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

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

DOI:https://doi.org/10.1007/JHEP09(2016)038· OSTI ID:1395542

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

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

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

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

Sponsoring Organization:: USDOE

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

OSTI ID:: 1395542

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: 151 works

Citation information provided by
Web of Science

References (59)

Topological censorship Friedman, John L.; Schleich, Kristin; Witt, Donald M. Physical Review Letters, Vol. 71, Issue 10 https://doi.org/10.1103/PhysRevLett.71.1486	journal	September 1993
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
Wess-Zumino Consistency Condition for Entanglement Entropy Banerjee, Shamik Physical Review Letters, Vol. 109, Issue 1 https://doi.org/10.1103/PhysRevLett.109.010402	journal	July 2012
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
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
Higher derivative gravity, causality and positivity of energy in a UV complete QFT Hofman, Diego M. Nuclear Physics B, Vol. 823, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2009.08.001	journal	December 2009
Modular Hamiltonian for Excited States in Conformal Field Theory Lashkari, Nima Physical Review Letters, Vol. 117, Issue 4 https://doi.org/10.1103/PhysRevLett.117.041601	journal	July 2016
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 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
Gauge theory correlators from non-critical string theory Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M. Physics Letters B, Vol. 428, Issue 1-2 https://doi.org/10.1016/S0370-2693(98)00377-3	journal	May 1998
Entanglement Entropy of Electromagnetic Edge Modes Donnelly, William; Wall, Aron C. Physical Review Letters, Vol. 114, Issue 11 https://doi.org/10.1103/PhysRevLett.114.111603	journal	March 2015
Shape dependence of entanglement entropy in conformal field theories Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar Journal of High Energy Physics, Vol. 2016, Issue 4 https://doi.org/10.1007/JHEP04(2016)088	journal	April 2016
Holographic entanglement entropy and gravitational anomalies Castro, Alejandra; Detournay, Stephane; Iqbal, Nabil Journal of High Energy Physics, Vol. 2014, Issue 7 https://doi.org/10.1007/JHEP07(2014)114	journal	July 2014
Mutual information and the F-theorem Casini, Horacio; Huerta, Marina; Myers, Robert C. Journal of High Energy Physics, Vol. 2015, Issue 10 https://doi.org/10.1007/JHEP10(2015)003	journal	October 2015
Bulk emergence and the RG flow of entanglement entropy Faulkner, Thomas Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/JHEP05(2015)033	journal	May 2015
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
Entanglement entropy of gapped phases and topological order in three dimensions Grover, Tarun; Turner, Ari M.; Vishwanath, Ashvin Physical Review B, Vol. 84, Issue 19 https://doi.org/10.1103/PhysRevB.84.195120	journal	November 2011
Anomalies and entanglement entropy Nishioka, Tatsuma; Yarom, Amos Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)077	journal	March 2016
A finite entanglement entropy and the c-theorem Casini, H.; Huerta, M. Physics Letters B, Vol. 600, Issue 1-2 https://doi.org/10.1016/j.physletb.2004.08.072	journal	October 2004
Anti de Sitter space and holography Witten, Edward Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2 https://doi.org/10.4310/ATMP.1998.v2.n2.a2	journal	January 1998
The averaged null energy condition for general quantum field theories in two dimensions Verch, Rainer Journal of Mathematical Physics, Vol. 41, Issue 1 https://doi.org/10.1063/1.533130	journal	January 2000
Entanglement entropy for relevant and geometric perturbations Rosenhaus, Vladimir; Smolkin, Michael Journal of High Energy Physics, Vol. 2015, Issue 2 https://doi.org/10.1007/JHEP02(2015)015	journal	February 2015
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
A coarse-grained generalized second law for holographic conformal field theories Bunting, William; Fu, Zicao; Marolf, Donald Classical and Quantum Gravity, Vol. 33, Issue 5 https://doi.org/10.1088/0264-9381/33/5/055008	journal	February 2016
Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity Camanho, Xián O.; Edelstein, José D. Journal of High Energy Physics, Vol. 2010, Issue 4 https://doi.org/10.1007/JHEP04(2010)007	journal	April 2010
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
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
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
On the quantum structure of a black hole 't Hooft, Gerard Nuclear Physics B, Vol. 256 https://doi.org/10.1016/0550-3213(85)90418-3	journal	January 1985
Conformal collider physics: energy and charge correlations Hofman, Diego M.; Maldacena, Juan Journal of High Energy Physics, Vol. 2008, Issue 05 https://doi.org/10.1088/1126-6708/2008/05/012	journal	May 2008
Geodesic focusing, energy conditions and singularities Borde, A. Classical and Quantum Gravity, Vol. 4, Issue 2 https://doi.org/10.1088/0264-9381/4/2/015	journal	March 1987
Holographic GB gravity in arbitrary dimensions Buchel, Alex; Escobedo, Jorge; Myers, Robert C. Journal of High Energy Physics, Vol. 2010, Issue 3 https://doi.org/10.1007/JHEP03(2010)111	journal	March 2010
Constraining gravity using entanglement in AdS/CFT Banerjee, Shamik; Bhattacharyya, Arpan; Kaviraj, Apratim Journal of High Energy Physics, Vol. 2014, Issue 5 https://doi.org/10.1007/JHEP05(2014)029	journal	May 2014
Localization of Negative Energy and the Bekenstein Bound Blanco, David D.; Casini, Horacio Physical Review Letters, Vol. 111, Issue 22 https://doi.org/10.1103/PhysRevLett.111.221601	journal	November 2013
Energy Flux Positivity and Unitarity in Conformal Field Theories Kulaxizi, Manuela; Parnachev, Andrei Physical Review Letters, Vol. 106, Issue 1 https://doi.org/10.1103/PhysRevLett.106.011601	journal	January 2011
Relative Entropies in Conformal Field Theory Lashkari, Nima Physical Review Letters, Vol. 113, Issue 5 https://doi.org/10.1103/PhysRevLett.113.051602	journal	July 2014
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
’t Hooft suppression and holographic entropy Kelly, William R.; Kuns, Kevin; Marolf, Donald Journal of High Energy Physics, Vol. 2015, Issue 10 https://doi.org/10.1007/JHEP10(2015)059	journal	October 2015
Entanglement entropy: a perturbative calculation Rosenhaus, Vladimir; Smolkin, Michael Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)179	journal	December 2014
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
Relative entropy and the Bekenstein bound Casini, H. arXiv https://doi.org/10.48550/arxiv.0804.2182	text	January 2008
Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT Hofman, Diego M. arXiv https://doi.org/10.48550/arxiv.0907.1625	text	January 2009
Holographic GB gravity in arbitrary dimensions Buchel, Alex; Escobedo, Jorge; Myers, Robert C. arXiv https://doi.org/10.48550/arxiv.0911.4257	text	January 2009
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
Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions Grover, Tarun; Turner, Ari M.; Vishwanath, Ashvin arXiv https://doi.org/10.48550/arxiv.1108.4038	text	January 2011
Quantum corrections to holographic entanglement entropy Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1307.2892	text	January 2013
Localization of Negative Energy and the Bekenstein Bound Blanco, David D.; Casini, Horacio arXiv https://doi.org/10.48550/arxiv.1309.1121	text	January 2013
Constraining gravity using entanglement in AdS/CFT Banerjee, Shamik; Bhattacharyya, Arpan; Kaviraj, Apratim arXiv https://doi.org/10.48550/arxiv.1401.5089	text	January 2014
Entanglement Entropy: A Perturbative Calculation Rosenhaus, Vladimir; Smolkin, Michael arXiv https://doi.org/10.48550/arxiv.1403.3733	text	January 2014
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
Entanglement Entropy for Relevant and Geometric Perturbations Rosenhaus, Vladimir; Smolkin, Michael arXiv https://doi.org/10.48550/arxiv.1410.6530	text	January 2014
Bulk Emergence and the RG Flow of Entanglement Entropy Faulkner, Thomas arXiv https://doi.org/10.48550/arxiv.1412.5648	text	January 2014
Causality Constraints in Conformal Field Theory Hartman, Thomas; Jain, Sachin; Kundu, Sandipan arXiv https://doi.org/10.48550/arxiv.1509.00014	text	January 2015
Shape Dependence of Entanglement Entropy in Conformal Field Theories Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar arXiv https://doi.org/10.48550/arxiv.1511.05179	text	January 2015
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
Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality Bhattacharyya, Arpan; Cheng, Long; Hung, Ling-Yan arXiv https://doi.org/10.48550/arxiv.1605.02553	text	January 2016
Gauge Theory Correlators from Non-Critical String Theory Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M. arXiv https://doi.org/10.48550/arxiv.hep-th/9802109	text	January 1998
Anti De Sitter Space And Holography Witten, Edward arXiv https://doi.org/10.48550/arxiv.hep-th/9802150	text	January 1998

Cited By (42)

The holographic dual of the entanglement wedge symplectic form Kirklin, Josh Journal of High Energy Physics, Vol. 2020, Issue 1 https://doi.org/10.1007/jhep01(2020)071	journal	January 2020
Implications of ANEC for SCFTs in four dimensions Manenti, Andrea; Stergiou, Andreas; Vichi, Alessandro Journal of High Energy Physics, Vol. 2020, Issue 1 https://doi.org/10.1007/jhep01(2020)093	journal	January 2020
Universal bounds on operator dimensions from the average null energy condition Córdova, Clay; Diab, Kenan Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/jhep02(2018)131	journal	February 2018
A bound on massive higher spin particles Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein Journal of High Energy Physics, Vol. 2019, Issue 4 https://doi.org/10.1007/jhep04(2019)056	journal	April 2019
Entanglement entropy in (1+1)D CFTs with multiple local excitations Guo, Wu-zhong; He, Song; Luo, Zhu-Xi Journal of High Energy Physics, Vol. 2018, Issue 5 https://doi.org/10.1007/jhep05(2018)154	journal	May 2018
Bulk phase shift, CFT Regge limit and Einstein gravity Kulaxizi, Manuela; Parnachev, Andrei; Zhiboedov, Alexander Journal of High Energy Physics, Vol. 2018, Issue 6 https://doi.org/10.1007/jhep06(2018)121	journal	June 2018
Beyond a = c : gravitational couplings to matter and the stress tensor OPE Meltzer, David; Perlmutter, Eric Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/jhep07(2018)157	journal	July 2018
Einstein gravity from ANEC correlators Belin, Alexandre; Hofman, Diego M.; Mathys, Grégoire Journal of High Energy Physics, Vol. 2019, Issue 8 https://doi.org/10.1007/jhep08(2019)032	journal	August 2019
Graviton scattering and a sum rule for the c anomaly in 4D CFT Gillioz, Marc; Lu, Xiaochuan; Luty, Markus A. Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/jhep09(2018)025	journal	September 2018
Entanglement of a chiral fermion on the torus Blanco, David; Garbarz, Alan; Pérez-Nadal, Guillem Journal of High Energy Physics, Vol. 2019, Issue 9 https://doi.org/10.1007/jhep09(2019)076	journal	September 2019
A conformal collider for holographic CFTs Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/jhep10(2018)156	journal	October 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
Conformal bootstrap in the Regge limit Li, Daliang; Meltzer, David; Poland, David Journal of High Energy Physics, Vol. 2017, Issue 12 https://doi.org/10.1007/jhep12(2017)013	journal	December 2017
Traversable wormholes via a double trace deformation Gao, Ping; Jafferis, Daniel Louis; Wall, Aron C. Journal of High Energy Physics, Vol. 2017, Issue 12 https://doi.org/10.1007/jhep12(2017)151	journal	December 2017
The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/jhep12(2019)063	journal	December 2019
A perturbative perspective on self-supporting wormholes Fu, Zicao; Grado-White, Brianna; Marolf, Donald Classical and Quantum Gravity, Vol. 36, Issue 4 https://doi.org/10.1088/1361-6382/aafcea	journal	January 2019
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
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
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
The holographic dual of the entanglement wedge symplectic form Kirklin, Josh Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.53403	text	January 2020
The holographic dual of the entanglement wedge symplectic form Kirklin, Josh Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.63253	text	January 2020
Einstein gravity 3-point functions from conformal field theory Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan arXiv https://doi.org/10.48550/arxiv.1610.09378	text	January 2016
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
Bulk Phase Shift, CFT Regge Limit and Einstein Gravity Kulaxizi, Manuela; Parnachev, Andrei; Zhiboedov, Alexander arXiv https://doi.org/10.48550/arxiv.1705.02934	text	January 2017
Nonlinear Gravity from Entanglement in Conformal Field Theories Faulkner, Thomas; Haehl, Felix M.; Hijano, Eliot arXiv https://doi.org/10.48550/arxiv.1705.03026	text	January 2017
Conformal Bootstrap in the Regge Limit Li, Daliang; Meltzer, David; Poland, David arXiv https://doi.org/10.48550/arxiv.1705.03453	text	January 2017
Charting the space of 3D CFTs with a continuous global symmetry Dymarsky, Anatoly; Penedones, Joao; Trevisani, Emilio arXiv https://doi.org/10.48550/arxiv.1705.04278	text	January 2017
Anisotropic Unruh temperatures Arias, Raul; Casini, Horacio; Huerta, Marina arXiv https://doi.org/10.48550/arxiv.1707.05375	text	January 2017
Shockwaves from the Operator Product Expansion Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan arXiv https://doi.org/10.48550/arxiv.1709.03597	preprint	January 2017
Universal Bounds on Operator Dimensions from the Average Null Energy Condition Cordova, Clay; Diab, Kenan arXiv https://doi.org/10.48550/arxiv.1712.01089	text	January 2017
Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE Meltzer, David; Perlmutter, Eric arXiv https://doi.org/10.48550/arxiv.1712.04861	text	January 2017
Entanglement entropy in (1+1)D CFTs with multiple local excitations Guo, Wu-zhong; He, Song; Luo, Zhu-Xi arXiv https://doi.org/10.48550/arxiv.1802.08815	text	January 2018
Light-ray operators in conformal field theory Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1805.00098	text	January 2018
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications Poland, David; Rychkov, Slava; Vichi, Alessandro arXiv https://doi.org/10.48550/arxiv.1805.04405	text	January 2018
A Conformal Collider for Holographic CFTs Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein arXiv https://doi.org/10.48550/arxiv.1805.07393	text	January 2018
A perturbative perspective on self-supporting wormholes Fu, Zicao; Grado-White, Brianna; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1807.07917	text	January 2018
Bootstrap and collider physics of parity violating conformal field theories in $d=3$ Chowdhury, Subham Dutta; David, Justin R.; Prakash, Shiroman arXiv https://doi.org/10.48550/arxiv.1812.07774	preprint	January 2018
The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1905.08762	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
The Holographic Dual of the Entanglement Wedge Symplectic Form Kirklin, Josh arXiv https://doi.org/10.48550/arxiv.1910.00457	text	January 2019

Similar Records

A general proof of the quantum null energy condition

Journal Article · Tue Sep 03 00:00:00 EDT 2019 · Journal of High Energy Physics (Online) · OSTI ID:1395542

Balakrishnan, Srivatsan; Faulkner, Thomas; Khandker, Zuhair U.; +1 more

Global aspects of conformal symmetry and the ANEC in dS and AdS

Journal Article · Mon Mar 30 00:00:00 EDT 2020 · Journal of High Energy Physics (Online) · OSTI ID:1395542

Rosso, Felipe

Shape dependence of entanglement entropy in conformal field theories

Journal Article · Thu Apr 14 00:00:00 EDT 2016 · Journal of High Energy Physics (Online) · OSTI ID:1395542

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

Related Subjects

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

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

Citation Formats

References (59)

Cited By (42)

Similar Records

Related Subjects