Abstract
In this note I elaborate on some features of a recent proposal of Papadodimas and Raju for a CFT description of the interior of a one-sided AdS black hole in a pure state. I clarify the treatment of 1/N corrections, and explain how the proposal is able to avoid some of the pitfalls that have disrupted other recent ideas. I argue however that the proposal has the uncomfortable property that states in the CFT Hilbert space do not have definite physical interpretations, unlike in ordinary quantum mechanics. I also contrast the “state-dependence” of the proposal with more familiar phenomena, arguing that, unlike in quantum mechanics, the measurement process (including the apparatus) in something like the PR proposal or its earlier manifestations cannot be described by unitary evolution. These issues render the proposal somewhat ambiguous, and it seems new ideas would be needed to make some version of it work. I close with some brief speculation on to what extent quantum mechanics should hold for the experience of an infalling observer.
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References
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199.
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: A Conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
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].
S.D. Mathur, The information paradox: A pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
S.B. Giddings, Models for unitary black hole disintegration, Phys. Rev. D 85 (2012) 044038 [arXiv:1108.2015] [INSPIRE].
S.L. Braunstein, S. Pirandola and K. Życzkowski, Better Late than Never: Information Retrieval from Black Holes, Phys. Rev. Lett. 110 (2013) 101301 [arXiv:0907.1190] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [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].
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An Apologia for Firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].
R. Bousso, Firewalls From Double Purity, Phys. Rev. D 88 (2013) 084035 [arXiv:1308.2665] [INSPIRE].
D. Marolf and J. Polchinski, Gauge/Gravity Duality and the Black Hole Interior, Phys. Rev. Lett. 111 (2013) 171301 [arXiv:1307.4706] [INSPIRE].
K. Papadodimas and S. Raju, Black Hole Interior in the Holographic Correspondence and the Information Paradox, Phys. Rev. Lett. 112 (2014) 051301 [arXiv:1310.6334] [INSPIRE].
K. Papadodimas and S. Raju, State-Dependent Bulk-Boundary Maps and Black Hole Complementarity, Phys. Rev. D 89 (2014) 086010 [arXiv:1310.6335] [INSPIRE].
R. Bousso, Complementarity Is Not Enough, Phys. Rev. D 87 (2013) 124023 [arXiv:1207.5192] [INSPIRE].
L. Susskind, The Transfer of Entanglement: The Case for Firewalls, arXiv:1210.2098 [INSPIRE].
K. Papadodimas and S. Raju, An Infalling Observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].
E. Verlinde and H. Verlinde, Black Hole Entanglement and Quantum Error Correction, JHEP 10 (2013) 107 [arXiv:1211.6913] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
L. Susskind, New Concepts for Old Black Holes, arXiv:1311.3335 [INSPIRE].
L. Susskind, Computational Complexity and Black Hole Horizons, arXiv:1402.5674 [INSPIRE].
L. Susskind, Addendum to Computational Complexity and Black Hole Horizons, arXiv:1403.5695 [INSPIRE].
R. Bousso, Violations of the Equivalence Principle by a Nonlocally Reconstructed Vacuum at the Black Hole Horizon, Phys. Rev. Lett. 112 (2014) 041102 [arXiv:1308.3697] [INSPIRE].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
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].
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].
I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, Bulk and Transhorizon Measurements in AdS/CFT, JHEP 10 (2012) 165 [arXiv:1201.3664] [INSPIRE].
B. Freivogel and L. Susskind, A framework for the landscape, Phys. Rev. D 70 (2004) 126007 [hep-th/0408133] [INSPIRE].
G. Horowitz, A. Lawrence and E. Silverstein, Insightful D-branes, JHEP 07 (2009) 057 [arXiv:0904.3922] [INSPIRE].
I. Heemskerk, Construction of Bulk Fields with Gauge Redundancy, JHEP 09 (2012) 106 [arXiv:1201.3666] [INSPIRE].
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].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
D. Harlow and D. Stanford, Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
S. Leichenauer and V. Rosenhaus, AdS black holes, the bulk-boundary dictionary and smearing functions, Phys. Rev. D 88 (2013) 026003 [arXiv:1304.6821] [INSPIRE].
W. Donnelly, Decomposition of entanglement entropy in lattice gauge theory, Phys. Rev. D 85 (2012) 085004 [arXiv:1109.0036] [INSPIRE].
W. Donnelly and A.C. Wall, Do gauge fields really contribute negatively to black hole entropy?, Phys. Rev. D 86 (2012) 064042 [arXiv:1206.5831] [INSPIRE].
H. Casini, M. Huerta and J.A. Rosabal, Remarks on entanglement entropy for gauge fields, Phys. Rev. D 89 (2014) 085012 [arXiv:1312.1183] [INSPIRE].
D. Radicevic, Notes on Entanglement in Abelian Gauge Theories, arXiv:1404.1391 [INSPIRE].
R. Streater and A. Wightman, PCT, spin and statistics, and all that, Addison-Wesley Pub., (1989).
J.B. Hartle and S.W. Hawking, Path Integral Derivation of Black Hole Radiance, Phys. Rev. D 13 (1976) 2188 [INSPIRE].
W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
M. Srednicki, Thermal fluctuations in quantized chaotic systems, J. Phys. A 29 (1996) L75 [chao-dyn/9511001] [INSPIRE].
S. Lloyd, Black Holes, Demons, and the Loss of Coherence: How complex systems get information, and what they do with it, Ph.D. Thesis, The Rockefeller University, 1 April 1988, http://meche.mit.edu/people/?id=55.
M. Van Raamsdonk, Evaporating Firewalls, arXiv:1307.1796 [INSPIRE].
S.H. Shenker, The strength of nonperturbative effects in string theory, NATO Sci. B 262 (1991) 191.
E. Verlinde and H. Verlinde, Behind the Horizon in AdS/CFT, arXiv:1311.1137 [INSPIRE].
S.H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 03 (2014) 067 [arXiv:1306.0622] [INSPIRE].
S.H. Shenker and D. Stanford, Multiple Shocks, arXiv:1312.3296 [INSPIRE].
J.V. Rocha, Evaporation of large black holes in AdS: Coupling to the evaporon, JHEP 08 (2008) 075 [arXiv:0804.0055] [INSPIRE].
D. Harlow and P. Hayden, Quantum Computation vs. Firewalls, JHEP 06 (2013) 085 [arXiv:1301.4504] [INSPIRE].
D. Harlow, Complementarity, not firewalls, unpublished (2013).
S. Aaronson, The Cryptographic Hardness of Decoding Hawking Radiation, to appear.
J. Preskill, Lecture Notes on Quantum Computation, (1998), http://www.theory.caltech.edu/people/preskill/ph229/.
G.T. Horowitz and J.M. Maldacena, The black hole final state, JHEP 02 (2004) 008 [hep-th/0310281] [INSPIRE].
D. Gottesman and J. Preskill, Comment on ‘The black hole final state’, JHEP 03 (2004) 026 [hep-th/0311269] [INSPIRE].
S. Lloyd and J. Preskill, Unitarity of black hole evaporation in final-state projection models, JHEP 08 (2014) 126 [arXiv:1308.4209] [INSPIRE].
R. Bousso and D. Stanford, Measurements without Probabilities in the Final State Proposal, Phys. Rev. D 89 (2014) 044038 [arXiv:1310.7457] [INSPIRE].
S.D. Mathur and D. Turton, The flaw in the firewall argument, Nucl. Phys. B 884 (2014) 566 [arXiv:1306.5488] [INSPIRE].
D. Harlow and L. Susskind, Crunches, Hats and a Conjecture, arXiv:1012.5302 [INSPIRE].
R. Bousso and L. Susskind, The Multiverse Interpretation of Quantum Mechanics, Phys. Rev. D 85 (2012) 045007 [arXiv:1105.3796] [INSPIRE].
J.D. Bekenstein, A Universal Upper Bound on the Entropy to Energy Ratio for Bounded Systems, Phys. Rev. D 23 (1981) 287 [INSPIRE].
H. Casini, Relative entropy and the Bekenstein bound, Class. Quant. Grav. 25 (2008) 205021 [arXiv:0804.2182] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
M. Headrick, V. Hubeny, A. Lawrence and M. Rangamani, Causality and holographic entanglement entropy, in preperation.
D. Harlow, Complementarity, not Firewalls, arXiv:1207.6243.
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Harlow, D. Aspects of the Papadodimas-Raju proposal for the black hole interior. J. High Energ. Phys. 2014, 55 (2014). https://doi.org/10.1007/JHEP11(2014)055
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DOI: https://doi.org/10.1007/JHEP11(2014)055