A stereoscopic look into the bulk

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Mosk, Benjamin; Sully, James

doi:10.1007/JHEP07(2016)129

Title: A stereoscopic look into the bulk

Abstract

Here, we present the foundation for a holographic dictionary with depth perception. The dictionary consists of natural CFT operators whose duals are simple, diffeomorphism-invariant bulk operators. The CFT operators of interest are the “OPE blocks,” contributions to the OPE from a single conformal family. In holographic theories, we show that the OPE blocks are dual at leading order in 1/N to integrals of effective bulk fields along geodesics or homogeneous minimal surfaces in anti-de Sitter space. One widely studied example of an OPE block is the modular Hamiltonian, which is dual to the fluctuation in the area of a minimal surface. Thus, our operators pave the way for generalizing the Ryu-Takayanagi relation to other bulk fields. Although the OPE blocks are non-local operators in the CFT, they admit a simple geometric description as fields in kinematic space — the space of pairs of CFT points. We develop the tools for constructing local bulk operators in terms of these non-local objects. The OPE blocks also allow for conceptually clean and technically simple derivations of many results known in the literature, including linearized Einstein’s equations and the relation between conformal blocks and geodesic Witten diagrams.

Authors:

Czech, Bartlomiej ^[1]; Lamprou, Lampros ^[1]; McCandlish, Samuel ^[1]; Mosk, Benjamin ^[1]; Sully, James ^[2]

Stanford Univ., Stanford, CA (United States)
SLAC National Accelerator Lab., Menlo Park, CA (United States)

Publication Date:: Tue Jul 26 00:00:00 EDT 2016

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1281030

Grant/Contract Number:: AC02-76SF00515

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 7; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; AdS-CFT correspondence; Gauge-gravity correspondence

Citation Formats


                    Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, Mosk, Benjamin, and Sully, James. A stereoscopic look into the bulk.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP07(2016)129.

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                    Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, Mosk, Benjamin, & Sully, James. A stereoscopic look into the bulk.  United States.  https://doi.org/10.1007/JHEP07(2016)129

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                    Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, Mosk, Benjamin, and Sully, James. Tue .  
"A stereoscopic look into the bulk".  United States.  https://doi.org/10.1007/JHEP07(2016)129.  https://www.osti.gov/servlets/purl/1281030.

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@article{osti_1281030,

  title        = {A stereoscopic look into the bulk},

  author       = {Czech, Bartlomiej and Lamprou, Lampros and McCandlish, Samuel and Mosk, Benjamin and Sully, James},

  abstractNote = {Here, we present the foundation for a holographic dictionary with depth perception. The dictionary consists of natural CFT operators whose duals are simple, diffeomorphism-invariant bulk operators. The CFT operators of interest are the “OPE blocks,” contributions to the OPE from a single conformal family. In holographic theories, we show that the OPE blocks are dual at leading order in 1/N to integrals of effective bulk fields along geodesics or homogeneous minimal surfaces in anti-de Sitter space. One widely studied example of an OPE block is the modular Hamiltonian, which is dual to the fluctuation in the area of a minimal surface. Thus, our operators pave the way for generalizing the Ryu-Takayanagi relation to other bulk fields. Although the OPE blocks are non-local operators in the CFT, they admit a simple geometric description as fields in kinematic space — the space of pairs of CFT points. We develop the tools for constructing local bulk operators in terms of these non-local objects. The OPE blocks also allow for conceptually clean and technically simple derivations of many results known in the literature, including linearized Einstein’s equations and the relation between conformal blocks and geodesic Witten diagrams.},

  doi          = {10.1007/JHEP07(2016)129},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 7,

  volume       = 2016,

  place        = {United States},

  year         = {Tue Jul 26 00:00:00 EDT 2016},

  month        = {Tue Jul 26 00:00:00 EDT 2016}

}

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Works referenced in this record:

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Maldacena, Juan
International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133
DOI: 10.1023/A:1026654312961

Wilson Loops in Large $N$ Field Theories
journal, June 1998

Maldacena, Juan
Physical Review Letters, Vol. 80, Issue 22
DOI: 10.1103/PhysRevLett.80.4859

Insightful D-branes
journal, July 2009

Horowitz, Gary; Lawrence, Albion; Silverstein, Eva
Journal of High Energy Physics, Vol. 2009, Issue 07
DOI: 10.1088/1126-6708/2009/07/057

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

Ryu, Shinsei; Takayanagi, Tadashi
Physical Review Letters, Vol. 96, Issue 18
DOI: 10.1103/PhysRevLett.96.181602

Aspects of holographic entanglement entropy
journal, August 2006

Ryu, Shinsei; Takayanagi, Tadashi
Journal of High Energy Physics, Vol. 2006, Issue 08
DOI: 10.1088/1126-6708/2006/08/045

Towards a derivation of holographic entanglement entropy
journal, May 2011

Casini, Horacio; Huerta, Marina; Myers, Robert C.
Journal of High Energy Physics, Vol. 2011, Issue 5
DOI: 10.1007/JHEP05(2011)036

Integral geometry and holography
journal, October 2015

Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel
Journal of High Energy Physics, Vol. 2015, Issue 10
DOI: 10.1007/JHEP10(2015)175

Holographic de Sitter Geometry from Entanglement in Conformal Field Theory
journal, February 2016

de Boer, Jan; Heller, Michal P.; Myers, Robert C.
Physical Review Letters, Vol. 116, Issue 6
DOI: 10.1103/PhysRevLett.116.061602

Construction of bulk fields with gauge redundancy
journal, September 2012

Heemskerk, Idse
Journal of High Energy Physics, Vol. 2012, Issue 9
DOI: 10.1007/JHEP09(2012)106

Bulk and transhorizon measurements in AdS/CFT
journal, October 2012

Heemskerk, Idse; Marolf, Donald; Polchinski, Joseph
Journal of High Energy Physics, Vol. 2012, Issue 10
DOI: 10.1007/JHEP10(2012)165

Worldline approach to semi-classical conformal blocks
journal, July 2015

Hijano, Eliot; Kraus, Per; Snively, River
Journal of High Energy Physics, Vol. 2015, Issue 7
DOI: 10.1007/JHEP07(2015)131

Witten diagrams revisited: the AdS geometry of conformal blocks
journal, January 2016

Hijano, Eliot; Kraus, Per; Perlmutter, Eric
Journal of High Energy Physics, Vol. 2016, Issue 1
DOI: 10.1007/JHEP01(2016)146

Semiclassical Virasoro blocks from AdS3 gravity
journal, December 2015

Hijano, Eliot; Kraus, Per; Perlmutter, Eric
Journal of High Energy Physics, Vol. 2015, Issue 12
DOI: 10.1007/JHEP12(2015)077

Gravitational dynamics from entanglement “thermodynamics”
journal, April 2014

Lashkari, Nima; McDermott, Michael B.; Van Raamsdonk, Mark
Journal of High Energy Physics, Vol. 2014, Issue 4
DOI: 10.1007/JHEP04(2014)195

Gravitation from entanglement in holographic CFTs
journal, March 2014

Faulkner, Thomas; Guica, Monica; Hartman, Thomas
Journal of High Energy Physics, Vol. 2014, Issue 3
DOI: 10.1007/JHEP03(2014)051

Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994

Osborn, H.; Petkou, A.
Annals of Physics, Vol. 231, Issue 2
DOI: 10.1006/aphy.1994.1045

Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984

Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B.
Nuclear Physics B, Vol. 241, Issue 2
DOI: 10.1016/0550-3213(84)90052-X

Bulk locality and quantum error correction in AdS/CFT
journal, April 2015

Almheiri, Ahmed; Dong, Xi; Harlow, Daniel
Journal of High Energy Physics, Vol. 2015, Issue 4
DOI: 10.1007/JHEP04(2015)163

Locality of Gravitational Systems from Entanglement of Conformal Field Theories
journal, June 2015

Lin, Jennifer; Marcolli, Matilde; Ooguri, Hirosi
Physical Review Letters, Vol. 114, Issue 22
DOI: 10.1103/PhysRevLett.114.221601

Radon, Cosine and Sine Transforms on Real Hyperbolic Space
journal, September 2002

Rubin, B.
Advances in Mathematics, Vol. 170, Issue 2
DOI: 10.1016/S0001-8708(02)92074-8

Anti de Sitter space and holography
journal, January 1998

Witten, Edward
Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
DOI: 10.4310/ATMP.1998.v2.n2.a2

The ultrahyperbolic differential equation with four independent variables
journal, June 1938

John, Fritz
Duke Mathematical Journal, Vol. 4, Issue 2
DOI: 10.1215/S0012-7094-38-00423-5

Quantum corrections to holographic entanglement entropy
journal, November 2013

Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan
Journal of High Energy Physics, Vol. 2013, Issue 11
DOI: 10.1007/JHEP11(2013)074

Bulk equations of motion from CFT correlators
journal, September 2015

Kabat, Daniel; Lifschytz, Gilad
Journal of High Energy Physics, Vol. 2015, Issue 9
DOI: 10.1007/JHEP09(2015)059

Geometry of the 2+1 black hole
journal, August 1993

Bañados, Máximo; Henneaux, Marc; Teitelboim, Claudio
Physical Review D, Vol. 48, Issue 4
DOI: 10.1103/PhysRevD.48.1506

Entwinement and the emergence of spacetime
journal, January 2015

Balasubramanian, Vijay; Chowdhury, Borun D.; Czech, Bartłlomiej
Journal of High Energy Physics, Vol. 2015, Issue 1
DOI: 10.1007/JHEP01(2015)048

Virasoro conformal blocks and thermality from classical background fields
journal, November 2015

Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
Journal of High Energy Physics, Vol. 2015, Issue 11
DOI: 10.1007/JHEP11(2015)200

Entanglement renormalization and integral geometry
journal, December 2015

Huang, Xing; Lin, Feng-Li
Journal of High Energy Physics, Vol. 2015, Issue 12
DOI: 10.1007/JHEP12(2015)081

De Sitter Musings
journal, May 2012

Anninos, Dionysios
International Journal of Modern Physics A, Vol. 27, Issue 13
DOI: 10.1142/S0217751X1230013X

The dS/CFT correspondence
journal, October 2001

Strominger, Andrew
Journal of High Energy Physics, Vol. 2001, Issue 10
DOI: 10.1088/1126-6708/2001/10/034

Conformal covariant correlation functions
journal, June 1972

Ferrara, S.; Parisi, G.
Nuclear Physics B, Vol. 42
DOI: 10.1016/0550-3213(72)90480-4

Covariant expansion of the conformal four -point function
journal, December 1972

Ferrara, S.; Grillo, A. F.; Parisi, G.
Nuclear Physics B, Vol. 49
DOI: 10.1016/0550-3213(72)90587-1

Nonequivalence between conformal covariant Wilson expansion in Euclidean and Minkowski space
journal, September 1972

Ferrara, S.; Grillo, A. F.; Parisi, G.
Lettere al Nuovo Cimento, Vol. 5, Issue 2
DOI: 10.1007/BF02815915

The shadow operator formalism for conformal algebra. Vacuum expectation values and operator products
journal, May 1972

Ferrara, S.; Grillo, A. F.; Parisi, G.
Lettere al Nuovo Cimento, Vol. 4, Issue 4
DOI: 10.1007/BF02907130

Projectors, shadows, and conformal blocks
journal, April 2014

Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2014, Issue 4
DOI: 10.1007/JHEP04(2014)146

Future boundary conditions in de Sitter space
journal, February 2012

Anninos, Dionysios; Ng, Gim Seng; Strominger, Andrew
Journal of High Energy Physics, Vol. 2012, Issue 2
DOI: 10.1007/JHEP02(2012)032

Radon, Cosine and Sine Transforms on Real Hyperbolic Space
journal, September 2002

Rubin, Boris
Advances in Mathematics, Vol. 170, Issue 2
DOI: 10.1006/aima.2002.2074

The Radon transform
journal, January 1981

Ditkin, V. A.
USSR Computational Mathematics and Mathematical Physics, Vol. 21, Issue 4
DOI: 10.1016/0041-5553(81)90058-6

The Shadow Operator Formalism for Conformal Algebra. Vacuum Expectation Values and Operator Products
text, January 1972

,
INFN Open Access Repository
DOI: 10.15161/oar.it/1448458731.44

Integral geometry and Radon transforms
book, October 2000

Helgason, Sigurdur
Groups and Geometric Analysis
DOI: 10.1090/surv/083/02

Integral Geometry and Geometric Probability
book, January 2004

Santaló, Luis A.
Integral Geometry and Geometric Probability
DOI: 10.1017/cbo9780511617331.004

Insightful D-branes
text, January 2009

Horowitz, Gary; Lawrence, Albion; Silverstein, Eva
arXiv
DOI: 10.48550/arxiv.0904.3922

Towards a derivation of holographic entanglement entropy
text, January 2011

Casini, Horacio; Huerta, Marina; Myers, Robert C.
arXiv
DOI: 10.48550/arxiv.1102.0440

Future Boundary Conditions in De Sitter Space
text, January 2011

Anninos, Dionysios; Ng, Gim Seng; Strominger, Andrew
arXiv
DOI: 10.48550/arxiv.1106.1175

Bulk and Transhorizon Measurements in AdS/CFT
text, January 2012

Heemskerk, Idse; Marolf, Donald; Polchinski, Joseph
arXiv
DOI: 10.48550/arxiv.1201.3664

Projectors, Shadows, and Conformal Blocks
text, January 2012

Simmons-Duffin, David
arXiv
DOI: 10.48550/arxiv.1204.3894

Quantum corrections to holographic entanglement entropy
text, January 2013

Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan
arXiv
DOI: 10.48550/arxiv.1307.2892

Entwinement and the emergence of spacetime
text, January 2014

Balasubramanian, Vijay; Chowdhury, Borun D.; Czech, Bartlomiej
arXiv
DOI: 10.48550/arxiv.1406.5859

Worldline approach to semi-classical conformal blocks
preprint, January 2015

Hijano, Eliot; Kraus, Per; Snively, River
arXiv
DOI: 10.48550/arxiv.1501.02260

Virasoro Conformal Blocks and Thermality from Classical Background Fields
text, January 2015

Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
arXiv
DOI: 10.48550/arxiv.1501.05315

Bulk equations of motion from CFT correlators
preprint, January 2015

Kabat, Daniel; Lifschytz, Gilad
arXiv
DOI: 10.48550/arxiv.1505.03755

Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
text, January 2015

Hijano, Eliot; Kraus, Per; Perlmutter, Eric
arXiv
DOI: 10.48550/arxiv.1508.00501

Semiclassical Virasoro Blocks from AdS$_3$ Gravity
text, January 2015

Hijano, Eliot; Kraus, Per; Perlmutter, Eric
arXiv
DOI: 10.48550/arxiv.1508.04987

Geometry of the 2+1 Black Hole
text, January 1993

Banados, Maximo; Henneaux, Marc; Teitelboim, Claudio
arXiv
DOI: 10.48550/arxiv.gr-qc/9302012

Aspects of Holographic Entanglement Entropy
text, January 2006

Ryu, Shinsei; Takayanagi, Tadashi
arXiv
DOI: 10.48550/arxiv.hep-th/0605073

Anti De Sitter Space And Holography
text, January 1998

Witten, Edward
arXiv
DOI: 10.48550/arxiv.hep-th/9802150

Works referencing / citing this record:

Holographic subregion complexity from kinematic space
journal, January 2019

Abt, Raimond; Erdmenger, Johanna; Gerbershagen, Marius
Journal of High Energy Physics, Vol. 2019, Issue 1
DOI: 10.1007/jhep01(2019)012

Comments on holographic complexity
journal, March 2017

Carmi, Dean; Myers, Robert C.; Rath, Pratik
Journal of High Energy Physics, Vol. 2017, Issue 3
DOI: 10.1007/jhep03(2017)118

Holographic relations for OPE blocks in excited states
journal, March 2019

Cresswell, Jesse C.; Jardine, Ian T.; Peet, Amanda W.
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/jhep03(2019)058

Entanglement entropy in (1+1)D CFTs with multiple local excitations
journal, May 2018

Guo, Wu-zhong; He, Song; Luo, Zhu-Xi
Journal of High Energy Physics, Vol. 2018, Issue 5
DOI: 10.1007/jhep05(2018)154

Geodesic diagrams, gravitational interactions & OPE structures
journal, June 2017

Castro, Alejandra; Llabrés, Eva; Rejon-Barrera, Fernando
Journal of High Energy Physics, Vol. 2017, Issue 6
DOI: 10.1007/jhep06(2017)099

The bulk-to-boundary propagator in black hole microstate backgrounds
journal, June 2019

Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared
Journal of High Energy Physics, Vol. 2019, Issue 6
DOI: 10.1007/jhep06(2019)107

Entanglement, holography and causal diamonds
journal, August 2016

de Boer, Jan; Haehl, Felix M.; Heller, Michal P.
Journal of High Energy Physics, Vol. 2016, Issue 8
DOI: 10.1007/jhep08(2016)162

Solving the Schwarzian via the conformal bootstrap
journal, August 2017

Mertens, Thomas G.; Turiaci, Gustavo J.; Verlinde, Herman L.
Journal of High Energy Physics, Vol. 2017, Issue 8
DOI: 10.1007/jhep08(2017)136

Witten diagrams for torus conformal blocks
journal, September 2017

Kraus, Per; Maloney, Alexander; Maxfield, Henry
Journal of High Energy Physics, Vol. 2017, Issue 9
DOI: 10.1007/jhep09(2017)149

A conformal collider for holographic CFTs
journal, October 2018

Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein
Journal of High Energy Physics, Vol. 2018, Issue 10
DOI: 10.1007/jhep10(2018)156

Spectrum of modular Hamiltonian in the vacuum and excited states
journal, October 2019

Das, Suchetan; Ezhuthachan, Bobby
Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/jhep10(2019)009

Spinning geodesic Witten diagrams
journal, November 2017

Dyer, Ethan; Freedman, Daniel Z.; Sully, James
Journal of High Energy Physics, Vol. 2017, Issue 11
DOI: 10.1007/jhep11(2017)060

Kinematic space for conical defects
journal, November 2017

Cresswell, Jesse C.; Peet, Amanda W.
Journal of High Energy Physics, Vol. 2017, Issue 11
DOI: 10.1007/jhep11(2017)155

Towards entanglement of purification for conformal field theories
journal, June 2018

Hirai, Hayato; Tamaoka, Kotaro; Yokoya, Tsuyoshi
Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 6
DOI: 10.1093/ptep/pty063

Berry curvature, horocycles, and scattering states in ${AdS}_{3} / {CFT}_{2}$
journal, December 2019

Lévay, Péter
Physical Review D, Vol. 100, Issue 12
DOI: 10.1103/physrevd.100.126022

Geodesic Witten diagrams with antisymmetric tensor exchange
journal, October 2017

Tamaoka, Kotaro
Physical Review D, Vol. 96, Issue 8
DOI: 10.1103/physrevd.96.086007

What’s the point? Hole-ography in Poincaré AdS
journal, January 2018

Espíndola, Ricardo; Güijosa, Alberto; Landetta, Alberto
The European Physical Journal C, Vol. 78, Issue 1
DOI: 10.1140/epjc/s10052-018-5563-0

Entanglement wedge reconstruction and entanglement of purification
journal, August 2018

Espíndola, Ricardo; Güijosa, Alberto; Pedraza, Juan F.
The European Physical Journal C, Vol. 78, Issue 8
DOI: 10.1140/epjc/s10052-018-6140-2

Holographic complexity from Crofton’s formula in Lorentzian AdS ₃
journal, December 2019

Huang, Xing; Zhang, Le
International Journal of Modern Physics A, Vol. 34, Issue 35
DOI: 10.1142/s0217751x19502373

QCD, with strings attached
journal, October 2016

Güijosa, Alberto
International Journal of Modern Physics E, Vol. 25, Issue 10
DOI: 10.1142/s021830131630006x

Towards a Fisher-Information Description of Complexity in de Sitter Universe
journal, November 2019

Chen, Chong-Bin; Shu, Fu-Wen
Universe, Vol. 5, Issue 12
DOI: 10.3390/universe5120221

Equivalence of Emergent de Sitter Spaces from Conformal Field Theory
text, January 2016

Asplund, Curtis T.; Callebaut, Nele; Zukowski, Claire
arXiv
DOI: 10.48550/arxiv.1604.02687

QCD, with Strings Attached
text, January 2016

Guijosa, Alberto
arXiv
DOI: 10.48550/arxiv.1611.07472

Anatomy of Geodesic Witten Diagrams
text, January 2017

Chen, Heng-Yu; Kuo, En-Jui; Kyono, Hideki
arXiv
DOI: 10.48550/arxiv.1702.08818

CFT descriptions of bulk local states in the AdS black holes
text, January 2017

Goto, Kanato; Takayanagi, Tadashi
arXiv
DOI: 10.48550/arxiv.1704.00053

Modular Hamiltonians of excited states, OPE blocks and emergent bulk fields
text, January 2017

Sárosi, Gábor; Ugajin, Tomonori
arXiv
DOI: 10.48550/arxiv.1705.01486

Witten Diagrams for Torus Conformal Blocks
text, January 2017

Kraus, Per; Maloney, Alexander; Maxfield, Henry
arXiv
DOI: 10.48550/arxiv.1706.00047

Einstein's Equations from Varying Complexity
text, January 2017

Czech, Bartlomiej
arXiv
DOI: 10.48550/arxiv.1706.00965

Weight Shifting Operators and Conformal Blocks
text, January 2017

Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David
arXiv
DOI: 10.48550/arxiv.1706.07813

What's the Point? Hole-ography in Poincare AdS
text, January 2017

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arXiv
DOI: 10.48550/arxiv.1708.02958

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text, January 2017

Cresswell, Jesse C.; Peet, Amanda W.
arXiv
DOI: 10.48550/arxiv.1708.09838

Shockwaves from the Operator Product Expansion
preprint, January 2017

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arXiv
DOI: 10.48550/arxiv.1709.03597

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text, January 2018

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DOI: 10.48550/arxiv.1802.08815

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text, January 2018

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DOI: 10.48550/arxiv.1803.10539

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text, January 2018

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arXiv
DOI: 10.48550/arxiv.1804.05855

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text, January 2018

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arXiv
DOI: 10.48550/arxiv.1805.00098

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text, January 2018

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DOI: 10.48550/arxiv.1805.07393

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text, January 2018

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DOI: 10.48550/arxiv.1809.09107

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preprint, January 2018

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arXiv
DOI: 10.48550/arxiv.1810.02436

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text, January 2019

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arXiv
DOI: 10.48550/arxiv.1901.01267

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DOI: 10.48550/arxiv.1906.00726

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Journal Article Agon, Cesar A. ; Faulkner, Thomas - Journal of High Energy Physics (Online)

We compute the leading contribution to the mutual information (MI) of two disjoint spheres in the large distance regime for arbitrary conformal field theories (CFT) in any dimension. This is achieved by refining the operator product expansion method introduced by Cardy [1]. For CFTs with holographic duals the leading contribution to the MI at long distances comes from bulk quantum corrections to the Ryu-Takayanagi area formula. According to the FLM proposal [2] this equals the bulk MI between the two disjoint regions spanned by the boundary spheres and their corresponding minimal area surfaces. We compute this quantum correction and providemore »« less
Cited by 37
https://doi.org/10.1007/JHEP08(2016)118

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Bulk reconstruction beyond the entanglement wedge

Journal Article Bao, Ning ; Chatwin-Davies, Aidan ; Niehoff, Benjamin E. ; ... - Physical Review D

We study the portion of an asymptotically Anti–de Sitter geometry’s bulk where the metric can be reconstructed, given the areas of minimal two-surfaces anchored to a fixed boundary subregion. We exhibit situations in which this region can reach parametrically far outside of the entanglement wedge. If the setting is furthermore holographic, so that the bulk geometry is dual to a state in a conformal field theory (CFT), these minimal two-surface areas can be deduced from the expectation values of operators localized within the boundary subregion. This presents us with an alternative: either the reduced CFT state encodes significant information aboutmore »« less
Cited by 8
https://doi.org/10.1103/PhysRevD.101.066011

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Title: A stereoscopic look into the bulk

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Citation Formats

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

Wilson Loops in Large N Field Theories journal, June 1998

Insightful D-branes journal, July 2009

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence journal, May 2006

Aspects of holographic entanglement entropy journal, August 2006

Towards a derivation of holographic entanglement entropy journal, May 2011

Integral geometry and holography journal, October 2015

Holographic de Sitter Geometry from Entanglement in Conformal Field Theory journal, February 2016

Construction of bulk fields with gauge redundancy journal, September 2012

Bulk and transhorizon measurements in AdS/CFT journal, October 2012

Worldline approach to semi-classical conformal blocks journal, July 2015

Witten diagrams revisited: the AdS geometry of conformal blocks journal, January 2016

Semiclassical Virasoro blocks from AdS3 gravity journal, December 2015

Gravitational dynamics from entanglement “thermodynamics” journal, April 2014

Gravitation from entanglement in holographic CFTs journal, March 2014

Implications of Conformal Invariance in Field Theories for General Dimensions journal, May 1994

Infinite conformal symmetry in two-dimensional quantum field theory journal, July 1984

Bulk locality and quantum error correction in AdS/CFT journal, April 2015

Locality of Gravitational Systems from Entanglement of Conformal Field Theories journal, June 2015

Radon, Cosine and Sine Transforms on Real Hyperbolic Space journal, September 2002

Anti de Sitter space and holography journal, January 1998

The ultrahyperbolic differential equation with four independent variables journal, June 1938

Quantum corrections to holographic entanglement entropy journal, November 2013

Bulk equations of motion from CFT correlators journal, September 2015

Geometry of the 2+1 black hole journal, August 1993

Entwinement and the emergence of spacetime journal, January 2015

Virasoro conformal blocks and thermality from classical background fields journal, November 2015

Entanglement renormalization and integral geometry journal, December 2015

De Sitter Musings journal, May 2012

The dS/CFT correspondence journal, October 2001

Conformal covariant correlation functions journal, June 1972

Covariant expansion of the conformal four -point function journal, December 1972

Nonequivalence between conformal covariant Wilson expansion in Euclidean and Minkowski space journal, September 1972

The shadow operator formalism for conformal algebra. Vacuum expectation values and operator products journal, May 1972

Projectors, shadows, and conformal blocks journal, April 2014

Future boundary conditions in de Sitter space journal, February 2012

Radon, Cosine and Sine Transforms on Real Hyperbolic Space journal, September 2002

The Radon transform journal, January 1981

The Shadow Operator Formalism for Conformal Algebra. Vacuum Expectation Values and Operator Products text, January 1972

Integral geometry and Radon transforms book, October 2000

Integral Geometry and Geometric Probability book, January 2004

Insightful D-branes text, January 2009

Towards a derivation of holographic entanglement entropy text, January 2011

Future Boundary Conditions in De Sitter Space text, January 2011

Bulk and Transhorizon Measurements in AdS/CFT text, January 2012

Projectors, Shadows, and Conformal Blocks text, January 2012

Quantum corrections to holographic entanglement entropy text, January 2013

Entwinement and the emergence of spacetime text, January 2014

Worldline approach to semi-classical conformal blocks preprint, January 2015

Virasoro Conformal Blocks and Thermality from Classical Background Fields text, January 2015

Bulk equations of motion from CFT correlators preprint, January 2015

Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks text, January 2015

Semiclassical Virasoro Blocks from AdS$_3$ Gravity text, January 2015

Geometry of the 2+1 Black Hole text, January 1993

Aspects of Holographic Entanglement Entropy text, January 2006

Anti De Sitter Space And Holography text, January 1998

Holographic subregion complexity from kinematic space journal, January 2019

Comments on holographic complexity journal, March 2017

Holographic relations for OPE blocks in excited states journal, March 2019

Entanglement entropy in (1+1)D CFTs with multiple local excitations journal, May 2018

Geodesic diagrams, gravitational interactions & OPE structures journal, June 2017

The bulk-to-boundary propagator in black hole microstate backgrounds journal, June 2019

Entanglement, holography and causal diamonds journal, August 2016

Solving the Schwarzian via the conformal bootstrap journal, August 2017

Witten diagrams for torus conformal blocks journal, September 2017

A conformal collider for holographic CFTs journal, October 2018

Spectrum of modular Hamiltonian in the vacuum and excited states journal, October 2019

Spinning geodesic Witten diagrams journal, November 2017

Kinematic space for conical defects journal, November 2017

Towards entanglement of purification for conformal field theories journal, June 2018

Berry curvature, horocycles, and scattering states in AdS 3 / CFT 2 journal, December 2019

Geodesic Witten diagrams with antisymmetric tensor exchange journal, October 2017

What’s the point? Hole-ography in Poincaré AdS journal, January 2018

Entanglement wedge reconstruction and entanglement of purification journal, August 2018

Holographic complexity from Crofton’s formula in Lorentzian AdS 3 journal, December 2019

QCD, with strings attached journal, October 2016

Towards a Fisher-Information Description of Complexity in de Sitter Universe journal, November 2019

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Wilson Loops in Large $N$ Field Theories
journal, June 1998

Insightful D-branes
journal, July 2009

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

Aspects of holographic entanglement entropy
journal, August 2006

Towards a derivation of holographic entanglement entropy
journal, May 2011

Integral geometry and holography
journal, October 2015

Holographic de Sitter Geometry from Entanglement in Conformal Field Theory
journal, February 2016

Construction of bulk fields with gauge redundancy
journal, September 2012

Bulk and transhorizon measurements in AdS/CFT
journal, October 2012

Worldline approach to semi-classical conformal blocks
journal, July 2015

Witten diagrams revisited: the AdS geometry of conformal blocks
journal, January 2016

Semiclassical Virasoro blocks from AdS3 gravity
journal, December 2015

Gravitational dynamics from entanglement “thermodynamics”
journal, April 2014

Gravitation from entanglement in holographic CFTs
journal, March 2014

Implications of Conformal Invariance in Field Theories for General Dimensions
journal, May 1994

Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984

Bulk locality and quantum error correction in AdS/CFT
journal, April 2015

Locality of Gravitational Systems from Entanglement of Conformal Field Theories
journal, June 2015

Radon, Cosine and Sine Transforms on Real Hyperbolic Space
journal, September 2002

Anti de Sitter space and holography
journal, January 1998

The ultrahyperbolic differential equation with four independent variables
journal, June 1938

Quantum corrections to holographic entanglement entropy
journal, November 2013

Bulk equations of motion from CFT correlators
journal, September 2015

Geometry of the 2+1 black hole
journal, August 1993

Entwinement and the emergence of spacetime
journal, January 2015

Virasoro conformal blocks and thermality from classical background fields
journal, November 2015

Entanglement renormalization and integral geometry
journal, December 2015

De Sitter Musings
journal, May 2012

The dS/CFT correspondence
journal, October 2001

Conformal covariant correlation functions
journal, June 1972

Covariant expansion of the conformal four -point function
journal, December 1972

Nonequivalence between conformal covariant Wilson expansion in Euclidean and Minkowski space
journal, September 1972

The shadow operator formalism for conformal algebra. Vacuum expectation values and operator products
journal, May 1972

Projectors, shadows, and conformal blocks
journal, April 2014

Future boundary conditions in de Sitter space
journal, February 2012

Radon, Cosine and Sine Transforms on Real Hyperbolic Space
journal, September 2002

The Radon transform
journal, January 1981

The Shadow Operator Formalism for Conformal Algebra. Vacuum Expectation Values and Operator Products
text, January 1972

Integral geometry and Radon transforms
book, October 2000

Integral Geometry and Geometric Probability
book, January 2004

Insightful D-branes
text, January 2009

Towards a derivation of holographic entanglement entropy
text, January 2011

Future Boundary Conditions in De Sitter Space
text, January 2011

Bulk and Transhorizon Measurements in AdS/CFT
text, January 2012

Projectors, Shadows, and Conformal Blocks
text, January 2012

Quantum corrections to holographic entanglement entropy
text, January 2013

Entwinement and the emergence of spacetime
text, January 2014

Worldline approach to semi-classical conformal blocks
preprint, January 2015

Virasoro Conformal Blocks and Thermality from Classical Background Fields
text, January 2015

Bulk equations of motion from CFT correlators
preprint, January 2015

Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
text, January 2015

Semiclassical Virasoro Blocks from AdS$_3$ Gravity
text, January 2015

Geometry of the 2+1 Black Hole
text, January 1993

Aspects of Holographic Entanglement Entropy
text, January 2006

Anti De Sitter Space And Holography
text, January 1998

Holographic subregion complexity from kinematic space
journal, January 2019

Comments on holographic complexity
journal, March 2017

Holographic relations for OPE blocks in excited states
journal, March 2019

Entanglement entropy in (1+1)D CFTs with multiple local excitations
journal, May 2018

Geodesic diagrams, gravitational interactions & OPE structures
journal, June 2017

The bulk-to-boundary propagator in black hole microstate backgrounds
journal, June 2019

Entanglement, holography and causal diamonds
journal, August 2016

Solving the Schwarzian via the conformal bootstrap
journal, August 2017

Witten diagrams for torus conformal blocks
journal, September 2017

A conformal collider for holographic CFTs
journal, October 2018

Spectrum of modular Hamiltonian in the vacuum and excited states
journal, October 2019

Spinning geodesic Witten diagrams
journal, November 2017

Kinematic space for conical defects
journal, November 2017

Towards entanglement of purification for conformal field theories
journal, June 2018

Berry curvature, horocycles, and scattering states in ${AdS}_{3} / {CFT}_{2}$
journal, December 2019

Geodesic Witten diagrams with antisymmetric tensor exchange
journal, October 2017

What’s the point? Hole-ography in Poincaré AdS
journal, January 2018

Entanglement wedge reconstruction and entanglement of purification
journal, August 2018

Holographic complexity from Crofton’s formula in Lorentzian AdS ₃
journal, December 2019

QCD, with strings attached
journal, October 2016

Towards a Fisher-Information Description of Complexity in de Sitter Universe
journal, November 2019

Equivalence of Emergent de Sitter Spaces from Conformal Field Theory
text, January 2016

QCD, with Strings Attached
text, January 2016

Anatomy of Geodesic Witten Diagrams
text, January 2017