Skip to main content
SpringerLink
Log in

Bulk and transhorizon measurements in AdS/CFT

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We discuss the construction of bulk operators in asymptotically AdS space-times, including the interiors of AdS black holes. We use this to address the question “If Schrodinger’s cat were behind the horizon of an AdS black hole, could we determine its state by a measurement in the dual CFT?” We argue that the answer is affirmative, but this assumes a complete knowledge of both the bulk and boundary dynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [INSPIRE].

  2. L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. T. Banks, W. Fischler, S. Shenker and L. Susskind, M theory as a matrix model: A Conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  4. J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].

  5. L. Susskind, L. Thorlacius and J. Uglum, The Stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  6. C.R. Stephens, G. ’t Hooft and B.F. Whiting, Black hole evaporation without information loss, Class. Quant. Grav. 11 (1994) 621 [gr-qc/9310006] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A Boundary view of horizons and locality, Phys. Rev. D 73 (2006) 086003 [hep-th/0506118] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  8. A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, arXiv:1207.3123 [INSPIRE].

  9. 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].

    MathSciNet  ADS  Google Scholar 

  10. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  11. T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].

  12. V. Balasubramanian, P. Kraus, A.E. Lawrence and S.P. Trivedi, Holographic probes of anti-de Sitter space-times, Phys. Rev. D 59 (1999) 104021 [hep-th/9808017] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  13. D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].

  14. L. Hormander, A remark on Holmgren’s uniqueness theorem, J. Diff. Geom. 6 (1971) 129.

    MathSciNet  Google Scholar 

  15. I. Bena, On the construction of local fields in the bulk of AdS 5 and other spaces, Phys. Rev. D 62 (2000) 066007 [hep-th/9905186] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  16. D. Kabat, G. Lifschytz and D.A. Lowe, Constructing local bulk observables in interacting AdS/CFT, Phys. Rev. D 83 (2011) 106009 [arXiv:1102.2910] [INSPIRE].

    ADS  Google Scholar 

  17. A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Holographic representation of local bulk operators, Phys. Rev. D 74 (2006) 066009 [hep-th/0606141] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  18. A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A Holographic description of the black hole interior, Phys. Rev. D 75 (2007) 106001 [Erratum ibid. D 75 (2007) 129902] [hep-th/0612053] [INSPIRE].

  19. S.B. Giddings, Flat space scattering and bulk locality in the AdS/CFT correspondence, Phys. Rev. D 61 (2000) 106008 [hep-th/9907129] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  20. J. Polchinski, S matrices from AdS space-time, hep-th/9901076 [INSPIRE].

  21. L. Susskind, Holography in the flat space limit, hep-th/9901079 [INSPIRE].

  22. M. Gary, S.B. Giddings and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80 (2009) 085005 [arXiv:0903.4437] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  23. I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. I. Heemskerk, Construction of Bulk Fields with Gauge Redundancy, JHEP 09 (2012) 106 [arXiv:1201.3666] [INSPIRE].

    Article  ADS  Google Scholar 

  25. D. Kabat, G. Lifschytz, S. Roy and D. Sarkar, Holographic representation of bulk fields with spin in AdS/CFT, Phys. Rev. D 86 (2012) 026004 [arXiv:1204.0126] [INSPIRE].

    ADS  Google Scholar 

  26. J. Polchinski, L. Susskind and N. Toumbas, Negative energy, superluminosity and holography, Phys. Rev. D 60 (1999) 084006 [hep-th/9903228] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  27. B. Freivogel and L. Susskind, A framework for the landscape, Phys. Rev. D 70 (2004) 126007 [hep-th/0408133] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  28. D. Marolf, Holographic Thought Experiments, Phys. Rev. D 79 (2009) 024029 [arXiv:0808.2845] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  29. V. Balasubramanian and S.F. Ross, Holographic particle detection, Phys. Rev. D 61 (2000) 044007 [hep-th/9906226] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  30. L. Susskind and N. Toumbas, Wilson loops as precursors, Phys. Rev. D 61 (2000) 044001 [hep-th/9909013] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  32. V.E. Hubeny, Precursors see inside black holes, Int. J. Mod. Phys. D 12 (2003) 1693 [hep-th/0208047] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  33. P. Kraus, H. Ooguri and S. Shenker, Inside the horizon with AdS/CFT, Phys. Rev. D 67 (2003) 124022 [hep-th/0212277] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  34. L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The black hole singularity in AdS/CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. D. Marolf, Unitarity and Holography in Gravitational Physics, Phys. Rev. D 79 (2009) 044010 [arXiv:0808.2842] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  36. G. Horowitz, A. Lawrence and E. Silverstein, Insightful D-branes, JHEP 07 (2009) 057 [arXiv:0904.3922] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. R.D. Sorkin, Impossible measurements on quantum fields, in College Park 1993, Directions in general relativity, volume II, pg. 293 [gr-qc/9302018] [INSPIRE].

  38. D. Beckman, D. Gottesman, A. Kitaev and J. Preskill, Measurability of Wilson loop operators, Phys. Rev. D 65 (2002) 065022 [hep-th/0110205] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  39. S.D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. R. Bousso, S. Leichenauer and V. Rosenhaus, Light-sheets and AdS/CFT, Phys. Rev. D 86 (2012) 046009 [arXiv:1203.6619] [INSPIRE].

    ADS  Google Scholar 

  41. S.B. Giddings, D. Marolf and J.B. Hartle, Observables in effective gravity, Phys. Rev. D 74 (2006) 064018 [hep-th/0512200] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  42. S.B. Giddings and D. Marolf, A global picture of quantum de Sitter space, Phys. Rev. D 76 (2007) 064023 [arXiv:0705.1178] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  43. C. Rovelli, Quantum mechanics without time: a model, Phys. Rev. D 42 (1990) 2638 [INSPIRE].

    ADS  Google Scholar 

  44. C. Rovelli, What is observable in classical and quantum gravity?, Class. Quant. Grav. 8 (1991) 297 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. C. Rovelli, Quantum reference systems, Class. Quant. Grav. 8 (1991) 317 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. C. Rovelli, Partial observables, Phys. Rev. D 65 (2002) 124013 [gr-qc/0110035] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  47. D. Marolf, Quantum observables and recollapsing dynamics, Class. Quant. Grav. 12 (1995) 1199 [gr-qc/9404053] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. D. Marolf, Almost ideal clocks in quantum cosmology: a brief derivation of time, Class. Quant. Grav. 12 (1995) 2469 [gr-qc/9412016] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. I. Heemskerk and J. Polchinski, Holographic and Wilsonian Renormalization Groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. T. Faulkner, H. Liu and M. Rangamani, Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm, JHEP 08 (2011) 051 [arXiv:1010.4036] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  51. S.-S. Lee, Holographic description of large-N gauge theory, Nucl. Phys. B 851 (2011) 143 [arXiv:1011.1474] [INSPIRE].

    Article  ADS  Google Scholar 

  52. M. Li, A Note on relation between holographic RG equation and Polchinski’s RG equation, Nucl. Phys. B 579 (2000) 525 [hep-th/0001193] [INSPIRE].

    Article  ADS  Google Scholar 

  53. A.C. Petkou, Boundary multitrace deformations and OPEs in AdS/CFT correspondence, JHEP 06 (2002) 009 [hep-th/0201258] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. E.T. Akhmedov, Notes on multitrace operators and holographic renormalization group, hep-th/0202055 [INSPIRE].

  55. C. Becchi, S. Giusto and C. Imbimbo, The Wilson-Polchinski renormalization group equation in the planar limit, Nucl. Phys. B 633 (2002) 250 [hep-th/0202155] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  56. J. Louko, D. Marolf and S.F. Ross, On geodesic propagators and black hole holography, Phys. Rev. D 62 (2000) 044041 [hep-th/0002111] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  57. S.B. Giddings and M. Lippert, Precursors, black holes and a locality bound, Phys. Rev. D 65 (2002) 024006 [hep-th/0103231] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  58. B. Freivogel, S.B. Giddings and M. Lippert, Toward a theory of precursors, Phys. Rev. D 66 (2002) 106002 [hep-th/0207083] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  59. J. Polchinski, M theory and the light cone, Prog. Theor. Phys. Suppl. 134 (1999) 158 [hep-th/9903165] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of California, Santa Barbara, CA, 93106, USA

    Idse Heemskerk, Donald Marolf, Joseph Polchinski & James Sully

  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106-4030, USA

    Donald Marolf & Joseph Polchinski

Authors
  1. Idse Heemskerk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Donald Marolf
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joseph Polchinski
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. James Sully
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joseph Polchinski.

Additional information

ArXiv ePrint: 1201.3664

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heemskerk, I., Marolf, D., Polchinski, J. et al. Bulk and transhorizon measurements in AdS/CFT. J. High Energ. Phys. 2012, 165 (2012). https://doi.org/10.1007/JHEP10(2012)165

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP10(2012)165

Keywords

Search

Navigation