Abstract
After turning on an interaction that couples the two boundaries of an eternal BTZ black hole, we find a quantum matter stress tensor with negative average null energy, whose gravitational backreaction renders the Einstein-Rosen bridge traversable. Such a traversable wormhole has an interesting interpretation in the context of ER=EPR, which we suggest might be related to quantum teleportation. However, it cannot be used to violate causality. We also discuss the implications for the energy and holographic entropy in the dual CFT description.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
O. Aharony, M. Berkooz and B. Katz, Non-local effects of multi-trace deformations in the AdS/CFT correspondence, JHEP 10 (2005) 097 [hep-th/0504177] [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Effective action and all order gravitational eikonal at Planckian energies, Nucl. Phys. B 403 (1993) 707 [INSPIRE].
R.E. Arias, M. Botta Cantcheff and G.A. Silva, Lorentzian AdS, Wormholes and Holography, Phys. Rev. D 83 (2011) 066015 [arXiv:1012.4478] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [Erratum ibid. D 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
C. Barcelo and M. Visser, Traversable wormholes from massless conformally coupled scalar fields, Phys. Lett. B 466 (1999) 127 [gr-qc/9908029] [INSPIRE].
T. Barrella, X. Dong, S.A. Hartnoll and V.L. Martin, Holographic entanglement beyond classical gravity, JHEP 09 (2013) 109 [arXiv:1306.4682] [INSPIRE].
M. Berkooz, A. Sever and A. Shomer, ’Double trace’deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].
B. Bhawal and S. Kar, Lorentzian wormholes in Einstein-Gauss-Bonnet theory, Phys. Rev. D 46 (1992) 2464 [INSPIRE].
R. Bousso, A covariant entropy conjecture, JHEP 07 (1999) 004 [hep-th/9905177] [INSPIRE].
R. Bousso, Z. Fisher, S. Leichenauer and A.C. Wall, Quantum focusing conjecture, Phys. Rev. D 93 (2016) 064044 [arXiv:1506.02669] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
W. Bunting, Z. Fu and D. Marolf, A coarse-grained generalized second law for holographic conformal field theories, Class. Quant. Grav. 33 (2016) 055008 [arXiv:1509.00074] [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
S. Carlip, The (2 + 1)-dimensional black hole, Class. Quant. Grav. 12 (1995) 2853 [gr-qc/9506079] [INSPIRE].
X. Dong, D. Harlow and A.C. Wall, Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality, Phys. Rev. Lett. 117 (2016) 021601 [arXiv:1601.05416] [INSPIRE].
X. Dong and A. Lewkowycz, Entropy, Extremality, Euclidean Variations and the Equations of Motion, arXiv:1705.08453 [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].
T. Faulkner, R.G. Leigh, O. Parrikar and H. Wang, Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition, JHEP 09 (2016) 038 [arXiv:1605.08072] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
E.E. Flanagan, D. Marolf and R.M. Wald, Proof of classical versions of the Bousso entropy bound and of the generalized second law, Phys. Rev. D 62 (2000) 084035 [hep-th/9908070] [INSPIRE].
N. Graham and K.D. Olum, Achronal averaged null energy condition, Phys. Rev. D 76 (2007) 064001 [arXiv:0705.3193] [INSPIRE].
R. Haag, N.M. Hugenholtz and M. Winnink, On the equilibrium states in quantum statistical mechanics, Commun. Math. Phys. 5 (1967) 215 [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
D. Hochberg and M. Visser, Null energy condition in dynamic wormholes, Phys. Rev. Lett. 81 (1998) 746 [gr-qc/9802048] [INSPIRE].
D.M. Hofman, D. Li, D. Meltzer, D. Poland and F. Rejon-Barrera, A Proof of the Conformal Collider Bounds, JHEP 06 (2016) 111 [arXiv:1603.03771] [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
I. Ichinose and Y. Satoh, Entropies of scalar fields on three-dimensional black holes, Nucl. Phys. B 447 (1995) 340 [hep-th/9412144] [INSPIRE].
W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [INSPIRE].
W.R. Kelly and A.C. Wall, Holographic proof of the averaged null energy condition, Phys. Rev. D 90 (2014) 106003 [arXiv:1408.3566] [INSPIRE].
J. Koeller and S. Leichenauer, Holographic Proof of the Quantum Null Energy Condition, Phys. Rev. D 94 (2016) 024026 [arXiv:1512.06109] [INSPIRE].
E.-A. Kontou and K.D. Olum, Averaged null energy condition in a classical curved background, Phys. Rev. D 87 (2013) 064009 [arXiv:1212.2290] [INSPIRE].
E.-A. Kontou and K.D. Olum, Proof of the averaged null energy condition in a classical curved spacetime using a null-projected quantum inequality, Phys. Rev. D 92 (2015) 124009 [arXiv:1507.00297] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
D. Marolf and A.C. Wall, Eternal black holes and superselection in AdS/CFT, Class. Quant. Grav. 30 (2013) 025001 [arXiv:1210.3590] [INSPIRE].
M.S. Morris and K.S. Thorne, Wormholes in space-time and their use for interstellar travel: A tool for teaching general relativity, Am. J. Phys. 56 (1988) 395 [INSPIRE].
M.S. Morris, K.S. Thorne and U. Yurtsever, Wormholes, time machines and the weak energy condition, Phys. Rev. Lett. 61 (1988) 1446 [INSPIRE].
T. Numasawa, N. Shiba, T. Takayanagi and K. Watanabe, EPR pairs, local projections and quantum teleportation in holography, JHEP 08 (2016) 077 [arXiv:1604.01772] [INSPIRE].
K. Papadodimas and S. Raju, An infalling observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].
L. Parker and D. Toms, Quantum field theory in curved spacetime: quantized field(s an)d gravity, Cambridge University Press, Cambridge U.K. (2009).
A.P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, Integrals and series, volume 3: More special functions, Gordon and Breach, New York U.A.A. (1992).
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
M.J. Schlosser, Multiple hypergeometric series: Appell series and beyond, in Computer Algebra in Quantum Field Theory, Springer, Heidelberg Germany (2013), pg. 305.
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
S.N. Solodukhin, Restoring unitarity in BTZ black hole, Phys. Rev. D 71 (2005) 064006 [hep-th/0501053] [INSPIRE].
A. Strominger and D.M. Thompson, A Quantum Bousso bound, Phys. Rev. D 70 (2004) 044007 [hep-th/0303067] [INSPIRE].
L. Susskind, ER=EPR, GHZ and the consistency of quantum measurements, Fortsch. Phys. 64 (2016) 72 [arXiv:1412.8483] [INSPIRE].
M. Thibeault, C. Simeone and E.F. Eiroa, Thin-shell wormholes in Einstein-Maxwell theory with a Gauss-Bonnet term, Gen. Rel. Grav. 38 (2006) 1593 [gr-qc/0512029] [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
M. Visser, Lorentzian wormholes: From Einstein to Hawking, AIP Press, College Park U.S.A. (1996).
M. Visser, S. Kar and N. Dadhich, Traversable wormholes with arbitrarily small energy condition violations, Phys. Rev. Lett. 90 (2003) 201102 [gr-qc/0301003] [INSPIRE].
A.C. Wall, Ten proofs of the generalized second law, JHEP 06 (2009) 021 [arXiv:0901.3865] [INSPIRE].
A.C. Wall, Proving the Achronal Averaged Null Energy Condition from the Generalized Second Law, Phys. Rev. D 81 (2010) 024038 [arXiv:0910.5751] [INSPIRE].
A.C. Wall, A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices, Phys. Rev. D 85 (2012) 104049 [arXiv:1105.3445] [INSPIRE].
A.C. Wall, The generalized second law implies a quantum singularity theorem, Class. Quant. Grav. 30 (2013) 165003 [Erratum ibid. 30 (2013) 199501] [arXiv:1010.5513] [INSPIRE].
E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
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: 1608.05687
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Gao, P., Jafferis, D.L. & Wall, A.C. Traversable wormholes via a double trace deformation. J. High Energ. Phys. 2017, 151 (2017). https://doi.org/10.1007/JHEP12(2017)151
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2017)151