Abstract
We discuss aspects of the holographic description of crunching AdS cosmologies. We argue that crunching FRW models with hyperbolic spatial sections are dual to semiclassical condensates in deformed de Sitter CFTs. De Sitter-invariant condensates with a sharply defined energy scale are induced by effective negative-definite relevant or marginal operators, which may or may not destabilize the CFT. We find this result by explicitly constructing a ‘complementarity map’ for this model, given by a conformal transformation of the de Sitter CFT into a static time-frame, which reveals the crunch as an infinite potential-energy fall in finite time. We show that, quite generically, the crunch is associated to a finite mass black hole if the de Sitter O(d, 1)-invariance is an accidental IR symmetry, broken down to U(1) × O(d) in the UV. Any such regularization cuts off the eternity of de Sitter space-time. Equivalently, the dimension of the Hilbert space propagating into the crunch is finite only when de Sitter is not eternal.
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References
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [SPIRES].
L.F. Abbott and S.R. Coleman, The Collapse Of An Anti-De Sitter Bubble, Nucl. Phys. B 259 (1985) 170 [SPIRES].
J.L.F. Barbón and E. Rabinovici, Holography of AdS vacuum bubbles, JHEP 04 (2010) 123 [arXiv:1003.4966] [SPIRES].
J. Maldacena, Vacuum decay into Anti de Sitter space, arXiv:1012.0274 [SPIRES].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
L. Susskind, L. Thorlacius and J. Uglum, The Stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [SPIRES].
S. Hawking, J.M. Maldacena and A. Strominger, DeSitter entropy, quantum entanglement and AdS/CFT, JHEP 05 (2001) 001 [hep-th/0002145] [SPIRES].
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] [SPIRES].
A. Buchel, P. Langfelder and J. Walcher, Does the tachyon matter?, Annals Phys. 302 (2002) 78 [hep-th/0207235] [SPIRES].
A. Buchel, Gauge/gravity correspondence in accelerating universe, Phys. Rev. D 65 (2002) 125015 [hep-th/0203041] [SPIRES].
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] [SPIRES].
T. Hirayama, A holographic dual of CFT with flavor on de Sitter space, JHEP 06 (2006) 013 [hep-th/0602258] [SPIRES].
M. Alishahiha, A. Karch, E. Silverstein and D. Tong, The dS/dS correspondence, AIP Conf. Proc. 743 (2005) 393 [hep-th/0407125] [SPIRES].
A. Buchel, Inflation on the resolved warped deformed conifold, Phys. Rev. D 74 (2006) 046009 [hep-th/0601013] [SPIRES].
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] [SPIRES].
V. Balasubramanian and S.F. Ross, The dual of nothing, Phys. Rev. D 66 (2002) 086002 [hep-th/0205290] [SPIRES].
S.F. Ross and G. Titchener, Time-dependent spacetimes in AdS/CFT: Bubble and black hole, JHEP 02 (2005) 021 [hep-th/0411128] [SPIRES].
R.-G. Cai, Constant curvature black hole and dual field theory, Phys. Lett. B 544 (2002) 176 [hep-th/0206223] [SPIRES].
V. Balasubramanian, K. Larjo and J. Simon, Much ado about nothing, Class. Quant. Grav. 22 (2005) 4149 [hep-th/0502111] [SPIRES].
J. He and M. Rozali, On Bubbles of Nothing in AdS/CFT, JHEP 09 (2007) 089 [hep-th/0703220] [SPIRES].
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] [SPIRES].
D. Marolf, M. Rangamani and M. Van Raamsdonk, Holographic models of de Sitter QFTs, arXiv:1007.3996 [SPIRES].
T. Hertog and G.T. Horowitz, Holographic description of AdS cosmologies, JHEP 04 (2005) 005 [hep-th/0503071] [SPIRES].
T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [SPIRES].
G. Horowitz, A. Lawrence and E. Silverstein, Insightful D-branes, JHEP 07 (2009) 057 [arXiv:0904.3922] [SPIRES].
J.B. Hartle and S.W. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [SPIRES].
A.M. Polyakov, Decay of Vacuum Energy, Nucl. Phys. B 834 (2010) 316 [arXiv:0912.5503] [SPIRES].
E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B 195 (1982) 481 [SPIRES].
D. Harlow and L. Susskind, Crunches, Hats and a Conjecture, arXiv:1012.5302 [SPIRES].
D. Harlow, Metastability in Anti de Sitter Space, arXiv:1003.5909 [SPIRES].
T. Banks, Heretics of the false vacuum: Gravitational effects on and of vacuum decay. II, hep-th/0211160 [SPIRES].
T. Banks, Landskepticism or why effective potentials don’t count string models, hep-th/0412129 [SPIRES].
T. Banks, TASI Lectures on Holographic Space-Time, SUSY and Gravitational Effective Field Theory, arXiv:1007.4001 [SPIRES].
T. Banks and W. Fischler, Space-like singularities and thermalization, hep-th/0606260 [SPIRES].
T. Banks, Pedagogical notes on black holes, de Sitter space, and bifurcated horizons, arXiv:1007.4003 [SPIRES].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Ann. Phys. 144 (1982) 249 [SPIRES].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [SPIRES].
J.L.F. Barbón and J. Martínez-Magán, Spontaneous fragmentation of topological black holes, JHEP 08 (2010) 031 [arXiv:1005.4439] [SPIRES].
S.K. Blau, E.I. Guendelman and A.H. Guth, The Dynamics of False Vacuum Bubbles, Phys. Rev. D 35 (1987) 1747 [SPIRES].
G.L. Alberghi, D.A. Lowe and M. Trodden, Charged false vacuum bubbles and the AdS/CFT correspondence, JHEP 07 (1999) 020 [hep-th/9906047] [SPIRES].
B. Freivogel et al., Inflation in AdS/CFT, JHEP 03 (2006) 007 [hep-th/0510046] [SPIRES].
W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B 44S10 (1966) 1 [Erratum ibid. B 48 (1967) 463] [SPIRES].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [SPIRES].
G.L. Alberghi, D.A. Lowe and M. Trodden, Charged false vacuum bubbles and the AdS/CFT correspondence, JHEP 07 (1999) 020 [hep-th/9906047] [SPIRES].
E. Witten, Multi-trace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [SPIRES].
M. Berkooz, A. Sever and A. Shomer, Double-trace deformations, boundary conditions and spacetime singularities, JHEP 05 (2002) 034 [hep-th/0112264] [SPIRES].
S. Fubini, A New Approach To Conformal Invariant Field Theories, Nuovo Cim. A 34 (1976) 521.
V. Asnin, E. Rabinovici and M. Smolkin, On rolling, tunneling and decaying in some large-N vector models, JHEP 08 (2009) 001 [arXiv:0905.3526] [SPIRES].
O. Aharony, B. Kol and S. Yankielowicz, On exactly marginal deformations of N = 4 SYM and type IIB supergravity on AdS 5 × S 5, JHEP 06 (2002) 039 [hep-th/0205090] [SPIRES].
A. Bernamonti and B. Craps, D-Brane Potentials from Multi-Trace Deformations in AdS/CFT, JHEP 08 (2009) 112 [arXiv:0907.0889] [SPIRES].
S. Elitzur, A. Giveon, M. Porrati and E. Rabinovici, Multitrace deformations of vector and adjoint theories and their holographic duals, JHEP 02 (2006) 006 [hep-th/0511061] [SPIRES].
B. Craps, T. Hertog and N. Turok, Quantum Resolution of Cosmological Singularities using AdS/CFT, arXiv:0712.4180 [SPIRES].
N. Turok, B. Craps and T. Hertog, From Big Crunch to Big Bang with AdS/CFT, arXiv:0711.1824 [SPIRES].
S. de Haro and A.C. Petkou, Instantons and conformal holography, JHEP 12 (2006) 076 [hep-th/0606276] [SPIRES].
S. de Haro, I. Papadimitriou and A.C. Petkou, Conformally coupled scalars, instantons and vacuum instability in AdS 4, Phys. Rev. Lett. 98 (2007) 231601 [hep-th/0611315] [SPIRES].
I. Papadimitriou, Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT, JHEP 05 (2007) 075 [hep-th/0703152] [SPIRES].
L. Battarra and T. Hertog, Particle Production near an AdS Crunch, JHEP 12 (2010) 017 [arXiv:1009.0992] [SPIRES].
L. Kofman, Tachyonic preheating, hep-ph/0107280 [SPIRES].
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Barbón, J.L.F., Rabinovici, E. AdS crunches, CFT falls and cosmological complementarity. J. High Energ. Phys. 2011, 44 (2011). https://doi.org/10.1007/JHEP04(2011)044
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DOI: https://doi.org/10.1007/JHEP04(2011)044