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Traversable wormholes via a double trace deformation

  • Regular Article - Theoretical Physics
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  • Published: 28 December 2017
  • volume 2017, Article number: 151 (2017)
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Traversable wormholes via a double trace deformation
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  • Ping Gao  ORCID: orcid.org/0000-0002-5028-76151,
  • Daniel Louis Jafferis1 &
  • Aron C. Wall2 
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A preprint version of the article is available at arXiv.

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.

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References

  1. 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].

    Article  MathSciNet  ADS  Google Scholar 

  2. D. Amati, M. Ciafaloni and G. Veneziano, Effective action and all order gravitational eikonal at Planckian energies, Nucl. Phys. B 403 (1993) 707 [INSPIRE].

    Article  ADS  Google Scholar 

  3. 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].

  4. 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].

  5. M. Bañados, C. Teitelboim and J. Zanelli, Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  6. C. Barcelo and M. Visser, Traversable wormholes from massless conformally coupled scalar fields, Phys. Lett. B 466 (1999) 127 [gr-qc/9908029] [INSPIRE].

  7. T. Barrella, X. Dong, S.A. Hartnoll and V.L. Martin, Holographic entanglement beyond classical gravity, JHEP 09 (2013) 109 [arXiv:1306.4682] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  8. M. Berkooz, A. Sever and A. Shomer, ’Double trace’deformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].

  9. B. Bhawal and S. Kar, Lorentzian wormholes in Einstein-Gauss-Bonnet theory, Phys. Rev. D 46 (1992) 2464 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  10. R. Bousso, A covariant entropy conjecture, JHEP 07 (1999) 004 [hep-th/9905177] [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  11. R. Bousso, Z. Fisher, S. Leichenauer and A.C. Wall, Quantum focusing conjecture, Phys. Rev. D 93 (2016) 064044 [arXiv:1506.02669] [INSPIRE].

  12. P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  13. 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].

  14. 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].

    Article  MathSciNet  ADS  Google Scholar 

  15. S. Carlip, The (2 + 1)-dimensional black hole, Class. Quant. Grav. 12 (1995) 2853 [gr-qc/9506079] [INSPIRE].

  16. 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].

    Article  MathSciNet  ADS  Google Scholar 

  17. X. Dong and A. Lewkowycz, Entropy, Extremality, Euclidean Variations and the Equations of Motion, arXiv:1705.08453 [INSPIRE].

  18. N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].

    Article  ADS  Google Scholar 

  19. 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].

    Article  MathSciNet  ADS  Google Scholar 

  20. T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].

    Article  ADS  Google Scholar 

  21. 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].

  22. N. Graham and K.D. Olum, Achronal averaged null energy condition, Phys. Rev. D 76 (2007) 064001 [arXiv:0705.3193] [INSPIRE].

  23. R. Haag, N.M. Hugenholtz and M. Winnink, On the equilibrium states in quantum statistical mechanics, Commun. Math. Phys. 5 (1967) 215 [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  24. P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. D. Hochberg and M. Visser, Null energy condition in dynamic wormholes, Phys. Rev. Lett. 81 (1998) 746 [gr-qc/9802048] [INSPIRE].

  26. 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].

    Article  MathSciNet  ADS  Google Scholar 

  27. D.M. Hofman and J. Maldacena, Conformal collider physics: Energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].

    Article  ADS  Google Scholar 

  28. V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. I. Ichinose and Y. Satoh, Entropies of scalar fields on three-dimensional black holes, Nucl. Phys. B 447 (1995) 340 [hep-th/9412144] [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  30. W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. 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].

    ADS  Google Scholar 

  32. J. Koeller and S. Leichenauer, Holographic Proof of the Quantum Null Energy Condition, Phys. Rev. D 94 (2016) 024026 [arXiv:1512.06109] [INSPIRE].

  33. 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].

  34. 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].

    MathSciNet  ADS  Google Scholar 

  35. J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  36. J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. D. Marolf and A.C. Wall, Eternal black holes and superselection in AdS/CFT, Class. Quant. Grav. 30 (2013) 025001 [arXiv:1210.3590] [INSPIRE].

  38. 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].

    Article  MATH  ADS  Google Scholar 

  39. M.S. Morris, K.S. Thorne and U. Yurtsever, Wormholes, time machines and the weak energy condition, Phys. Rev. Lett. 61 (1988) 1446 [INSPIRE].

    Article  ADS  Google Scholar 

  40. 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].

    Article  MathSciNet  ADS  Google Scholar 

  41. K. Papadodimas and S. Raju, An infalling observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].

    Article  ADS  Google Scholar 

  42. L. Parker and D. Toms, Quantum field theory in curved spacetime: quantized field(s an)d gravity, Cambridge University Press, Cambridge U.K. (2009).

  43. 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).

  44. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  45. M.J. Schlosser, Multiple hypergeometric series: Appell series and beyond, in Computer Algebra in Quantum Field Theory, Springer, Heidelberg Germany (2013), pg. 305.

  46. S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  47. S.N. Solodukhin, Restoring unitarity in BTZ black hole, Phys. Rev. D 71 (2005) 064006 [hep-th/0501053] [INSPIRE].

  48. A. Strominger and D.M. Thompson, A Quantum Bousso bound, Phys. Rev. D 70 (2004) 044007 [hep-th/0303067] [INSPIRE].

  49. L. Susskind, ER=EPR, GHZ and the consistency of quantum measurements, Fortsch. Phys. 64 (2016) 72 [arXiv:1412.8483] [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  50. 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].

  51. W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].

    ADS  Google Scholar 

  52. M. Visser, Lorentzian wormholes: From Einstein to Hawking, AIP Press, College Park U.S.A. (1996).

  53. 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].

  54. A.C. Wall, Ten proofs of the generalized second law, JHEP 06 (2009) 021 [arXiv:0901.3865] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  55. 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].

  56. 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].

  57. 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].

  58. E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].

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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.

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Authors and Affiliations

  1. Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA, U.S.A.

    Ping Gao & Daniel Louis Jafferis

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, U.S.A.

    Aron C. Wall

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  1. Ping Gao
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  2. Daniel Louis Jafferis
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  3. Aron C. Wall
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Correspondence to Daniel Louis Jafferis.

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ArXiv ePrint: 1608.05687

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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

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  • Received: 14 September 2017

  • Accepted: 14 December 2017

  • Published: 28 December 2017

  • DOI: https://doi.org/10.1007/JHEP12(2017)151

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Keywords

  • Black Holes
  • Gauge-gravity correspondence
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