Abstract
The classical gravity approximation is often employed in AdS/CFT to study the dual field theory, as it allows for many computations. A drawback is however the generic presence of singularities in classical gravity, which limits the applicability of AdS/CFT to regimes where the singularities are avoided by bulk probes, or some other form of regularisation is applicable. At the same time, quantum gravity is expected to resolve those singularities and thus to extend the range of applicability of AdS/CFT also in classically singular regimes. This paper exemplifies such a computation. We use an effective quantum corrected Kasner-AdS metric inspired by results from non-perturbative canonical quantum gravity to compute the 2-point correlator in the geodesic approximation for a negative Kasner exponent. The correlator derived in the classical gravity approximation has previously been shown to contain a pole at finite distance as a signature of the singularity. Using the quantum corrected metric, we show explicitly how the pole is resolved and that a new subdominant long-distance contribution to the correlator emerges, caused by geodesics passing arbitrarily close to the resolved classical singularity. In order to compute analytically in this paper, two key simplifications in the quantum corrected metric are necessary. They are lifted in a companion paper using numerical techniques, leading to the same qualitative results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
S.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].
M. Ammon and J. Erdmenger, Gauge/gravity duality: foundations and applications, Cambridge University Press, Cambridge, U.K. (2015) [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].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Spacetime geometry in higher spin gravity, JHEP 10 (2011) 053 [arXiv:1106.4788] [INSPIRE].
C. Krishnan and S. Roy, Desingularization of the Milne universe, Phys. Lett. B 734 (2014) 92 [arXiv:1311.7315] [INSPIRE].
B. Craps, C. Krishnan and A. Saurabh, Low tension strings on a cosmological singularity, JHEP 08 (2014) 065 [arXiv:1405.3935] [INSPIRE].
K.S. Kiran, C. Krishnan, A. Saurabh and J. Simón, Strings vs. spins on the null orbifold, JHEP 12 (2014) 002 [arXiv:1408.3296] [INSPIRE].
M. Hanada, What lattice theorists can do for superstring/M-theory, Int. J. Mod. Phys. A 31 (2016) 1643006 [arXiv:1604.05421] [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].
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].
N. Turok, B. Craps and T. Hertog, From big crunch to big bang with AdS/CFT, arXiv:0711.1824 [INSPIRE].
S.R. Das, J. Michelson, K. Narayan and S.P. Trivedi, Cosmologies with null singularities and their gauge theory duals, Phys. Rev. D 75 (2007) 026002 [hep-th/0610053] [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].
A. Awad, S.R. Das, K. Narayan and S.P. Trivedi, Gauge theory duals of cosmological backgrounds and their energy momentum tensors, Phys. Rev. D 77 (2008) 046008 [arXiv:0711.2994] [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].
J.L.F. Barbón and E. Rabinovici, AdS crunches, CFT falls and cosmological complementarity, JHEP 04 (2011) 044 [arXiv:1102.3015] [INSPIRE].
M. Smolkin and N. Turok, Dual description of a 4d cosmology, arXiv:1211.1322 [INSPIRE].
S. Chatterjee, S.P. Chowdhury, S. Mukherji and Y.K. Srivastava, Nonvacuum AdS cosmology and comments on gauge theory correlator, Phys. Rev. D 95 (2017) 046011 [arXiv:1608.08401] [INSPIRE].
V. Balasubramanian and S.F. Ross, Holographic particle detection, Phys. Rev. D 61 (2000) 044007 [hep-th/9906226] [INSPIRE].
A. Ashtekar and E. Wilson-Ewing, The covariant entropy bound and loop quantum cosmology, Phys. Rev. D 78 (2008) 064047 [arXiv:0805.3511] [INSPIRE].
R. Bousso, A covariant entropy conjecture, JHEP 07 (1999) 004 [hep-th/9905177] [INSPIRE].
N. Bodendorfer, F.M. Mele and J. Münch, Holographic signatures of resolved cosmological singularities II: numerical investigations, arXiv:1804.01387 [INSPIRE].
A. Ashtekar, A. Corichi and P. Singh, Robustness of key features of loop quantum cosmology, Phys. Rev. D 77 (2008) 024046 [arXiv:0710.3565] [INSPIRE].
N. Bodendorfer, An elementary introduction to loop quantum gravity, arXiv:1607.05129 [INSPIRE].
N. Bodendorfer, State refinements and coarse graining in a full theory embedding of loop quantum cosmology, Class. Quant. Grav. 34 (2017) 135016 [arXiv:1607.06227] [INSPIRE].
N. Bodendorfer, An embedding of loop quantum cosmology in (b, v) variables into a full theory context, Class. Quant. Grav. 33 (2016) 125014 [arXiv:1512.00713] [INSPIRE].
D. Oriti, L. Sindoni and E. Wilson-Ewing, Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates, Class. Quant. Grav. 33 (2016) 224001 [arXiv:1602.05881] [INSPIRE].
E. Alesci and F. Cianfrani, Improved regularization from quantum reduced loop gravity, arXiv:1604.02375 [INSPIRE].
A.H. Chamseddine and V. Mukhanov, Resolving cosmological singularities, JCAP 03 (2017) 009 [arXiv:1612.05860] [INSPIRE].
I. Agullo, A. Ashtekar and W. Nelson, A quantum gravity extension of the inflationary scenario, Phys. Rev. Lett. 109 (2012) 251301 [arXiv:1209.1609] [INSPIRE].
A. Ashtekar and A. Barrau, Loop quantum cosmology: from pre-inflationary dynamics to observations, Class. Quant. Grav. 32 (2015) 234001 [arXiv:1504.07559] [INSPIRE].
B. Bolliet, A. Barrau, J. Grain and S. Schander, Observational exclusion of a consistent loop quantum cosmology scenario, Phys. Rev. D 93 (2016) 124011 [arXiv:1510.08766] [INSPIRE].
A. Ashtekar, T. Pawlowski and P. Singh, Quantum nature of the big bang: improved dynamics, Phys. Rev. D 74 (2006) 084003 [gr-qc/0607039] [INSPIRE].
B. Gupt and P. Singh, Quantum gravitational Kasner transitions in Bianchi-I spacetime, Phys. Rev. D 86 (2012) 024034 [arXiv:1205.6763] [INSPIRE].
N. Bodendorfer, Quantum reduction to Bianchi I models in loop quantum gravity, Phys. Rev. D 91 (2015) 081502 [arXiv:1410.5608] [INSPIRE].
T. Cailleteau, J. Mielczarek, A. Barrau and J. Grain, Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology, Class. Quant. Grav. 29 (2012) 095010 [arXiv:1111.3535] [INSPIRE].
M. Bojowald and J. Mielczarek, Some implications of signature-change in cosmological models of loop quantum gravity, JCAP 08 (2015) 052 [arXiv:1503.09154] [INSPIRE].
J. Ben Achour, S. Brahma, J. Grain and A. Marciano, A new look at scalar perturbations in loop quantum cosmology: (un)deformed algebra approach using self dual variables, arXiv:1610.07467 [INSPIRE].
A. Ashtekar, W. Kaminski and J. Lewandowski, Quantum field theory on a cosmological, quantum space-time, Phys. Rev. D 79 (2009) 064030 [arXiv:0901.0933] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
N. Engelhardt and A.C. Wall, Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].
N. Bodendorfer, A note on quantum supergravity and AdS/CFT, arXiv:1509.02036 [INSPIRE].
P. Singh, Is classical flat Kasner spacetime flat in quantum gravity?, Int. J. Mod. Phys. D 25 (2016) 1642001 [arXiv:1604.03828] [INSPIRE].
S.G. Naculich, H.J. Schnitzer and N. Wyllard, 1/N corrections to anomalies and the AdS/CFT correspondence for orientifolded N = 2 orbifold and N = 1 conifold models, Int. J. Mod. Phys. A 17 (2002) 2567 [hep-th/0106020] [INSPIRE].
S.S. Gubser and I. Mitra, Double trace operators and one loop vacuum energy in AdS/CFT, Phys. Rev. D 67 (2003) 064018 [hep-th/0210093] [INSPIRE].
F. Denef, S.A. Hartnoll and S. Sachdev, Black hole determinants and quasinormal modes, Class. Quant. Grav. 27 (2010) 125001 [arXiv:0908.2657] [INSPIRE].
S. Caron-Huot and O. Saremi, Hydrodynamic long-time tails from anti de Sitter space, JHEP 11 (2010) 013 [arXiv:0909.4525] [INSPIRE].
D. Jorrin, N. Kovensky and M. Schvellinger, Towards 1/N corrections to deep inelastic scattering from the gauge/gravity duality, JHEP 04 (2016) 113 [arXiv:1601.01627] [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT d /AdS d+1 correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [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].
L. Freidel, Reconstructing AdS/CFT, arXiv:0804.0632 [INSPIRE].
N. Bodendorfer, T. Thiemann and A. Thurn, Towards loop quantum supergravity (LQSG), Phys. Lett. B 711 (2012) 205 [arXiv:1106.1103] [INSPIRE].
B. Dittrich and J. Hnybida, Ising model from intertwiners, arXiv:1312.5646 [INSPIRE].
V. Bonzom, F. Costantino and E.R. Livine, Duality between spin networks and the 2D Ising model, Commun. Math. Phys. 344 (2016) 531 [arXiv:1504.02822] [INSPIRE].
V. Bonzom and B. Dittrich, 3D holography: from discretum to continuum, JHEP 03 (2016) 208 [arXiv:1511.05441] [INSPIRE].
L. Smolin, Holographic relations in loop quantum gravity, arXiv:1608.02932 [INSPIRE].
M. Han and L.-Y. Hung, Loop quantum gravity, exact holographic mapping and holographic entanglement entropy, Phys. Rev. D 95 (2017) 024011 [arXiv:1610.02134] [INSPIRE].
B. Dittrich, C. Goeller, E. Livine and A. Riello, Quasi-local holographic dualities in non-perturbative 3d quantum gravity I — convergence of multiple approaches and examples of Ponzano-Regge statistical duals, Nucl. Phys. B 938 (2019) 807 [arXiv:1710.04202] [INSPIRE].
B. Dittrich, C. Goeller, E.R. Livine and A. Riello, Quasi-local holographic dualities in non-perturbative 3d quantum gravity II — from coherent quantum boundaries to BMS 3 characters, Nucl. Phys. B 938 (2019) 878 [arXiv:1710.04237] [INSPIRE].
A. Ashtekar and M. Bojowald, Black hole evaporation: a paradigm, Class. Quant. Grav. 22 (2005) 3349 [gr-qc/0504029] [INSPIRE].
A.H. Chamseddine and V. Mukhanov, Nonsingular black hole, Eur. Phys. J. C 77 (2017) 183 [arXiv:1612.05861] [INSPIRE].
P. Kraus, H. Ooguri and S. Shenker, Inside the horizon with AdS/CFT, Phys. Rev. D 67 (2003) 124022 [hep-th/0212277] [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].
N. Engelhardt and G.T. Horowitz, Entanglement entropy near cosmological singularities, JHEP 06 (2013) 041 [arXiv:1303.4442] [INSPIRE].
V.A. Belinskii, E.M. Lifshitz and I.M. Khalatnikov, Oscillatory approach to the singular point in relativistic cosmology, Sov. Phys. Usp. 13 (1971) 745.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1612.06679
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Bodendorfer, N., Schäfer, A. & Schliemann, J. Holographic signatures of resolved cosmological singularities. J. High Energ. Phys. 2019, 43 (2019). https://doi.org/10.1007/JHEP06(2019)043
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2019)043