The gravity duals of modular Hamiltonians

Jafferis, Daniel L.; Suh, S. Josephine

doi:10.1007/JHEP09(2016)068

Title: The gravity duals of modular Hamiltonians

Journal Article · Mon Sep 12 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP09(2016)068· OSTI ID:1362133

Jafferis, Daniel L. ^[1]; Suh, S. Josephine ^[2]

Harvard Univ., Cambridge, MA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-like to the causal completion of the region.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0012567

OSTI ID:: 1362133

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 61 works

Citation information provided by
Web of Science

References (52)

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
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
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 evolution of the mutual information Allais, Andrea; Tonni, Erik Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)102	journal	January 2012
Strong subadditivity and the covariant holographic entanglement entropy formula Callan, Robert; He, Jianyang; Headrick, Matthew Journal of High Energy Physics, Vol. 2012, Issue 6 https://doi.org/10.1007/JHEP06(2012)081	journal	June 2012
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
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
Relative entropy and the Bekenstein bound Casini, H. Classical and Quantum Gravity, Vol. 25, Issue 20 https://doi.org/10.1088/0264-9381/25/20/205021	journal	September 2008
Geometric and renormalized entropy in conformal field theory Holzhey, Christoph; Larsen, Finn; Wilczek, Frank Nuclear Physics B, Vol. 424, Issue 3 https://doi.org/10.1016/0550-3213(94)90402-2	journal	August 1994
Local Quantum Physics Haag, Rudolf Theoretical and Mathematical Physics https://doi.org/10.1007/978-3-642-61458-3	book	January 1996
On the duality condition for a Hermitian scalar field Bisognano, Joseph J.; Wichmann, Eyvind H. Journal of Mathematical Physics, Vol. 16, Issue 4 https://doi.org/10.1063/1.522605	journal	April 1975
On the duality condition for quantum fields Bisognano, Joseph J. Journal of Mathematical Physics, Vol. 17, Issue 3 https://doi.org/10.1063/1.522898	journal	January 1976
Towards a derivation of holographic entanglement entropy Casini, Horacio; Huerta, Marina; Myers, Robert C. Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)036	journal	May 2011
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
Causal holographic information Hubeny, Veronika E.; Rangamani, Mukund Journal of High Energy Physics, Vol. 2012, Issue 6 https://doi.org/10.1007/JHEP06(2012)114	journal	June 2012
Cool horizons for entangled black holes Maldacena, J.; Susskind, L. Fortschritte der Physik, Vol. 61, Issue 9 https://doi.org/10.1002/prop.201300020	journal	August 2013
Black Hole Interior in the Holographic Correspondence and the Information Paradox Papadodimas, Kyriakos; Raju, Suvrat Physical Review Letters, Vol. 112, Issue 5 https://doi.org/10.1103/PhysRevLett.112.051301	journal	February 2014
Relative entropy and holography Blanco, David D.; Casini, Horacio; Hung, Ling-Yan Journal of High Energy Physics, Vol. 2013, Issue 8 https://doi.org/10.1007/JHEP08(2013)060	journal	August 2013
Construction of bulk fields with gauge redundancy Heemskerk, Idse Journal of High Energy Physics, Vol. 2012, Issue 9 https://doi.org/10.1007/JHEP09(2012)106	journal	September 2012
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
Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime Engelhardt, Netta; Wall, Aron C. Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)073	journal	January 2015
Some properties of the Noether charge and a proposal for dynamical black hole entropy Iyer, Vivek; Wald, Robert M. Physical Review D, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevD.50.846	journal	July 1994
Gravitation from entanglement in holographic CFTs Faulkner, Thomas; Guica, Monica; Hartman, Thomas Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)051	journal	March 2014
Bulk and transhorizon measurements in AdS/CFT Heemskerk, Idse; Marolf, Donald; Polchinski, Joseph Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/JHEP10(2012)165	journal	October 2012
The Black Hole Singularity in AdS/CFT Fidkowski, Lukasz; Hubeny, Veronika; Kleban, Matthew Journal of High Energy Physics, Vol. 2004, Issue 02 https://doi.org/10.1088/1126-6708/2004/02/014	journal	February 2004
Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence de Haro, Sebastian; Skenderis, Kostas; Solodukhin, Sergey N. Communications in Mathematical Physics, Vol. 217, Issue 3 https://doi.org/10.1007/s002200100381	journal	March 2001
Setting the boundary free in AdS/CFT Compère, Geoffrey; Marolf, Donald Classical and Quantum Gravity, Vol. 25, Issue 19 https://doi.org/10.1088/0264-9381/25/19/195014	journal	September 2008
An infalling observer in AdS/CFT Papadodimas, Kyriakos; Raju, Suvrat Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)212	journal	October 2013
Generalized Free Fields and the AdS-CFT Correspondence Dütsch, Michael; Rehren, Karl-Henning Annales Henri Poincaré, Vol. 4, Issue 4 https://doi.org/10.1007/s00023-003-0141-9	journal	August 2003
Geometry of deformations of relativistic membranes Capovilla, Riccardo; Guven, Jemal Physical Review D, Vol. 51, Issue 12 https://doi.org/10.1103/PhysRevD.51.6736	journal	June 1995
Implications of Conformal Invariance in Field Theories for General Dimensions Osborn, H.; Petkou, A. Annals of Physics, Vol. 231, Issue 2 https://doi.org/10.1006/aphy.1994.1045	journal	May 1994
Conserved currents and the energy-momentum tensor in conformally invariant theories for general dimensions Erdmenger, J.; Osborn, H. Nuclear Physics B, Vol. 483, Issue 1-2 https://doi.org/10.1016/S0550-3213(96)00545-7	journal	January 1997
Comments on unparticles Grinstein, Benjamin; Intriligator, Kenneth; Rothstein, Ira Z. Physics Letters B, Vol. 662, Issue 4 https://doi.org/10.1016/j.physletb.2008.03.020	journal	May 2008
Local quantum physics Landsman, N. P. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Vol. 27, Issue 4 https://doi.org/10.1016/s1355-2198(96)00020-2	journal	December 1996
Holographic reconstruction of spacetime and renormalization in the AdS/CFT correspondence De Haro, S.; Skenderis, K.; Solodukhin, Sn Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.22093	text	January 2001
Local Quantum Physics Haag, Rudolf Theoretical and Mathematical Physics (TMP) https://doi.org/10.1007/978-3-642-97306-2	book	January 1992
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
Comments on Unparticles Grinstein, Benjamin; Intriligator, Kenneth; Rothstein, Ira Z. arXiv https://doi.org/10.48550/arxiv.0801.1140	text	January 2008
Relative entropy and the Bekenstein bound Casini, H. arXiv https://doi.org/10.48550/arxiv.0804.2182	text	January 2008
Towards a derivation of holographic entanglement entropy Casini, Horacio; Huerta, Marina; Myers, Robert C. arXiv https://doi.org/10.48550/arxiv.1102.0440	text	January 2011
Bulk and Transhorizon Measurements in AdS/CFT Heemskerk, Idse; Marolf, Donald; Polchinski, Joseph arXiv https://doi.org/10.48550/arxiv.1201.3664	text	January 2012
Strong subadditivity and the covariant holographic entanglement entropy formula Callan, Robert; He, Jianyang; Headrick, Matthew arXiv https://doi.org/10.48550/arxiv.1204.2309	text	January 2012
An Infalling Observer in AdS/CFT Papadodimas, Kyriakos; Raju, Suvrat arXiv https://doi.org/10.48550/arxiv.1211.6767	text	January 2012
Generalized gravitational entropy Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1304.4926	text	January 2013
Cool horizons for entangled black holes Maldacena, Juan; Susskind, Leonard arXiv https://doi.org/10.48550/arxiv.1306.0533	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
Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime Engelhardt, Netta; Wall, Aron C. arXiv https://doi.org/10.48550/arxiv.1408.3203	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
Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence de Haro, Sebastian; Skenderis, Kostas; Solodukhin, Sergey N. arXiv https://doi.org/10.48550/arxiv.hep-th/0002230	text	January 2000
The Black Hole Singularity in AdS/CFT Fidkowski, Lukasz; Hubeny, Veronika; Kleban, Matthew arXiv https://doi.org/10.48550/arxiv.hep-th/0306170	text	January 2003
Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions Erdmenger, J.; Osborn, H. arXiv https://doi.org/10.48550/arxiv.hep-th/9605009	text	January 1996
Generalized free fields and the AdS-CFT correspondence Duetsch, M.; Rehren, K. -H. arXiv https://doi.org/10.48550/arxiv.math-ph/0209035	text	January 2002

Cited By (19)

Connecting Fisher information to bulk entanglement in holography Banerjee, Souvik; Erdmenger, Johanna; Sarkar, Debajyoti Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/jhep08(2018)001	journal	August 2018
Spectrum of modular Hamiltonian in the vacuum and excited states Das, Suchetan; Ezhuthachan, Bobby Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)009	journal	October 2019
On volumes of subregions in holography and complexity Ben-Ami, Omer; Carmi, Dean Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/jhep11(2016)129	journal	November 2016
Modular Hamiltonians on the null plane and the Markov property of the vacuum state Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 36 https://doi.org/10.1088/1751-8121/aa7eaa	journal	August 2017
Holographic entanglement contour, bit threads, and the entanglement tsunami Kudler-Flam, Jonah; MacCormack, Ian; Ryu, Shinsei Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 32 https://doi.org/10.1088/1751-8121/ab2dae	journal	July 2019
Entanglement and relative entropy of a chiral fermion on the torus Fries, Pascal; Reyes, Ignacio A. Physical Review D, Vol. 100, Issue 10 https://doi.org/10.1103/physrevd.100.105015	journal	November 2019
First law of entanglement rates from holography O’Bannon, Andy; Probst, Jonas; Rodgers, Ronnie Physical Review D, Vol. 96, Issue 6 https://doi.org/10.1103/physrevd.96.066028	journal	September 2017
Entanglement Spectrum of Chiral Fermions on the Torus Fries, Pascal; Reyes, Ignacio A. Physical Review Letters, Vol. 123, Issue 21 https://doi.org/10.1103/physrevlett.123.211603	journal	November 2019
Entanglement wedge reconstruction and entanglement of purification Espíndola, Ricardo; Güijosa, Alberto; Pedraza, Juan F. The European Physical Journal C, Vol. 78, Issue 8 https://doi.org/10.1140/epjc/s10052-018-6140-2	journal	August 2018
Entanglement Entropy and Duality Radicevic, Djordje arXiv https://doi.org/10.48550/arxiv.1605.09396	preprint	January 2016
Connecting Fisher information to bulk entanglement in holography Banerjee, Souvik; Erdmenger, Johanna; Sarkar, Debajyoti arXiv https://doi.org/10.48550/arxiv.1701.02319	text	January 2017
Modular Hamiltonians on the null plane and the Markov property of the vacuum state Casini, Horacio; Teste, Eduardo; Torroba, Gonzalo arXiv https://doi.org/10.48550/arxiv.1703.10656	text	January 2017
Modular Hamiltonians of excited states, OPE blocks and emergent bulk fields Sárosi, Gábor; Ugajin, Tomonori arXiv https://doi.org/10.48550/arxiv.1705.01486	text	January 2017
Entanglement Wedge Reconstruction and Entanglement of Purification Espíndola, Ricardo; Guijosa, Alberto; Pedraza, Juan F. arXiv https://doi.org/10.48550/arxiv.1804.05855	text	January 2018
Entanglement negativity and minimal entanglement wedge cross sections in holographic theories Kudler-Flam, Jonah; Ryu, Shinsei arXiv https://doi.org/10.48550/arxiv.1808.00446	text	January 2018
Holographic Renyi Entropy from Quantum Error Correction Akers, Chris; Rath, Pratik arXiv https://doi.org/10.48550/arxiv.1811.05171	text	January 2018
Holographic entanglement contour, bit threads, and the entanglement tsunami Kudler-Flam, Jonah; MacCormack, Ian; Ryu, Shinsei arXiv https://doi.org/10.48550/arxiv.1902.04654	text	January 2019
Spectrum of Modular Hamiltonian in the Vacuum and Excited States Das, Suchetan; Ezhuthachan, Bobby arXiv https://doi.org/10.48550/arxiv.1906.00726	text	January 2019
The entanglement and relative entropy of a chiral fermion on the torus Fries, Pascal; Reyes, Ignacio A. arXiv https://doi.org/10.48550/arxiv.1906.02207	text	January 2019

Similar Records

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

Journal Article · Thu Sep 08 00:00:00 EDT 2016 · Journal of High Energy Physics (Online) · OSTI ID:1362133

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; +1 more

The gravity dual of Rényi entropy

Journal Article · Fri Aug 12 00:00:00 EDT 2016 · Nature Communications · OSTI ID:1362133

Dong, Xi

What is the entropy in entropic gravity?

Journal Article · Tue Jun 21 00:00:00 EDT 2016 · Physical Review D · OSTI ID:1362133

Carroll, Sean M.; Remmen, Grant N.

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AdS-CFT correspondence
field theories in higher dimensions

Title: The gravity duals of modular Hamiltonians

Citation Formats

References (52)

Cited By (19)

Similar Records

Related Subjects