Abstract
The bulk reconstruction formula for a Euclidean anti-de Sitter space is directly related to the inverse of the Gel’fand-Graev-Radon transform. Correlation functions of a conformal scalar field theory in the boundary are thereby related to correlation functions of a self-interacting scalar field theory in the bulk at different loop orders.
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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].
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].
V. Balasubramanian, S.B. Giddings and A.E. Lawrence, What do CFTs tell us about Anti-de Sitter space-times?, JHEP 03 (1999) 001 [hep-th/9902052] [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].
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. Kabat and G. Lifschytz, Decoding the hologram: Scalar fields interacting with gravity, Phys. Rev. D 89 (2014) 066010 [arXiv:1311.3020] [INSPIRE].
D. Kabat and G. Lifschytz, Bulk equations of motion from CFT correlators, JHEP 09 (2015) 059 [arXiv:1505.03755] [INSPIRE].
S.R. Roy and D. Sarkar, Hologram of a pure state black hole, Phys. Rev. D 92 (2015) 126003 [arXiv:1505.03895] [INSPIRE].
D. Kabat and G. Lifschytz, Local bulk physics from intersecting modular Hamiltonians, JHEP 06 (2017) 120 [arXiv:1703.06523] [INSPIRE].
F. Sanches and S.J. Weinberg, Boundary dual of bulk local operators, Phys. Rev. D 96 (2017) 026004 [arXiv:1703.07780] [INSPIRE].
K. Goto and T. Takayanagi, CFT descriptions of bulk local states in the AdS black holes, arXiv:1704.00053 [INSPIRE].
S.R. Roy and D. Sarkar, Holographic bulk reconstruction beyond (super)gravity, arXiv:1704.06294 [INSPIRE].
G. Sárosi and T. Ugajin, Modular Hamiltonians of excited states, OPE blocks and emergent bulk fields, arXiv:1705.01486 [INSPIRE].
I.M. Gel’fand and M.I. Graev, Generalized Functions: Integral geometry and representation theory, Generalized functions, Academic Press (1966).
S. Helgason, Integral Geometry and Radon Transforms, Springer (2011).
G. Solanes, Integral geometry and curvature integrals in hyperbolic space, http://mat.uab.es/∼egallego/gil/tesiEng.pdf.
S. Rychkov, EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions, SpringerBriefs in Physics, Springer (2017) [arXiv:1601.05000] [INSPIRE].
I.M. Tolfree, An Alternative Path to the Boundary: The CFT as the Fourier Space of AdS, Phys. Rev. D 78 (2008) 106002 [arXiv:0809.0485] [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].
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ArXiv ePrint: 1705.06985
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Bhowmick, S., Ray, K. & Sen, S. Bulk reconstruction in AdS and Gel’fand-Graev-Radon transform. J. High Energ. Phys. 2017, 82 (2017). https://doi.org/10.1007/JHEP10(2017)082
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DOI: https://doi.org/10.1007/JHEP10(2017)082