Abstract
We calculate frequency space holographic correlators in an asymptotically AdS crunching background, dual to a relevant deformation of the M2-brane CFT placed in de Sitter spacetime. For massless bulk scalars, exploiting the connection to a solvable supersymmetric quantum mechanical problem, we obtain the exact frequency space correlator for the dual operator in the deformed CFT. Controlling the shape of the crunching surface in the Penrose diagram by smoothly dialling the deformation from zero to infinity, we observe that in the large deformation limit the Penrose diagram becomes a ‘square’, and the exact holographic correlators display striking similarities to their counterparts in the BTZ black hole and its higher dimensional generalisations. We numerically determine quasinormal poles for relevant and irrelevant operators, and find an intricate pattern of these in the complex frequency plane. In the case of relevant operators, the deformation parameter has an infinite sequence of critical values, each one characterised by a pair of poles colliding and moving away from the imaginary frequency axis with increasing deformation. In the limit of infinite deformation all scalar operators have identical quasinormal spectra. We compare and contrast our strongly coupled de Sitter QFT results with strongly coupled thermal correlators from AdS black holes.
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References
M. Spradlin, A. Strominger and A. Volovich, Les Houches lectures on de Sitter space, hep-th/0110007 [INSPIRE].
N.D. Birrell and P.C.W. Davies, Quantum Fields in Curved Space, Cambridge University Press (1984).
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].
L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The black hole singularity in AdS/CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].
G. Festuccia and H. Liu, Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I., JHEP 04 (2006) 044 [hep-th/0506202] [INSPIRE].
G. Festuccia and H. Liu, A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes, Adv. Sci. Lett. 2 (2009) 221 [arXiv:0811.1033] [INSPIRE].
J. Maldacena, Vacuum decay into Anti de Sitter space, arXiv:1012.0274 [INSPIRE].
D. Harlow and L. Susskind, Crunches, Hats and a Conjecture, arXiv:1012.5302 [INSPIRE].
T. Hertog and G.T. Horowitz, Towards a big crunch dual, JHEP 07 (2004) 073 [hep-th/0406134] [INSPIRE].
T. Hertog and G.T. Horowitz, Holographic description of AdS cosmologies, JHEP 04 (2005) 005 [hep-th/0503071] [INSPIRE].
J.L.F. Barbon and E. Rabinovici, AdS Crunches, CFT Falls And Cosmological Complementarity, JHEP 04 (2011) 044 [arXiv:1102.3015] [INSPIRE].
J.L.F. Barbón and E. Rabinovici, Conformal Complementarity Maps, JHEP 12 (2013) 023 [arXiv:1308.1921] [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].
D. Marolf, M. Rangamani and M. Van Raamsdonk, Holographic models of de Sitter QFTs, Class. Quant. Grav. 28 (2011) 105015 [arXiv:1007.3996] [INSPIRE].
V. Balasubramanian and S.F. Ross, The dual of nothing, Phys. Rev. D 66 (2002) 086002 [hep-th/0205290] [INSPIRE].
S.R. Das, J. Michelson, K. Narayan and S.P. Trivedi, Time dependent cosmologies and their duals, Phys. Rev. D 74 (2006) 026002 [hep-th/0602107] [INSPIRE].
B. Craps, A. Rajaraman and S. Sethi, Effective dynamics of the matrix big bang, Phys. Rev. D 73 (2006) 106005 [hep-th/0601062] [INSPIRE].
A. Awad, S.R. Das, S. Nampuri, K. Narayan and S.P. Trivedi, Gauge Theories with Time Dependent Couplings and their Cosmological Duals, Phys. Rev. D 79 (2009) 046004 [arXiv:0807.1517] [INSPIRE].
N. Turok, B. Craps and T. Hertog, From big crunch to big bang with AdS/CFT, arXiv:0711.1824 [INSPIRE].
B. Craps, T. Hertog and N. Turok, On the Quantum Resolution of Cosmological Singularities using AdS/CFT, Phys. Rev. D 86 (2012) 043513 [arXiv:0712.4180] [INSPIRE].
N. Engelhardt, T. Hertog and G.T. Horowitz, Holographic Signatures of Cosmological Singularities, Phys. Rev. Lett. 113 (2014) 121602 [arXiv:1404.2309] [INSPIRE].
N. Engelhardt, T. Hertog and G.T. Horowitz, Further Holographic Investigations of Big Bang Singularities, JHEP 07 (2015) 044 [arXiv:1503.08838] [INSPIRE].
S.P. Kumar and V. Vaganov, Probing crunching AdS cosmologies, JHEP 02 (2016) 026 [arXiv:1510.03281] [INSPIRE].
I. Papadimitriou and K. Skenderis, AdS/CFT correspondence and geometry, IRMA Lect. Math. Theor. Phys. 8 (2005) 73 [hep-th/0404176] [INSPIRE].
I. Papadimitriou, Non-Supersymmetric Membrane Flows from Fake Supergravity and Multi-Trace Deformations, JHEP 02 (2007) 008 [hep-th/0606038] [INSPIRE].
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] [INSPIRE].
I. Papadimitriou, Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT, JHEP 05 (2007) 075 [hep-th/0703152] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
V.E. Hubeny, Probing Singularities, in String theory: From gauge interactions to cosmology, L. Baulieu et al. eds, Proceedings, NATO Advanced Study Institute, Cargese, France, 7-19 June 2004, NATO Sci. Ser. II 208 (2006) 329.
J. Maldacena and G.L. Pimentel, Entanglement entropy in de Sitter space, JHEP 02 (2013) 038 [arXiv:1210.7244] [INSPIRE].
W. Fischler, S. Kundu and J.F. Pedraza, Entanglement and out-of-equilibrium dynamics in holographic models of de Sitter QFTs, JHEP 07 (2014) 021 [arXiv:1311.5519] [INSPIRE].
N. Engelhardt and A.C. Wall, Extremal Surface Barriers, JHEP 03 (2014) 068 [arXiv:1312.3699] [INSPIRE].
A. Bzowski, T. Hertog and M. Schillo, Cosmological singularities encoded in IR boundary correlations, arXiv:1512.05761 [INSPIRE].
I. Amado and C. Hoyos-Badajoz, AdS black holes as reflecting cavities, JHEP 09 (2008) 118 [arXiv:0807.2337] [INSPIRE].
S.P. Kumar and V. Vaganov, Relevant deformations of \( \mathcal{N}=4 \) SYM and AdS crunches, in preparation.
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
F. Cooper, A. Khare and U. Sukhatme, Supersymmetry and quantum mechanics, Phys. Rept. 251 (1995) 267 [hep-th/9405029] [INSPIRE].
M. Bañados, A. Gomberoff and C. Martinez, Anti-de Sitter space and black holes, Class. Quant. Grav. 15 (1998) 3575 [hep-th/9805087] [INSPIRE].
G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
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Kumar, S.P., Vaganov, V. Quasinormal modes and holographic correlators in a crunching AdS geometry. J. High Energ. Phys. 2016, 65 (2016). https://doi.org/10.1007/JHEP02(2016)065
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DOI: https://doi.org/10.1007/JHEP02(2016)065