Abstract
Perturbative bulk reconstruction in AdS/CFT starts by representing a free bulk field ϕ(0) as a smeared operator in the CFT. A series of 1/N corrections must be added to ϕ(0) to represent an interacting bulk field ϕ. These corrections have been determined in the literature from several points of view. Here we develop a new perspective. We show that correlation functions involving ϕ(0) suffer from ambiguities due to analytic continuation. As a result ϕ(0) fails to be a well-defined linear operator in the CFT. This means bulk reconstruction can be understood as a procedure for building up well-defined operators in the CFT which thereby singles out the interacting field ϕ. We further propose that the difficulty with defining ϕ(0) as a linear operator can be re-interpreted as a breakdown of associativity. Presumably ϕ(0) can only be corrected to become an associative operator in perturbation theory. This suggests that quantum mechanics in the bulk is only valid in perturbation theory around a semiclassical bulk geometry.
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].
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].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
V.K. Dobrev, Intertwining operator realization of the AdS/CFT correspondence, Nucl. Phys. B 553 (1999) 559 [hep-th/9812194] [INSPIRE].
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].
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].
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].
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].
H. Verlinde, Poking Holes in AdS/CFT: Bulk Fields from Boundary States, arXiv:1505.05069 [INSPIRE].
M. Miyaji, T. Numasawa, N. Shiba, T. Takayanagi and K. Watanabe, Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Correspondence, Phys. Rev. Lett. 115 (2015) 171602 [arXiv:1506.01353] [INSPIRE].
Y. Nakayama and H. Ooguri, Bulk Locality and Boundary Creating Operators, JHEP 10 (2015) 114 [arXiv:1507.04130] [INSPIRE].
D. Kabat and G. Lifschytz, Local bulk physics from intersecting modular Hamiltonians, JHEP 06 (2017) 120 [arXiv:1703.06523] [INSPIRE].
T. Faulkner and A. Lewkowycz, Bulk locality from modular flow, JHEP 07 (2017) 151 [arXiv:1704.05464] [INSPIRE].
J. Cotler, P. Hayden, G. Salton, B. Swingle and M. Walter, Entanglement Wedge Reconstruction via Universal Recovery Channels, arXiv:1704.05839 [INSPIRE].
D. Kabat and G. Lifschytz, Bulk equations of motion from CFT correlators, JHEP 09 (2015) 059 [arXiv:1505.03755] [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].
A. Lewkowycz, G.J. Turiaci and H. Verlinde, A CFT Perspective on Gravitational Dressing and Bulk Locality, JHEP 01 (2017) 004 [arXiv:1608.08977] [INSPIRE].
M. Guica, Bulk fields from the boundary OPE, arXiv:1610.08952 [INSPIRE].
N. Anand, H. Chen, A.L. Fitzpatrick, J. Kaplan and D. Li, An Exact Operator That Knows Its Location, JHEP 02 (2018) 012 [arXiv:1708.04246] [INSPIRE].
H. Chen, A.L. Fitzpatrick, J. Kaplan and D. Li, The AdS 3 Propagator and the Fate of Locality, arXiv:1712.02351 [INSPIRE].
D. Kabat and G. Lifschytz, CFT representation of interacting bulk gauge fields in AdS, Phys. Rev. D 87 (2013) 086004 [arXiv:1212.3788] [INSPIRE].
D. Kabat and G. Lifschytz, Decoding the hologram: Scalar fields interacting with gravity, Phys. Rev. D 89 (2014) 066010 [arXiv:1311.3020] [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].
D. Sarkar and X. Xiao, Holographic Representation of Higher Spin Gauge Fields, Phys. Rev. D 91 (2015) 086004 [arXiv:1411.4657] [INSPIRE].
A. Almheiri, X. Dong and D. Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT, JHEP 04 (2015) 163 [arXiv:1411.7041] [INSPIRE].
E. Mintun, J. Polchinski and V. Rosenhaus, Bulk-Boundary Duality, Gauge Invariance and Quantum Error Corrections, Phys. Rev. Lett. 115 (2015) 151601 [arXiv:1501.06577] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks, JHEP 01 (2016) 146 [arXiv:1508.00501] [INSPIRE].
B. Czech, L. Lamprou, S. McCandlish, B. Mosk and J. Sully, A Stereoscopic Look into the Bulk, JHEP 07 (2016) 129 [arXiv:1604.03110] [INSPIRE].
B. Carneiro da Cunha and M. Guica, Exploring the BTZ bulk with boundary conformal blocks, arXiv:1604.07383 [INSPIRE].
J. de Boer, F.M. Haehl, M.P. Heller and R.C. Myers, Entanglement, holography and causal diamonds, JHEP 08 (2016) 162 [arXiv:1606.03307] [INSPIRE].
D. Kabat and G. Lifschytz, Locality, bulk equations of motion and the conformal bootstrap, JHEP 10 (2016) 091 [arXiv:1603.06800] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An Apologia for Firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].
K. Papadodimas and S. Raju, An Infalling Observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [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].
K. Papadodimas and S. Raju, Remarks on the necessity and implications of state-dependence in the black hole interior, Phys. Rev. D 93 (2016) 084049 [arXiv:1503.08825] [INSPIRE].
D. Berenstein and A. Miller, Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?, Phys. Rev. Lett. 118 (2017) 261601 [arXiv:1605.06166] [INSPIRE].
D.L. Jafferis, Bulk reconstruction and the Hartle-Hawking wavefunction, arXiv:1703.01519 [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: 1801.08101
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
Kabat, D., Lifschytz, G. Does boundary quantum mechanics imply quantum mechanics in the bulk?. J. High Energ. Phys. 2018, 151 (2018). https://doi.org/10.1007/JHEP03(2018)151
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2018)151