Abstract
We study quantum cosmological models for certain classes of bang/crunch singularities, using the duality between expanding bubbles in AdS with a FRW interior cosmology and perturbed CFTs on de Sitter space-time. It is pointed out that horizon complementarity in the AdS bulk geometries is realized as a conformal transformation in the dual deformed CFT. The quantum version of this map is described in full detail in a toy model involving conformal quantum mechanics. In this system the complementarity map acts as an exact duality between eternal and apocalyptic Hamiltonian evolutions. We calculate the commutation relation between the Hamiltonians corresponding to the different frames. It vanishes only on scale invariant states.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
J. Barbon and E. Rabinovici, AdS Crunches, CFT Falls And Cosmological Complementarity, JHEP 04 (2011) 044 [arXiv:1102.3015] [INSPIRE].
V. de Alfaro, S. Fubini and G. Furlan, Conformal Invariance in Quantum Mechanics, Nuovo Cim. A 34 (1976) 569 [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S. Hawking, J.M. Maldacena and A. Strominger, De Sitter entropy, quantum entanglement and AdS/CFT, JHEP 05 (2001) 001 [hep-th/0002145] [INSPIRE].
A. Buchel and A.A. Tseytlin, Curved space resolution of singularity of fractional D3-branes on conifold, Phys. Rev. D 65 (2002) 085019 [hep-th/0111017] [INSPIRE].
A. Buchel, P. Langfelder and J. Walcher, Does the tachyon matter?, Annals Phys. 302 (2002) 78 [hep-th/0207235] [INSPIRE].
A. Buchel, Gauge/gravity correspondence in accelerating universe, Phys. Rev. D 65 (2002) 125015 [hep-th/0203041] [INSPIRE].
A. Buchel, P. Langfelder and J. Walcher, On time dependent backgrounds in supergravity and string theory, Phys. Rev. D 67 (2003) 024011 [hep-th/0207214] [INSPIRE].
T. Hirayama, A holographic dual of CFT with flavor on de Sitter space, JHEP 06 (2006) 013 [hep-th/0602258] [INSPIRE].
M. Alishahiha, A. Karch, E. Silverstein and D. Tong, The dS/dS correspondence, AIP Conf. Proc. 743 (2005) 393 [hep-th/0407125] [INSPIRE].
A. Buchel, Inflation on the resolved warped deformed conifold, Phys. Rev. D 74 (2006) 046009 [hep-th/0601013] [INSPIRE].
O. Aharony, M. Fabinger, G.T. Horowitz and E. Silverstein, Clean time dependent string backgrounds from bubble baths, JHEP 07 (2002) 007 [hep-th/0204158] [INSPIRE].
V. Balasubramanian and S.F. Ross, The dual of nothing, Phys. Rev. D 66 (2002) 086002 [hep-th/0205290] [INSPIRE].
S.F. Ross and G. Titchener, Time-dependent spacetimes in AdS/CFT: Bubble and black hole, JHEP 02 (2005) 021 [hep-th/0411128] [INSPIRE].
R.-G. Cai, Constant curvature black hole and dual field theory, Phys. Lett. B 544 (2002) 176 [hep-th/0206223] [INSPIRE].
V. Balasubramanian, K. Larjo and J. Simon, Much ado about nothing, Class. Quant. Grav. 22 (2005) 4149 [hep-th/0502111] [INSPIRE].
J. He and M. Rozali, On bubbles of nothing in AdS/CFT, JHEP 09 (2007) 089 [hep-th/0703220] [INSPIRE].
J.A. Hutasoit, S.P. Kumar and J. Rafferty, Real time response on dS 3 : The Topological AdS Black Hole and the Bubble, JHEP 04 (2009) 063 [arXiv:0902.1658] [INSPIRE].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
B. Freivogel and L. Susskind, A framework for the landscape, Phys. Rev. D 70 (2004) 126007 [hep-th/0408133] [INSPIRE].
G. Horowitz, A. Lawrence and E. Silverstein, Insightful D-branes, JHEP 07 (2009) 057 [arXiv:0904.3922] [INSPIRE].
L. Susskind, The Transfer of Entanglement: The Case for Firewalls, arXiv:1210.2098 [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav. 42 (2010) 2323 [arXiv:1005.3035] [INSPIRE].
M. Van Raamsdonk, A patchwork description of dual spacetimes in AdS/CFT, Class. Quant. Grav. 28 (2011) 065002 [INSPIRE].
J.L. Barbon and J. Martinez-Magan, Spontaneous fragmentation of topological black holes, JHEP 08 (2010) 031 [arXiv:1005.4439] [INSPIRE].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].
A. Sen, State Operator Correspondence and Entanglement in AdS 2 /CF T 1, Entropy 13 (2011) 1305 [arXiv:1101.4254] [INSPIRE].
J. Hartle and S. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [INSPIRE].
J.L. Barbon and E. Rabinovici, Holography of AdS vacuum bubbles, JHEP 04 (2010) 123 [arXiv:1003.4966] [INSPIRE].
T. Hertog and G.T. Horowitz, Holographic description of AdS cosmologies, JHEP 04 (2005) 005 [hep-th/0503071] [INSPIRE].
T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [INSPIRE].
A. Bernamonti and B. Craps, D-Brane Potentials from Multi-Trace Deformations in AdS/CFT, JHEP 08 (2009) 112 [arXiv:0907.0889] [INSPIRE].
J. Maldacena, Vacuum decay into Anti de Sitter space, arXiv:1012.0274 [INSPIRE].
D. Harlow, Metastability in Anti de Sitter Space, arXiv:1003.5909 [INSPIRE].
D. Harlow and L. Susskind, Crunches, Hats and a Conjecture, arXiv:1012.5302 [INSPIRE].
B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, The Gravity Dual of a Density Matrix, Class. Quant. Grav. 29 (2012) 155009 [arXiv:1204.1330] [INSPIRE].
B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, Rindler Quantum Gravity, Class. Quant. Grav. 29 (2012) 235025 [arXiv:1206.1323] [INSPIRE].
P. Claus, M. Derix, R. Kallosh, J. Kumar, P.K. Townsend and A. Van Proeyen, Black holes and superconformal mechanics, Phys. Rev. Lett. 81 (1998) 4553 [hep-th/9804177] [INSPIRE].
E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B 195 (1982) 481 [INSPIRE].
D. Marolf, M. Rangamani and M. Van Raamsdonk, Holographic models of de Sitter QFTs, Class. Quant. Grav. 28 (2011) 105015 [arXiv:1007.3996] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
I. Bena, On the construction of local fields in the bulk of AdS 5 and other spaces, Phys. Rev. D 62 (2000) 066007 [hep-th/9905186] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A Boundary view of horizons and locality, Phys. Rev. D 73 (2006) 086003 [hep-th/0506118] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A Holographic description of the black hole interior, Phys. Rev. D 75 (2007) 106001 [Erratum ibid. D 75 (2007) 129902] [hep-th/0612053] [INSPIRE].
D. Kabat, G. Lifschytz and D.A. Lowe, Constructing local bulk observables in interacting AdS/CFT, Phys. Rev. D 83 (2011) 106009 [arXiv:1102.2910] [INSPIRE].
I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, Bulk and Transhorizon Measurements in AdS/CFT, JHEP 10 (2012) 165 [arXiv:1201.3664] [INSPIRE].
K. Papadodimas and S. Raju, An Infalling Observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1308.1921
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Barbón, J.L.F., Rabinovici, E. Conformal complementarity maps. J. High Energ. Phys. 2013, 23 (2013). https://doi.org/10.1007/JHEP12(2013)023
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2013)023