A modular toolkit for bulk reconstruction

Faulkner, Thomas; Li, Min; Wang, Huajia

doi:10.1007/jhep04(2019)119

Title: A modular toolkit for bulk reconstruction

Journal Article · Thu Apr 18 00:00:00 EDT 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep04(2019)119· OSTI ID:1612307

Faulkner, Thomas ^[1]; Li, Min ^[1]; Wang, Huajia ^[2]

Univ. of Illinois, Urbana IL (United States)
Univ. of Illinois, Urbana IL (United States); Univ. of California, Santa Barbara, CA (United States)

We introduce new tools for studying modular flow in AdS/CFT. These tools allow us to efficiently extract bulk information related to causality and locality. For example, we discuss the relation between analyticity in modular time and entanglement wedge nesting which can then be used to extract the location of the Ryu-Takayanagi (RT) surface directly from the boundary theory. Probing the RT surface close to the boundary our results reduce to the recent proof of the Quantum Null Energy Condition. We focus on heavy probe operators whose correlation functions are determined by spacelike geodesics. These geodesics interplay with the RT surface via a set of rules that we conjecture and give evidence for using the replica trick.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0015655; SC0019183

OSTI ID:: 1612307

Journal Information:: Journal of High Energy Physics (Online), Vol. 2019, Issue 4; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 45 works

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References (53)

The gravity dual of a density matrix Czech, Bartłomiej; Karczmarek, Joanna L.; Nogueira, Fernando Classical and Quantum Gravity, Vol. 29, Issue 15 https://doi.org/10.1088/0264-9381/29/15/155009	journal	July 2012
Towards a reconstruction of general bulk metrics Engelhardt, Netta; Horowitz, Gary T. Classical and Quantum Gravity, Vol. 34, Issue 1 https://doi.org/10.1088/1361-6382/34/1/015004	journal	December 2016
Extension of the Structure Theorem of Borchers and its Application to Half-Sided Modular Inclusions Araki, Huzihiro; ZsidÓ, LÁSzlÓ Reviews in Mathematical Physics, Vol. 17, Issue 05 https://doi.org/10.1142/S0129055X05002388	journal	June 2005
Writing CFT correlation functions as AdS scattering amplitudes Penedones, Joao Journal of High Energy Physics, Vol. 2011, Issue 3 https://doi.org/10.1007/JHEP03(2011)025	journal	March 2011
A bound on chaos Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)106	journal	August 2016
Causality constraints in conformal field theory Hartman, Thomas; Jain, Sachin; Kundu, Sandipan Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/JHEP05(2016)099	journal	May 2016
The gravity duals of modular Hamiltonians Jafferis, Daniel L.; Suh, S. Josephine Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)068	journal	September 2016
Averaged null energy condition from causality Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)066	journal	July 2017
The Large-N Limit of Superconformal Field Theories and Supergravity Maldacena, Juan International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133 https://doi.org/10.1023/A:1026654312961	journal	January 1999
Holographic Signatures of Cosmological Singularities Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T. Physical Review Letters, Vol. 113, Issue 12 https://doi.org/10.1103/PhysRevLett.113.121602	journal	September 2014
Holographic duality from random tensor networks Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/JHEP11(2016)009	journal	November 2016
Black holes and the butterfly effect Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)067	journal	March 2014
Looking for a bulk point Maldacena, Juan; Simmons-Duffin, David; Zhiboedov, Alexander Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/JHEP01(2017)013	journal	January 2017
Stringy effects in scrambling Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/JHEP05(2015)132	journal	May 2015
Analyticity in spin in conformal theories Caron-Huot, Simon Journal of High Energy Physics, Vol. 2017, Issue 9 https://doi.org/10.1007/JHEP09(2017)078	journal	September 2017
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence Ryu, Shinsei; Takayanagi, Tadashi Physical Review Letters, Vol. 96, Issue 18 https://doi.org/10.1103/PhysRevLett.96.181602	journal	May 2006
APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory Witten, Edward Reviews of Modern Physics, Vol. 90, Issue 4 https://doi.org/10.1103/RevModPhys.90.045003	journal	October 2018
Causality & holographic entanglement entropy Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)162	journal	December 2014
Bulk locality and quantum error correction in AdS/CFT Almheiri, Ahmed; Dong, Xi; Harlow, Daniel Journal of High Energy Physics, Vol. 2015, Issue 4 https://doi.org/10.1007/JHEP04(2015)163	journal	April 2015
Thermodynamics of Spacetime: The Einstein Equation of State Jacobson, Ted Physical Review Letters, Vol. 75, Issue 7 https://doi.org/10.1103/PhysRevLett.75.1260	journal	August 1995
Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy Wall, Aron C. Classical and Quantum Gravity, Vol. 31, Issue 22 https://doi.org/10.1088/0264-9381/31/22/225007	journal	November 2014
A proof of the conformal collider bounds Hofman, Diego M.; Li, Daliang; Meltzer, David Journal of High Energy Physics, Vol. 2016, Issue 6 https://doi.org/10.1007/JHEP06(2016)111	journal	June 2016
Modular flow as a disentangler Chen, Yiming; Dong, Xi; Lewkowycz, Aitor Journal of High Energy Physics, Vol. 2018, Issue 12 https://doi.org/10.1007/JHEP12(2018)083	journal	December 2018
Bulk locality from modular flow Faulkner, Thomas; Lewkowycz, Aitor Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)151	journal	July 2017
A covariant holographic entanglement entropy proposal Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi Journal of High Energy Physics, Vol. 2007, Issue 07 https://doi.org/10.1088/1126-6708/2007/07/062	journal	July 2007
Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence Pastawski, Fernando; Yoshida, Beni; Harlow, Daniel Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)149	journal	June 2015
Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality Dong, Xi; Harlow, Daniel; Wall, Aron C. Physical Review Letters, Vol. 117, Issue 2 https://doi.org/10.1103/PhysRevLett.117.021601	journal	July 2016
Generalized gravitational entropy Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 8 https://doi.org/10.1007/JHEP08(2013)090	journal	August 2013
Further holographic investigations of big bang singularities Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T. Journal of High Energy Physics, Vol. 2015, Issue 7 https://doi.org/10.1007/JHEP07(2015)044	journal	July 2015
Particle creation by black holes Hawking, S. W. Communications In Mathematical Physics, Vol. 43, Issue 3 https://doi.org/10.1007/BF02345020	journal	August 1975
Fermion families from two layer warped extra dimensions Guo, Zhi-qiang; Ma, Bo-Qiang Journal of High Energy Physics, Vol. 2008, Issue 08 https://doi.org/10.1088/1126-6708/2008/08/065	journal	August 2008
Nuclear maps and modular structures. I. General properties Buchholz, Detlev; D'Antoni, Claudio; Longo, Roberto Journal of Functional Analysis, Vol. 88, Issue 2 https://doi.org/10.1016/0022-1236(90)90104-S	journal	February 1990
Quantum corrections to holographic entanglement entropy Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)074	journal	November 2013
Relative entropy equals bulk relative entropy Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2016, Issue 6 https://doi.org/10.1007/JHEP06(2016)004	journal	June 2016
Holography from conformal field theory Heemskerk, Idse; Penedones, Joao; Polchinski, Joseph Journal of High Energy Physics, Vol. 2009, Issue 10 https://doi.org/10.1088/1126-6708/2009/10/079	journal	October 2009
On the Modular Structure of Local Algebras of Observables Fredenhagen, Klaus Quantum Field Theory https://doi.org/10.1007/978-3-642-70307-2_5	book	January 1985
A Covariant Holographic Entanglement Entropy Proposal Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi arXiv https://doi.org/10.48550/arxiv.0705.0016	text	January 2007
Fermion Families from Two Layer Warped Extra Dimensions Guo, Zhi-qiang; Ma, Bo-Qiang arXiv https://doi.org/10.48550/arxiv.0808.2136	text	January 2008
Holography from Conformal Field Theory Heemskerk, Idse; Penedones, Joao; Polchinski, Joseph arXiv https://doi.org/10.48550/arxiv.0907.0151	text	January 2009
Generalized gravitational entropy Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1304.4926	text	January 2013
Quantum corrections to holographic entanglement entropy Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1307.2892	text	January 2013
Holographic Signatures of Cosmological Singularities Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T. arXiv https://doi.org/10.48550/arxiv.1404.2309	text	January 2014
Causality & holographic entanglement entropy Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion arXiv https://doi.org/10.48550/arxiv.1408.6300	text	January 2014
Stringy effects in scrambling Shenker, Stephen H.; Stanford, Douglas arXiv https://doi.org/10.48550/arxiv.1412.6087	preprint	January 2014
The Gravity Duals of Modular Hamiltonians Jafferis, Daniel L.; Suh, S. Josephine arXiv https://doi.org/10.48550/arxiv.1412.8465	preprint	January 2014
A bound on chaos Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas arXiv https://doi.org/10.48550/arxiv.1503.01409	text	January 2015
Causality Constraints in Conformal Field Theory Hartman, Thomas; Jain, Sachin; Kundu, Sandipan arXiv https://doi.org/10.48550/arxiv.1509.00014	text	January 2015
Holographic duality from random tensor networks Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang arXiv https://doi.org/10.48550/arxiv.1601.01694	text	January 2016
A Proof of the Conformal Collider Bounds Hofman, Diego M.; Li, Daliang; Meltzer, David arXiv https://doi.org/10.48550/arxiv.1603.03771	text	January 2016
Towards a Reconstruction of General Bulk Metrics Engelhardt, Netta; Horowitz, Gary T. arXiv https://doi.org/10.48550/arxiv.1605.01070	text	January 2016
Analyticity in Spin in Conformal Theories Caron-Huot, Simon arXiv https://doi.org/10.48550/arxiv.1703.00278	text	January 2017
Thermodynamics of Spacetime: The Einstein Equation of State Jacobson, Ted arXiv https://doi.org/10.48550/arxiv.gr-qc/9504004	text	January 1995
Entanglement Negativity in Quantum Field Theory Calabrese, Pasquale; Cardy, John; Tonni, Erik Physical Review Letters, Vol. 109, Issue 13 https://doi.org/10.1103/physrevlett.109.130502	journal	September 2012

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Relative entropy for coherent states from Araki formula Casini, Horacio; Grillo, Sergio; Pontello, Diego Physical Review D, Vol. 99, Issue 12 https://doi.org/10.1103/physrevd.99.125020	journal	June 2019
Relative entropy for coherent states from Araki formula Casini, Horacio; Grillo, Sergio; Pontello, Diego arXiv https://doi.org/10.48550/arxiv.1903.00109	text	January 2019
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