operator content of two-dimensional conformally invariant theories
journal, January 1986


Entanglement scrambling in 2d conformal field theory
journal, September 2015

  • Asplund, Curtis T.; Bernamonti, Alice; Galli, Federico
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)110

Quantum dress for a naked singularity
journal, September 2016


Quantum Black Holes as Holograms in AdS Braneworlds
journal, August 2002


Black holes and wormholes in dimensions
journal, March 1998

  • Åminneborg, Stefan; Bengtsson, Ingemar; Brill, Dieter
  • Classical and Quantum Gravity, Vol. 15, Issue 3
  • DOI: 10.1088/0264-9381/15/3/013

Multiboundary wormholes and holographic entanglement
journal, September 2014


Towards a derivation of holographic entanglement entropy
journal, May 2011

  • Casini, Horacio; Huerta, Marina; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)036

Relative entropy and holography
journal, August 2013

  • Blanco, David D.; Casini, Horacio; Hung, Ling-Yan
  • Journal of High Energy Physics, Vol. 2013, Issue 8
  • DOI: 10.1007/JHEP08(2013)060

Entanglement spectrum in one-dimensional systems
journal, September 2008


Holographic calculations of Rényi entropy
journal, December 2011

  • Hung, Ling-Yan; Myers, Robert C.; Smolkin, Michael
  • Journal of High Energy Physics, Vol. 2011, Issue 12
  • DOI: 10.1007/JHEP12(2011)047

Rényi entropies of free bosons on the torus and holography
journal, April 2014


Comments on Rényi entropy in AdS3/CFT2
journal, May 2014


Short interval expansion of Rényi entropy on torus
journal, August 2016

  • Chen, Bin; Wu, Jun-Bao; Zhang, Jia-ju
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)130

Relative entropy equals bulk relative entropy
journal, June 2016

  • Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)004

De Sitter Musings
journal, May 2012


Thermo-field dynamics of black holes
journal, May 1976


    Works referencing / citing this record:

    Kinematic space and the orbit method
    journal, July 2019

    • Penna, Robert F.; Zukowski, Claire
    • Journal of High Energy Physics, Vol. 2019, Issue 7
    • DOI: 10.1007/jhep07(2019)045

    Kinematic space and the orbit method
    journal, July 2019

    • Penna, Robert F.; Zukowski, Claire
    • Journal of High Energy Physics, Vol. 2019, Issue 7
    • DOI: 10.1007/jhep07(2019)045

    Topological Complexity in AdS 3 /CFT 2
    journal, June 2018

    • Abt, Raimond; Erdmenger, Johanna; Hinrichsen, Haye
    • Fortschritte der Physik, Vol. 66, Issue 6
    • DOI: 10.1002/prop.201800034

    Kinematic space and wormholes
    journal, January 2017


    Holographic subregion complexity from kinematic space
    journal, January 2019

    • Abt, Raimond; Erdmenger, Johanna; Gerbershagen, Marius
    • Journal of High Energy Physics, Vol. 2019, Issue 1
    • DOI: 10.1007/jhep01(2019)012

    The gravitational dynamics of kinematic space
    journal, February 2019


    A defect in holographic interpretations of tensor networks
    journal, March 2017

    • Czech, Bartlomiej; Nguyen, Phuc H.; Swaminathan, Sivaramakrishnan
    • Journal of High Energy Physics, Vol. 2017, Issue 3
    • DOI: 10.1007/jhep03(2017)090

    Holographic relations for OPE blocks in excited states
    journal, March 2019

    • Cresswell, Jesse C.; Jardine, Ian T.; Peet, Amanda W.
    • Journal of High Energy Physics, Vol. 2019, Issue 3
    • DOI: 10.1007/jhep03(2019)058

    Kinematic space for conical defects
    journal, November 2017

    • Cresswell, Jesse C.; Peet, Amanda W.
    • Journal of High Energy Physics, Vol. 2017, Issue 11
    • DOI: 10.1007/jhep11(2017)155

    Berry curvature, horocycles, and scattering states in AdS 3 / CFT 2
    journal, December 2019


    Towards a Fisher-Information Description of Complexity in de Sitter Universe
    journal, November 2019