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

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; Wang, Huajia

doi:10.1007/JHEP09(2016)038

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

Abstract

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R^1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.

Authors:

Faulkner, Thomas ^[1]; Leigh, Robert G. ^[1]; Parrikar, Onkar ^[1]; Wang, Huajia ^[1]

Univ. of Illinois, Urbana, IL (United States). Dept. of Physics

Publication Date:: Thu Sep 08 00:00:00 EDT 2016

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1395542

Grant/Contract Number:: FG02-13ER42001; SC0009932

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: 9; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

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

Citation Formats


                    Faulkner, Thomas, Leigh, Robert G., Parrikar, Onkar, and Wang, Huajia. Modular Hamiltonians for deformed half-spaces and the averaged null energy condition.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP09(2016)038.

Copy to clipboard


                    Faulkner, Thomas, Leigh, Robert G., Parrikar, Onkar, & Wang, Huajia. Modular Hamiltonians for deformed half-spaces and the averaged null energy condition.  United States.  https://doi.org/10.1007/JHEP09(2016)038

Copy to clipboard


                    Faulkner, Thomas, Leigh, Robert G., Parrikar, Onkar, and Wang, Huajia. Thu .  
"Modular Hamiltonians for deformed half-spaces and the averaged null energy condition".  United States.  https://doi.org/10.1007/JHEP09(2016)038.  https://www.osti.gov/servlets/purl/1395542.

Copy to clipboard


                    
@article{osti_1395542,

  title        = {Modular Hamiltonians for deformed half-spaces and the averaged null energy condition},

  author       = {Faulkner, Thomas and Leigh, Robert G. and Parrikar, Onkar and Wang, Huajia},

  abstractNote = {We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.},

  doi          = {10.1007/JHEP09(2016)038},

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

  number       = 9,

  volume       = 2016,

  place        = {United States},

  year         = {Thu Sep 08 00:00:00 EDT 2016},

  month        = {Thu Sep 08 00:00:00 EDT 2016}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/JHEP09(2016)038

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 151 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Topological censorship
journal, September 1993

Friedman, John L.; Schleich, Kristin; Witt, Donald M.
Physical Review Letters, Vol. 71, Issue 10
DOI: 10.1103/PhysRevLett.71.1486

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
journal, January 2015

Engelhardt, Netta; Wall, Aron C.
Journal of High Energy Physics, Vol. 2015, Issue 1
DOI: 10.1007/JHEP01(2015)073

Wess-Zumino Consistency Condition for Entanglement Entropy
journal, July 2012

Banerjee, Shamik
Physical Review Letters, Vol. 109, Issue 1
DOI: 10.1103/PhysRevLett.109.010402

Relative entropy and the Bekenstein bound
journal, September 2008

Casini, H.
Classical and Quantum Gravity, Vol. 25, Issue 20
DOI: 10.1088/0264-9381/25/20/205021

Causality constraints in conformal field theory
journal, May 2016

Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
Journal of High Energy Physics, Vol. 2016, Issue 5
DOI: 10.1007/JHEP05(2016)099

Higher derivative gravity, causality and positivity of energy in a UV complete QFT
journal, December 2009

Hofman, Diego M.
Nuclear Physics B, Vol. 823, Issue 1-2
DOI: 10.1016/j.nuclphysb.2009.08.001

Modular Hamiltonian for Excited States in Conformal Field Theory
journal, July 2016

Lashkari, Nima
Physical Review Letters, Vol. 117, Issue 4
DOI: 10.1103/PhysRevLett.117.041601

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

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

Gauge theory correlators from non-critical string theory
journal, May 1998

Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
Physics Letters B, Vol. 428, Issue 1-2
DOI: 10.1016/S0370-2693(98)00377-3

Entanglement Entropy of Electromagnetic Edge Modes
journal, March 2015

Donnelly, William; Wall, Aron C.
Physical Review Letters, Vol. 114, Issue 11
DOI: 10.1103/PhysRevLett.114.111603

Shape dependence of entanglement entropy in conformal field theories
journal, April 2016

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
Journal of High Energy Physics, Vol. 2016, Issue 4
DOI: 10.1007/JHEP04(2016)088

Holographic entanglement entropy and gravitational anomalies
journal, July 2014

Castro, Alejandra; Detournay, Stephane; Iqbal, Nabil
Journal of High Energy Physics, Vol. 2014, Issue 7
DOI: 10.1007/JHEP07(2014)114

Mutual information and the F-theorem
journal, October 2015

Casini, Horacio; Huerta, Marina; Myers, Robert C.
Journal of High Energy Physics, Vol. 2015, Issue 10
DOI: 10.1007/JHEP10(2015)003

Bulk emergence and the RG flow of entanglement entropy
journal, May 2015

Faulkner, Thomas
Journal of High Energy Physics, Vol. 2015, Issue 5
DOI: 10.1007/JHEP05(2015)033

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

Entanglement entropy of gapped phases and topological order in three dimensions
journal, November 2011

Grover, Tarun; Turner, Ari M.; Vishwanath, Ashvin
Physical Review B, Vol. 84, Issue 19
DOI: 10.1103/PhysRevB.84.195120

Anomalies and entanglement entropy
journal, March 2016

Nishioka, Tatsuma; Yarom, Amos
Journal of High Energy Physics, Vol. 2016, Issue 3
DOI: 10.1007/JHEP03(2016)077

A finite entanglement entropy and the c-theorem
journal, October 2004

Casini, H.; Huerta, M.
Physics Letters B, Vol. 600, Issue 1-2
DOI: 10.1016/j.physletb.2004.08.072

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 averaged null energy condition for general quantum field theories in two dimensions
journal, January 2000

Verch, Rainer
Journal of Mathematical Physics, Vol. 41, Issue 1
DOI: 10.1063/1.533130

Entanglement entropy for relevant and geometric perturbations
journal, February 2015

Rosenhaus, Vladimir; Smolkin, Michael
Journal of High Energy Physics, Vol. 2015, Issue 2
DOI: 10.1007/JHEP02(2015)015

A proof of the conformal collider bounds
journal, June 2016

Hofman, Diego M.; Li, Daliang; Meltzer, David
Journal of High Energy Physics, Vol. 2016, Issue 6
DOI: 10.1007/JHEP06(2016)111

A coarse-grained generalized second law for holographic conformal field theories
journal, February 2016

Bunting, William; Fu, Zicao; Marolf, Donald
Classical and Quantum Gravity, Vol. 33, Issue 5
DOI: 10.1088/0264-9381/33/5/055008

Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity
journal, April 2010

Camanho, Xián O.; Edelstein, José D.
Journal of High Energy Physics, Vol. 2010, Issue 4
DOI: 10.1007/JHEP04(2010)007

A covariant holographic entanglement entropy proposal
journal, July 2007

Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
Journal of High Energy Physics, Vol. 2007, Issue 07
DOI: 10.1088/1126-6708/2007/07/062

On the duality condition for quantum fields
journal, January 1976

Bisognano, Joseph J.
Journal of Mathematical Physics, Vol. 17, Issue 3
DOI: 10.1063/1.522898

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
journal, July 2016

Dong, Xi; Harlow, Daniel; Wall, Aron C.
Physical Review Letters, Vol. 117, Issue 2
DOI: 10.1103/PhysRevLett.117.021601

On the quantum structure of a black hole
journal, January 1985

't Hooft, Gerard
Nuclear Physics B, Vol. 256
DOI: 10.1016/0550-3213(85)90418-3

Conformal collider physics: energy and charge correlations
journal, May 2008

Hofman, Diego M.; Maldacena, Juan
Journal of High Energy Physics, Vol. 2008, Issue 05
DOI: 10.1088/1126-6708/2008/05/012

Geodesic focusing, energy conditions and singularities
journal, March 1987

Borde, A.
Classical and Quantum Gravity, Vol. 4, Issue 2
DOI: 10.1088/0264-9381/4/2/015

Holographic GB gravity in arbitrary dimensions
journal, March 2010

Buchel, Alex; Escobedo, Jorge; Myers, Robert C.
Journal of High Energy Physics, Vol. 2010, Issue 3
DOI: 10.1007/JHEP03(2010)111

Constraining gravity using entanglement in AdS/CFT
journal, May 2014

Banerjee, Shamik; Bhattacharyya, Arpan; Kaviraj, Apratim
Journal of High Energy Physics, Vol. 2014, Issue 5
DOI: 10.1007/JHEP05(2014)029

Localization of Negative Energy and the Bekenstein Bound
journal, November 2013

Blanco, David D.; Casini, Horacio
Physical Review Letters, Vol. 111, Issue 22
DOI: 10.1103/PhysRevLett.111.221601

Energy Flux Positivity and Unitarity in Conformal Field Theories
journal, January 2011

Kulaxizi, Manuela; Parnachev, Andrei
Physical Review Letters, Vol. 106, Issue 1
DOI: 10.1103/PhysRevLett.106.011601

Relative Entropies in Conformal Field Theory
journal, July 2014

Lashkari, Nima
Physical Review Letters, Vol. 113, Issue 5
DOI: 10.1103/PhysRevLett.113.051602

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

Relative entropy equals bulk relative entropy
journal, June 2016

Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan
Journal of High Energy Physics, Vol. 2016, Issue 6
DOI: 10.1007/JHEP06(2016)004

’t Hooft suppression and holographic entropy
journal, October 2015

Kelly, William R.; Kuns, Kevin; Marolf, Donald
Journal of High Energy Physics, Vol. 2015, Issue 10
DOI: 10.1007/JHEP10(2015)059

Entanglement entropy: a perturbative calculation
journal, December 2014

Rosenhaus, Vladimir; Smolkin, Michael
Journal of High Energy Physics, Vol. 2014, Issue 12
DOI: 10.1007/JHEP12(2014)179

A Covariant Holographic Entanglement Entropy Proposal
text, January 2007

Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi
arXiv
DOI: 10.48550/arxiv.0705.0016

Relative entropy and the Bekenstein bound
text, January 2008

Casini, H.
arXiv
DOI: 10.48550/arxiv.0804.2182

Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
text, January 2009

Hofman, Diego M.
arXiv
DOI: 10.48550/arxiv.0907.1625

Holographic GB gravity in arbitrary dimensions
text, January 2009

Buchel, Alex; Escobedo, Jorge; Myers, Robert C.
arXiv
DOI: 10.48550/arxiv.0911.4257

Towards a derivation of holographic entanglement entropy
text, January 2011

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

Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
text, January 2011

Grover, Tarun; Turner, Ari M.; Vishwanath, Ashvin
arXiv
DOI: 10.48550/arxiv.1108.4038

Quantum corrections to holographic entanglement entropy
text, January 2013

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

Localization of Negative Energy and the Bekenstein Bound
text, January 2013

Blanco, David D.; Casini, Horacio
arXiv
DOI: 10.48550/arxiv.1309.1121

Constraining gravity using entanglement in AdS/CFT
text, January 2014

Banerjee, Shamik; Bhattacharyya, Arpan; Kaviraj, Apratim
arXiv
DOI: 10.48550/arxiv.1401.5089

Entanglement Entropy: A Perturbative Calculation
text, January 2014

Rosenhaus, Vladimir; Smolkin, Michael
arXiv
DOI: 10.48550/arxiv.1403.3733

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
text, January 2014

Engelhardt, Netta; Wall, Aron C.
arXiv
DOI: 10.48550/arxiv.1408.3203

Entanglement Entropy for Relevant and Geometric Perturbations
text, January 2014

Rosenhaus, Vladimir; Smolkin, Michael
arXiv
DOI: 10.48550/arxiv.1410.6530

Bulk Emergence and the RG Flow of Entanglement Entropy
text, January 2014

Faulkner, Thomas
arXiv
DOI: 10.48550/arxiv.1412.5648

Causality Constraints in Conformal Field Theory
text, January 2015

Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
arXiv
DOI: 10.48550/arxiv.1509.00014

Shape Dependence of Entanglement Entropy in Conformal Field Theories
text, January 2015

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
arXiv
DOI: 10.48550/arxiv.1511.05179

A Proof of the Conformal Collider Bounds
text, January 2016

Hofman, Diego M.; Li, Daliang; Meltzer, David
arXiv
DOI: 10.48550/arxiv.1603.03771

Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality
text, January 2016

Bhattacharyya, Arpan; Cheng, Long; Hung, Ling-Yan
arXiv
DOI: 10.48550/arxiv.1605.02553

Gauge Theory Correlators from Non-Critical String Theory
text, January 1998

Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
arXiv
DOI: 10.48550/arxiv.hep-th/9802109

Anti De Sitter Space And Holography
text, January 1998

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

Works referencing / citing this record:

The holographic dual of the entanglement wedge symplectic form
journal, January 2020

Kirklin, Josh
Journal of High Energy Physics, Vol. 2020, Issue 1
DOI: 10.1007/jhep01(2020)071

Implications of ANEC for SCFTs in four dimensions
journal, January 2020

Manenti, Andrea; Stergiou, Andreas; Vichi, Alessandro
Journal of High Energy Physics, Vol. 2020, Issue 1
DOI: 10.1007/jhep01(2020)093

Universal bounds on operator dimensions from the average null energy condition
journal, February 2018

Córdova, Clay; Diab, Kenan
Journal of High Energy Physics, Vol. 2018, Issue 2
DOI: 10.1007/jhep02(2018)131

A bound on massive higher spin particles
journal, April 2019

Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein
Journal of High Energy Physics, Vol. 2019, Issue 4
DOI: 10.1007/jhep04(2019)056

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

Bulk phase shift, CFT Regge limit and Einstein gravity
journal, June 2018

Kulaxizi, Manuela; Parnachev, Andrei; Zhiboedov, Alexander
Journal of High Energy Physics, Vol. 2018, Issue 6
DOI: 10.1007/jhep06(2018)121

Beyond a = c : gravitational couplings to matter and the stress tensor OPE
journal, July 2018

Meltzer, David; Perlmutter, Eric
Journal of High Energy Physics, Vol. 2018, Issue 7
DOI: 10.1007/jhep07(2018)157

Einstein gravity from ANEC correlators
journal, August 2019

Belin, Alexandre; Hofman, Diego M.; Mathys, Grégoire
Journal of High Energy Physics, Vol. 2019, Issue 8
DOI: 10.1007/jhep08(2019)032

Graviton scattering and a sum rule for the c anomaly in 4D CFT
journal, September 2018

Gillioz, Marc; Lu, Xiaochuan; Luty, Markus A.
Journal of High Energy Physics, Vol. 2018, Issue 9
DOI: 10.1007/jhep09(2018)025

Entanglement of a chiral fermion on the torus
journal, September 2019

Blanco, David; Garbarz, Alan; Pérez-Nadal, Guillem
Journal of High Energy Physics, Vol. 2019, Issue 9
DOI: 10.1007/jhep09(2019)076

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

Conformal bootstrap in the Regge limit
journal, December 2017

Li, Daliang; Meltzer, David; Poland, David
Journal of High Energy Physics, Vol. 2017, Issue 12
DOI: 10.1007/jhep12(2017)013

Traversable wormholes via a double trace deformation
journal, December 2017

Gao, Ping; Jafferis, Daniel Louis; Wall, Aron C.
Journal of High Energy Physics, Vol. 2017, Issue 12
DOI: 10.1007/jhep12(2017)151

The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
journal, December 2019

Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald
Journal of High Energy Physics, Vol. 2019, Issue 12
DOI: 10.1007/jhep12(2019)063

A perturbative perspective on self-supporting wormholes
journal, January 2019

Fu, Zicao; Grado-White, Brianna; Marolf, Donald
Classical and Quantum Gravity, Vol. 36, Issue 4
DOI: 10.1088/1361-6382/aafcea

Modular Hamiltonians on the null plane and the Markov property of the vacuum state
journal, August 2017

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo
Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 36
DOI: 10.1088/1751-8121/aa7eaa

Entanglement and relative entropy of a chiral fermion on the torus
journal, November 2019

Fries, Pascal; Reyes, Ignacio A.
Physical Review D, Vol. 100, Issue 10
DOI: 10.1103/physrevd.100.105015

Entanglement Spectrum of Chiral Fermions on the Torus
journal, November 2019

Fries, Pascal; Reyes, Ignacio A.
Physical Review Letters, Vol. 123, Issue 21
DOI: 10.1103/physrevlett.123.211603

The holographic dual of the entanglement wedge symplectic form
text, January 2020

Kirklin, Josh
Apollo - University of Cambridge Repository
DOI: 10.17863/cam.53403

The holographic dual of the entanglement wedge symplectic form
text, January 2020

Kirklin, Josh
Apollo - University of Cambridge Repository
DOI: 10.17863/cam.63253

Einstein gravity 3-point functions from conformal field theory
text, January 2016

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan
arXiv
DOI: 10.48550/arxiv.1610.09378

Modular Hamiltonians on the null plane and the Markov property of the vacuum state
text, January 2017

Casini, Horacio; Teste, Eduardo; Torroba, Gonzalo
arXiv
DOI: 10.48550/arxiv.1703.10656

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

Bulk Phase Shift, CFT Regge Limit and Einstein Gravity
text, January 2017

Kulaxizi, Manuela; Parnachev, Andrei; Zhiboedov, Alexander
arXiv
DOI: 10.48550/arxiv.1705.02934

Nonlinear Gravity from Entanglement in Conformal Field Theories
text, January 2017

Faulkner, Thomas; Haehl, Felix M.; Hijano, Eliot
arXiv
DOI: 10.48550/arxiv.1705.03026

Conformal Bootstrap in the Regge Limit
text, January 2017

Li, Daliang; Meltzer, David; Poland, David
arXiv
DOI: 10.48550/arxiv.1705.03453

Charting the space of 3D CFTs with a continuous global symmetry
text, January 2017

Dymarsky, Anatoly; Penedones, Joao; Trevisani, Emilio
arXiv
DOI: 10.48550/arxiv.1705.04278

Anisotropic Unruh temperatures
text, January 2017

Arias, Raul; Casini, Horacio; Huerta, Marina
arXiv
DOI: 10.48550/arxiv.1707.05375

Shockwaves from the Operator Product Expansion
preprint, January 2017

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan
arXiv
DOI: 10.48550/arxiv.1709.03597

Universal Bounds on Operator Dimensions from the Average Null Energy Condition
text, January 2017

Cordova, Clay; Diab, Kenan
arXiv
DOI: 10.48550/arxiv.1712.01089

Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
text, January 2017

Meltzer, David; Perlmutter, Eric
arXiv
DOI: 10.48550/arxiv.1712.04861

Entanglement entropy in (1+1)D CFTs with multiple local excitations
text, January 2018

Guo, Wu-zhong; He, Song; Luo, Zhu-Xi
arXiv
DOI: 10.48550/arxiv.1802.08815

Light-ray operators in conformal field theory
text, January 2018

Kravchuk, Petr; Simmons-Duffin, David
arXiv
DOI: 10.48550/arxiv.1805.00098

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
text, January 2018

Poland, David; Rychkov, Slava; Vichi, Alessandro
arXiv
DOI: 10.48550/arxiv.1805.04405

A Conformal Collider for Holographic CFTs
text, January 2018

Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein
arXiv
DOI: 10.48550/arxiv.1805.07393

A perturbative perspective on self-supporting wormholes
text, January 2018

Fu, Zicao; Grado-White, Brianna; Marolf, Donald
arXiv
DOI: 10.48550/arxiv.1807.07917

Bootstrap and collider physics of parity violating conformal field theories in $d=3$
preprint, January 2018

Chowdhury, Subham Dutta; David, Justin R.; Prakash, Shiroman
arXiv
DOI: 10.48550/arxiv.1812.07774

The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
text, January 2019

Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald
arXiv
DOI: 10.48550/arxiv.1905.08762

Spectrum of Modular Hamiltonian in the Vacuum and Excited States
text, January 2019

Das, Suchetan; Ezhuthachan, Bobby
arXiv
DOI: 10.48550/arxiv.1906.00726

The entanglement and relative entropy of a chiral fermion on the torus
text, January 2019

Fries, Pascal; Reyes, Ignacio A.
arXiv
DOI: 10.48550/arxiv.1906.02207

The Holographic Dual of the Entanglement Wedge Symplectic Form
text, January 2019

Kirklin, Josh
arXiv
DOI: 10.48550/arxiv.1910.00457

Similar Records in DOE PAGES and OSTI.GOV collections:

A general proof of the quantum null energy condition

Journal Article Balakrishnan, Srivatsan ; Faulkner, Thomas ; Khandker, Zuhair U. ; ... - Journal of High Energy Physics (Online)

We prove a conjectured lower bound on ⟨T_ _(x)⟩more »« less
Cited by 74
https://doi.org/10.1007/jhep09(2019)020

Full Text Available
Global aspects of conformal symmetry and the ANEC in dS and AdS

Journal Article Rosso, Felipe - Journal of High Energy Physics (Online)

Starting from the averaged null energy condition (ANEC) in Minkowski we show that conformal symmetry implies the ANEC for a conformal field theory (CFT) in a de Sitter and anti-de Sitter background. A similar and novel bound is also obtained for a CFT in the Lorentzian cylinder. Using monotonicity of relative entropy, we rederive these results for dS and the cylinder. As a byproduct we obtain the vacuum modular Hamiltonian and entanglement entropy associated to null deformed regions of CFTs in (A)dS and the cylinder. A third derivation of the ANEC in dS is shown to follow from bulk causalitymore »« less
https://doi.org/10.1007/jhep03(2020)186

Full Text Available
Shape dependence of entanglement entropy in conformal field theories

Journal Article Faulkner, Thomas ; Leigh, Robert G. ; Parrikar, Onkar - Journal of High Energy Physics (Online)

Here, we study universal features in the shape dependence of entanglement entropy in the vacuum state of a conformal field theory (CFT) on R^1,d--1. We consider the entanglement entropy across a deformed planar or spherical entangling surface in terms of a perturbative expansion in the infinitesimal shape deformation. In particular, we focus on the second order term in this expansion, known as the entanglement density. This quantity is known to be non-positive by the strong-subadditivity property. We also show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportionalmore »« less
Cited by 74
https://doi.org/10.1007/JHEP04(2016)088

Full Text Available
Scattering strings off quantum extremal surfaces

Journal Article Chandrasekaran, Venkatesa ; Faulkner, Thomas ; Levine, Adam - Journal of High Energy Physics (Online)

We consider a Hayden & Preskill like setup for both maximally chaotic and sub-maximally chaotic quantum field theories. We act on the vacuum with an operator in a Rindler like wedge R and transfer a small subregion I of R to the other wedge. The chaotic scrambling dynamics of the QFT Rindler time evolution reveals the information in the other wedge. The holographic dual of this process involves a particle excitation falling into the bulk and crossing into the entanglement wedge of the complement to r = R\I. With the goal of studying the locality of the emergent holographic theorymore »« less
https://doi.org/10.1007/jhep08(2022)143

Full Text Available
Entropy variations and light ray operators from replica defects

Journal Article Balakrishnan, Srivatsan ; Chandrasekaran, Venkatesa ; Faulkner, Thomas ; ... - Journal of High Energy Physics (Online)

We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as n approaches 1 a contact term can emerge when the OPE contains defect operators of twist d - 2. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the n → 1 limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in amore »« less
https://doi.org/10.1007/jhep09(2022)217

Full Text Available

Similar Records

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

Abstract

Citation Formats

Topological censorship journal, September 1993

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime journal, January 2015

Wess-Zumino Consistency Condition for Entanglement Entropy journal, July 2012

Relative entropy and the Bekenstein bound journal, September 2008

Causality constraints in conformal field theory journal, May 2016

Higher derivative gravity, causality and positivity of energy in a UV complete QFT journal, December 2009

Modular Hamiltonian for Excited States in Conformal Field Theory journal, July 2016

Towards a derivation of holographic entanglement entropy journal, May 2011

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

Gauge theory correlators from non-critical string theory journal, May 1998

Entanglement Entropy of Electromagnetic Edge Modes journal, March 2015

Shape dependence of entanglement entropy in conformal field theories journal, April 2016

Holographic entanglement entropy and gravitational anomalies journal, July 2014

Mutual information and the F-theorem journal, October 2015

Bulk emergence and the RG flow of entanglement entropy journal, May 2015

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

Entanglement entropy of gapped phases and topological order in three dimensions journal, November 2011

Anomalies and entanglement entropy journal, March 2016

A finite entanglement entropy and the c-theorem journal, October 2004

Anti de Sitter space and holography journal, January 1998

The averaged null energy condition for general quantum field theories in two dimensions journal, January 2000

Entanglement entropy for relevant and geometric perturbations journal, February 2015

A proof of the conformal collider bounds journal, June 2016

A coarse-grained generalized second law for holographic conformal field theories journal, February 2016

Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity journal, April 2010

A covariant holographic entanglement entropy proposal journal, July 2007

On the duality condition for quantum fields journal, January 1976

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality journal, July 2016

On the quantum structure of a black hole journal, January 1985

Conformal collider physics: energy and charge correlations journal, May 2008

Geodesic focusing, energy conditions and singularities journal, March 1987

Holographic GB gravity in arbitrary dimensions journal, March 2010

Constraining gravity using entanglement in AdS/CFT journal, May 2014

Localization of Negative Energy and the Bekenstein Bound journal, November 2013

Energy Flux Positivity and Unitarity in Conformal Field Theories journal, January 2011

Relative Entropies in Conformal Field Theory journal, July 2014

Quantum corrections to holographic entanglement entropy journal, November 2013

Relative entropy equals bulk relative entropy journal, June 2016

’t Hooft suppression and holographic entropy journal, October 2015

Entanglement entropy: a perturbative calculation journal, December 2014

A Covariant Holographic Entanglement Entropy Proposal text, January 2007

Relative entropy and the Bekenstein bound text, January 2008

Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT text, January 2009

Holographic GB gravity in arbitrary dimensions text, January 2009

Towards a derivation of holographic entanglement entropy text, January 2011

Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions text, January 2011

Quantum corrections to holographic entanglement entropy text, January 2013

Localization of Negative Energy and the Bekenstein Bound text, January 2013

Constraining gravity using entanglement in AdS/CFT text, January 2014

Entanglement Entropy: A Perturbative Calculation text, January 2014

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime text, January 2014

Entanglement Entropy for Relevant and Geometric Perturbations text, January 2014

Bulk Emergence and the RG Flow of Entanglement Entropy text, January 2014

Causality Constraints in Conformal Field Theory text, January 2015

Shape Dependence of Entanglement Entropy in Conformal Field Theories text, January 2015

A Proof of the Conformal Collider Bounds text, January 2016

Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality text, January 2016

Gauge Theory Correlators from Non-Critical String Theory text, January 1998

Anti De Sitter Space And Holography text, January 1998

The holographic dual of the entanglement wedge symplectic form journal, January 2020

Implications of ANEC for SCFTs in four dimensions journal, January 2020

Universal bounds on operator dimensions from the average null energy condition journal, February 2018

A bound on massive higher spin particles journal, April 2019

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

Bulk phase shift, CFT Regge limit and Einstein gravity journal, June 2018

Beyond a = c : gravitational couplings to matter and the stress tensor OPE journal, July 2018

Einstein gravity from ANEC correlators journal, August 2019

Graviton scattering and a sum rule for the c anomaly in 4D CFT journal, September 2018

Entanglement of a chiral fermion on the torus journal, September 2019

A conformal collider for holographic CFTs journal, October 2018

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

Conformal bootstrap in the Regge limit journal, December 2017

Traversable wormholes via a double trace deformation journal, December 2017

The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole journal, December 2019

A perturbative perspective on self-supporting wormholes journal, January 2019

Modular Hamiltonians on the null plane and the Markov property of the vacuum state journal, August 2017

Entanglement and relative entropy of a chiral fermion on the torus journal, November 2019

Topological censorship
journal, September 1993

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
journal, January 2015

Wess-Zumino Consistency Condition for Entanglement Entropy
journal, July 2012

Relative entropy and the Bekenstein bound
journal, September 2008

Causality constraints in conformal field theory
journal, May 2016

Higher derivative gravity, causality and positivity of energy in a UV complete QFT
journal, December 2009

Modular Hamiltonian for Excited States in Conformal Field Theory
journal, July 2016

Towards a derivation of holographic entanglement entropy
journal, May 2011

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

Gauge theory correlators from non-critical string theory
journal, May 1998

Entanglement Entropy of Electromagnetic Edge Modes
journal, March 2015

Shape dependence of entanglement entropy in conformal field theories
journal, April 2016

Holographic entanglement entropy and gravitational anomalies
journal, July 2014

Mutual information and the F-theorem
journal, October 2015

Bulk emergence and the RG flow of entanglement entropy
journal, May 2015

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

Entanglement entropy of gapped phases and topological order in three dimensions
journal, November 2011

Anomalies and entanglement entropy
journal, March 2016

A finite entanglement entropy and the c-theorem
journal, October 2004

Anti de Sitter space and holography
journal, January 1998

The averaged null energy condition for general quantum field theories in two dimensions
journal, January 2000

Entanglement entropy for relevant and geometric perturbations
journal, February 2015

A proof of the conformal collider bounds
journal, June 2016

A coarse-grained generalized second law for holographic conformal field theories
journal, February 2016

Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity
journal, April 2010

A covariant holographic entanglement entropy proposal
journal, July 2007

On the duality condition for quantum fields
journal, January 1976

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
journal, July 2016

On the quantum structure of a black hole
journal, January 1985

Conformal collider physics: energy and charge correlations
journal, May 2008

Geodesic focusing, energy conditions and singularities
journal, March 1987

Holographic GB gravity in arbitrary dimensions
journal, March 2010

Constraining gravity using entanglement in AdS/CFT
journal, May 2014

Localization of Negative Energy and the Bekenstein Bound
journal, November 2013

Energy Flux Positivity and Unitarity in Conformal Field Theories
journal, January 2011

Relative Entropies in Conformal Field Theory
journal, July 2014

Quantum corrections to holographic entanglement entropy
journal, November 2013

Relative entropy equals bulk relative entropy
journal, June 2016

’t Hooft suppression and holographic entropy
journal, October 2015

Entanglement entropy: a perturbative calculation
journal, December 2014

A Covariant Holographic Entanglement Entropy Proposal
text, January 2007

Relative entropy and the Bekenstein bound
text, January 2008

Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
text, January 2009

Holographic GB gravity in arbitrary dimensions
text, January 2009

Towards a derivation of holographic entanglement entropy
text, January 2011

Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
text, January 2011

Quantum corrections to holographic entanglement entropy
text, January 2013

Localization of Negative Energy and the Bekenstein Bound
text, January 2013

Constraining gravity using entanglement in AdS/CFT
text, January 2014

Entanglement Entropy: A Perturbative Calculation
text, January 2014

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
text, January 2014

Entanglement Entropy for Relevant and Geometric Perturbations
text, January 2014

Bulk Emergence and the RG Flow of Entanglement Entropy
text, January 2014

Causality Constraints in Conformal Field Theory
text, January 2015

Shape Dependence of Entanglement Entropy in Conformal Field Theories
text, January 2015

A Proof of the Conformal Collider Bounds
text, January 2016

Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality
text, January 2016

Gauge Theory Correlators from Non-Critical String Theory
text, January 1998

Anti De Sitter Space And Holography
text, January 1998

The holographic dual of the entanglement wedge symplectic form
journal, January 2020

Implications of ANEC for SCFTs in four dimensions
journal, January 2020

Universal bounds on operator dimensions from the average null energy condition
journal, February 2018

A bound on massive higher spin particles
journal, April 2019

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

Bulk phase shift, CFT Regge limit and Einstein gravity
journal, June 2018

Beyond a = c : gravitational couplings to matter and the stress tensor OPE
journal, July 2018

Einstein gravity from ANEC correlators
journal, August 2019

Graviton scattering and a sum rule for the c anomaly in 4D CFT
journal, September 2018

Entanglement of a chiral fermion on the torus
journal, September 2019

A conformal collider for holographic CFTs
journal, October 2018

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

Conformal bootstrap in the Regge limit
journal, December 2017

Traversable wormholes via a double trace deformation
journal, December 2017

The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
journal, December 2019

A perturbative perspective on self-supporting wormholes
journal, January 2019

Modular Hamiltonians on the null plane and the Markov property of the vacuum state
journal, August 2017

Entanglement and relative entropy of a chiral fermion on the torus
journal, November 2019

Entanglement Spectrum of Chiral Fermions on the Torus
journal, November 2019

The holographic dual of the entanglement wedge symplectic form
text, January 2020

The holographic dual of the entanglement wedge symplectic form
text, January 2020