Entropy, extremality, euclidean variations, and the equations of motion

Dong, Xi; Lewkowycz, Aitor

doi:10.1007/jhep01(2018)081

Title: Entropy, extremality, euclidean variations, and the equations of motion

Abstract

We study the Euclidean gravitational path integral computing the Rényi entropy and analyze its behavior under small variations. We argue that, in Einstein gravity, the extremality condition can be understood from the variational principle at the level of the action, without having to solve explicitly the equations of motion. This set-up is then generalized to arbitrary theories of gravity, where we show that the respective entanglement entropy functional needs to be extremized. We also extend this result to all orders in Newton’s constant G_N, providing a derivation of quantum extremality. Understanding quantum extremality for mixtures of states provides a generalization of the dual of the boundary modular Hamiltonian which is given by the bulk modular Hamiltonian plus the area operator, evaluated on the so-called modular extremal surface. This gives a bulk prescription for computing the relative entropies to all orders in G_N . We also comment on how these ideas can be used to derive an integrated version of the equations of motion, linearized around arbitrary states.

Authors:

^[1]; Lewkowycz, Aitor ^[2]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Univ. of California, Santa Barbara, CA (United States). Dept. of Physics
Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics

Publication Date:: Wed Jan 17 00:00:00 EST 2018

Research Org.:: Institute for Advanced Study, Princeton, NJ (United States)

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

OSTI Identifier:: 1502460

Grant/Contract Number:: SC0009988

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: 2018; Journal Issue: 1; 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; Gauge-gravity correspondence; Classical Theories of Gravity; Black Holes in String Theory

Citation Formats


                    Dong, Xi, and Lewkowycz, Aitor. Entropy, extremality, euclidean variations, and the equations of motion.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep01(2018)081.

Copy to clipboard


                    Dong, Xi, & Lewkowycz, Aitor. Entropy, extremality, euclidean variations, and the equations of motion.  United States.  https://doi.org/10.1007/jhep01(2018)081

Copy to clipboard


                    Dong, Xi, and Lewkowycz, Aitor. Wed .  
"Entropy, extremality, euclidean variations, and the equations of motion".  United States.  https://doi.org/10.1007/jhep01(2018)081.  https://www.osti.gov/servlets/purl/1502460.

Copy to clipboard


                    
@article{osti_1502460,

  title        = {Entropy, extremality, euclidean variations, and the equations of motion},

  author       = {Dong, Xi and Lewkowycz, Aitor},

  abstractNote = {We study the Euclidean gravitational path integral computing the Rényi entropy and analyze its behavior under small variations. We argue that, in Einstein gravity, the extremality condition can be understood from the variational principle at the level of the action, without having to solve explicitly the equations of motion. This set-up is then generalized to arbitrary theories of gravity, where we show that the respective entanglement entropy functional needs to be extremized. We also extend this result to all orders in Newton’s constant GN, providing a derivation of quantum extremality. Understanding quantum extremality for mixtures of states provides a generalization of the dual of the boundary modular Hamiltonian which is given by the bulk modular Hamiltonian plus the area operator, evaluated on the so-called modular extremal surface. This gives a bulk prescription for computing the relative entropies to all orders in GN . We also comment on how these ideas can be used to derive an integrated version of the equations of motion, linearized around arbitrary states.},

  doi          = {10.1007/jhep01(2018)081},

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

  number       = 1,

  volume       = 2018,

  place        = {United States},

  year         = {Wed Jan 17 00:00:00 EST 2018},

  month        = {Wed Jan 17 00:00:00 EST 2018}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/jhep01(2018)081

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 90 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

The four laws of black hole mechanics
journal, June 1973

Bardeen, J. M.; Carter, B.; Hawking, S. W.
Communications in Mathematical Physics, Vol. 31, Issue 2
DOI: 10.1007/BF01645742

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

The gravity dual of a density matrix
journal, July 2012

Czech, Bartłomiej; Karczmarek, Joanna L.; Nogueira, Fernando
Classical and Quantum Gravity, Vol. 29, Issue 15
DOI: 10.1088/0264-9381/29/15/155009

Nonlinear gravity from entanglement in conformal field theories
journal, August 2017

Faulkner, Thomas; Haehl, Felix M.; Hijano, Eliot
Journal of High Energy Physics, Vol. 2017, Issue 8
DOI: 10.1007/JHEP08(2017)057

The gravity dual of Rényi entropy
journal, August 2016

Dong, Xi
Nature Communications, Vol. 7, Issue 1
DOI: 10.1038/ncomms12472

The gravity duals of modular Hamiltonians
journal, September 2016

Jafferis, Daniel L.; Suh, S. Josephine
Journal of High Energy Physics, Vol. 2016, Issue 9
DOI: 10.1007/JHEP09(2016)068

Relative entropy and holography
journal, August 2013

Blanco, David D.; Casini, Horacio; Hung, Ling-Yan
Journal of High Energy Physics, Vol. 2013, Issue 8
DOI: 10.1007/JHEP08(2013)060

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

The Ryu–Takayanagi Formula from Quantum Error Correction
journal, May 2017

Harlow, Daniel
Communications in Mathematical Physics, Vol. 354, Issue 3
DOI: 10.1007/s00220-017-2904-z

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

Deriving covariant holographic entanglement
journal, November 2016

Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund
Journal of High Energy Physics, Vol. 2016, Issue 11
DOI: 10.1007/JHEP11(2016)028

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

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

Causality & holographic entanglement entropy
journal, December 2014

Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion
Journal of High Energy Physics, Vol. 2014, Issue 12
DOI: 10.1007/JHEP12(2014)162

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

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

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
journal, November 2014

Wall, Aron C.
Classical and Quantum Gravity, Vol. 31, Issue 22
DOI: 10.1088/0264-9381/31/22/225007

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
journal, September 2016

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
Journal of High Energy Physics, Vol. 2016, Issue 9
DOI: 10.1007/JHEP09(2016)038

Bulk locality from modular flow
journal, July 2017

Faulkner, Thomas; Lewkowycz, Aitor
Journal of High Energy Physics, Vol. 2017, Issue 7
DOI: 10.1007/JHEP07(2017)151

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

Generalized gravitational entropy
journal, August 2013

Lewkowycz, Aitor; Maldacena, Juan
Journal of High Energy Physics, Vol. 2013, Issue 8
DOI: 10.1007/JHEP08(2013)090

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

Holographic entanglement entropy for general higher derivative gravity
journal, January 2014

Dong, Xi
Journal of High Energy Physics, Vol. 2014, Issue 1
DOI: 10.1007/JHEP01(2014)044

Black hole entropy is the Noether charge
journal, October 1993

Wald, Robert M.
Physical Review D, Vol. 48, Issue 8
DOI: 10.1103/PhysRevD.48.R3427

Particle creation by black holes
journal, August 1975

Hawking, S. W.
Communications In Mathematical Physics, Vol. 43, Issue 3
DOI: 10.1007/BF02345020

Generalized entropy and higher derivative gravity
journal, March 2014

Camps, Joan
Journal of High Energy Physics, Vol. 2014, Issue 3
DOI: 10.1007/JHEP03(2014)070

Comparison of the Noether charge and Euclidean methods for computing the entropy of stationary black holes
journal, October 1995

Iyer, Vivek; Wald, Robert M.
Physical Review D, Vol. 52, Issue 8
DOI: 10.1103/PhysRevD.52.4430

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

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

Some properties of the Noether charge and a proposal for dynamical black hole entropy
journal, July 1994

Iyer, Vivek; Wald, Robert M.
Physical Review D, Vol. 50, Issue 2
DOI: 10.1103/PhysRevD.50.846

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

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

Some results on the shape dependence of entanglement and Rényi entropies
journal, February 2015

Allais, Andrea; Mezei, Márk
Physical Review D, Vol. 91, Issue 4
DOI: 10.1103/PhysRevD.91.046002

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

Particle creation by black holes
journal, June 1976

Hawking, S. W.
Communications in Mathematical Physics, Vol. 46, Issue 2
DOI: 10.1007/bf01608497

A Covariant Holographic Entanglement Entropy Proposal
text, January 2007

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

Generalized gravitational entropy
text, January 2013

Lewkowycz, Aitor; Maldacena, Juan
arXiv
DOI: 10.48550/arxiv.1304.4926

Entanglement Temperature and Entanglement Entropy of Excited States
text, January 2013

Wong, Gabriel; Klich, Israel; Zayas, Leopoldo A. Pando
arXiv
DOI: 10.48550/arxiv.1305.3291

Quantum corrections to holographic entanglement entropy
text, January 2013

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

Holographic Entanglement Entropy for General Higher Derivative Gravity
text, January 2013

Dong, Xi
arXiv
DOI: 10.48550/arxiv.1310.5713

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

Causality & holographic entanglement entropy
text, January 2014

Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion
arXiv
DOI: 10.48550/arxiv.1408.6300

Holographic Entanglement Entropy for the Most General Higher Derivative Gravity
text, January 2014

Miao, Rong-Xin; Guo, Wu-zhong
arXiv
DOI: 10.48550/arxiv.1411.5579

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

Faulkner, Thomas
arXiv
DOI: 10.48550/arxiv.1412.5648

The Gravity Duals of Modular Hamiltonians
preprint, January 2014

Jafferis, Daniel L.; Suh, S. Josephine
arXiv
DOI: 10.48550/arxiv.1412.8465

Universal Terms of Entanglement Entropy for 6d CFTs
preprint, January 2015

Miao, Rong-Xin
arXiv
DOI: 10.48550/arxiv.1503.05538

Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
text, January 2016

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar
arXiv
DOI: 10.48550/arxiv.1605.08072

Gravity duals of boundary cones
text, January 2016

Camps, Joan
arXiv
DOI: 10.48550/arxiv.1605.08588

State-Dependent Divergences in the Entanglement Entropy
text, January 2016

Marolf, Donald; Wall, Aron C.
arXiv
DOI: 10.48550/arxiv.1607.01246

The Ryu-Takayanagi Formula from Quantum Error Correction
text, January 2016

Harlow, Daniel
arXiv
DOI: 10.48550/arxiv.1607.03901

Deriving covariant holographic entanglement
text, January 2016

Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund
arXiv
DOI: 10.48550/arxiv.1607.07506

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

Black Hole Entropy is Noether Charge
text, January 1993

Wald, Robert M.
arXiv
DOI: 10.48550/arxiv.gr-qc/9307038

Aspects of Holographic Entanglement Entropy
text, January 2006

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

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

Universality in the geometric dependence of Rényi entropy
journal, January 2015

Lewkowycz, Aitor; Perlmutter, Eric
Journal of High Energy Physics, Vol. 2015, Issue 1
DOI: 10.1007/jhep01(2015)080

Generalized gravitational entropy
text, January 2013

Lewkowycz, Aitor; Maldacena, Juan
arXiv
DOI: 10.48550/arxiv.1304.4926

Quantum corrections to holographic entanglement entropy
text, January 2013

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

Entanglement Entropy: A Perturbative Calculation
text, January 2014

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

The Endpoint of Hawking Evaporation
text, January 1992

Russo, J.; Susskind, L.; Thorlacius, L.
arXiv
DOI: 10.48550/arxiv.hep-th/9206070

Works referencing / citing this record:

Superselection sectors of gravitational subregions
journal, January 2019

Camps, Joan
Journal of High Energy Physics, Vol. 2019, Issue 1
DOI: 10.1007/jhep01(2019)182

On actions for (entangling) surfaces and DCFTs
journal, April 2018

Armas, Jay; Tarrío, Javier
Journal of High Energy Physics, Vol. 2018, Issue 4
DOI: 10.1007/jhep04(2018)100

Losing the IR: a holographic framework for area theorems
journal, January 2019

Engelhardt, Netta; Fischetti, Sebastian
Classical and Quantum Gravity, Vol. 36, Issue 3
DOI: 10.1088/1361-6382/aafa0b

Entanglement entropy and subregion complexity in thermal perturbations around pure AdS spacetime
journal, December 2019

Bhattacharya, Aranya; Grosvenor, Kevin T.; Roy, Shibaji
Physical Review D, Vol. 100, Issue 12
DOI: 10.1103/physrevd.100.126004

Complete Einstein equations from the generalized First Law of Entanglement
journal, July 2018

Oh, Eunseok; Park, I. Y.; Sin, Sang-Jin
Physical Review D, Vol. 98, Issue 2
DOI: 10.1103/physrevd.98.026020

Bulk entanglement entropy in perturbative excited states
journal, January 2018

Belin, Alexandre; Iqbal, Nabil; Lokhande, Sagar F.
SciPost Physics, Vol. 5, Issue 3
DOI: 10.21468/scipostphys.5.3.024

Local phase space and edge modes for diffeomorphism-invariant theories
text, January 2017

Speranza, Antony J.
arXiv
DOI: 10.48550/arxiv.1706.05061

Complete Einstein equation from the generalized First Law of Entanglement
text, January 2017

Oh, Eunseok; Park, I. Y.; Sin, Sang-Jin
arXiv
DOI: 10.48550/arxiv.1709.05752

Learning the Alpha-bits of Black Holes
text, January 2018

Hayden, Patrick; Penington, Geoffrey
arXiv
DOI: 10.48550/arxiv.1807.06041

Holographic Renyi Entropy from Quantum Error Correction
text, January 2018

Akers, Chris; Rath, Pratik
arXiv
DOI: 10.48550/arxiv.1811.05171

Flat entanglement spectra in fixed-area states of quantum gravity
text, January 2018

Dong, Xi; Harlow, Daniel; Marolf, Donald
arXiv
DOI: 10.48550/arxiv.1811.05382

Entanglement Wedge Reconstruction using the Petz Map
text, January 2019

Chen, Chi-Fang; Penington, Geoffrey; Salton, Grant
arXiv
DOI: 10.48550/arxiv.1902.02844

Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole
text, January 2019

Chen, Yiming; Zhang, Pengfei
arXiv
DOI: 10.48550/arxiv.1903.10532

Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
text, January 2019

Bhattacharya, Aranya; Grosvenor, Kevin T.; Roy, Shibaji
arXiv
DOI: 10.48550/arxiv.1905.02220

Escaping the interiors of pure boundary-state black holes
journal, February 2023

Almheiri, Ahmed; Mousatov, Alexandros; Shyani, Milind
Journal of High Energy Physics, Vol. 2023, Issue 2
DOI: 10.1007/jhep02(2023)024

Petz reconstruction in random tensor networks
journal, October 2020

Jia, Hewei Frederic; Rangamani, Mukund
Journal of High Energy Physics, Vol. 2020, Issue 10
DOI: 10.1007/jhep10(2020)050

Microstate distinguishability, quantum complexity, and the eigenstate thermalization hypothesis
journal, July 2021

Bao, Ning; Pollack, Jason; Wakeham, David
Classical and Quantum Gravity, Vol. 38, Issue 15
DOI: 10.1088/1361-6382/ac0e17

Searching for butterflies in dS JT gravity
preprint, January 2020

Blommaert, Andreas
arXiv
DOI: 10.48550/arxiv.2010.14539

Similar Records in DOE PAGES and OSTI.GOV collections:

The gravity dual of Rényi entropy

Journal Article Dong, Xi - Nature Communications

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Re´nyi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometricmore »« less
Cited by 187
https://doi.org/10.1038/ncomms12472

Full Text Available
The Markov gap for geometric reflected entropy

Journal Article Hayden, Patrick ; Parrikar, Onkar ; Sorce, Jonathan - Journal of High Energy Physics (Online)

The reflected entropy S_R(A : B) of a density matrix ρ_AB is a bipartite correlation measure lower-bounded by the quantum mutual information I(A : B). In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-N² gap between S_R and I. We provide an information-theoretic interpretation of this gap by observing that S_R - I is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason,more »« less
https://doi.org/10.1007/jhep10(2021)047

Full Text Available
The Euclidean gravitational action as black hole entropy, singularities, and spacetime voids

Journal Article Castro, Carlos - Journal of Mathematical Physics

We argue why the static spherically symmetric vacuum solutions of Einstein's equations described by the textbook Hilbert metric g{sub {mu}}{sub {nu}}(r) is not diffeomorphic to the metric g{sub {mu}}{sub {nu}}(|r|) corresponding to the gravitational field of a point mass delta function source at r=0. By choosing a judicious radial function R(r)=r+2G|M|{theta}(r) involving the Heaviside step function, one has the correct boundary condition R(r=0)=0, while displacing the horizon from r=2G|M| to a location arbitrarily close to r=0 as one desires, r{sub h}{yields}0, where stringy geometry and quantum gravitational effects begin to take place. We solve the field equations due to amore »« less
https://doi.org/10.1063/1.2898115
Chiral gravity, log gravity, and extremal CFT

Journal Article Maloney, Alexander ; Wei, Song ; Center for the Fundamental Laws of Nature Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138 ; ... - Physical Review. D, Particles Fields

We show that the linearization of all exact solutions of classical chiral gravity around the AdS{sub 3} vacuum have positive energy. Nonchiral and negative-energy solutions of the linearized equations are infrared divergent at second order, and so are removed from the spectrum. In other words, chirality is confined and the equations of motion have linearization instabilities. We prove that the only stationary, axially symmetric solutions of chiral gravity are BTZ black holes, which have positive energy. It is further shown that classical log gravity--the theory with logarithmically relaxed boundary conditions--has finite asymptotic symmetry generators but is not chiral and hencemore »« less
https://doi.org/10.1103/PHYSREVD.81.064007
Euclidean and Noetherian entropies in AdS space

Journal Article Dutta, Suvankar ; Gopakumar, Rajesh - Physical Review. D, Particles Fields

We examine the Euclidean action approach, as well as that of Wald, to the entropy of black holes in asymptotically AdS spaces. From the point of view of holography these two approaches are somewhat complementary in spirit and it is not obvious why they should give the same answer in the presence of arbitrary higher derivative gravity corrections. For the case of the AdS{sub 5} Schwarzschild black hole, we explicitly study the leading correction to the Bekenstein-Hawking entropy in the presence of a variety of higher derivative corrections studied in the literature, including the Type IIB R{sup 4} term. Wemore »« less
https://doi.org/10.1103/PHYSREVD.74.044007

Similar Records

Title: Entropy, extremality, euclidean variations, and the equations of motion

Abstract

Citation Formats

The four laws of black hole mechanics journal, June 1973

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

The gravity dual of a density matrix journal, July 2012

Nonlinear gravity from entanglement in conformal field theories journal, August 2017

The gravity dual of Rényi entropy journal, August 2016

The gravity duals of modular Hamiltonians journal, September 2016

Relative entropy and holography journal, August 2013

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

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

The Ryu–Takayanagi Formula from Quantum Error Correction journal, May 2017

Entanglement Entropy of Electromagnetic Edge Modes journal, March 2015

Deriving covariant holographic entanglement journal, November 2016

Holographic entanglement entropy and gravitational anomalies journal, July 2014

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

Causality & holographic entanglement entropy journal, December 2014

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

Anti de Sitter space and holography journal, January 1998

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy journal, November 2014

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition journal, September 2016

Bulk locality from modular flow journal, July 2017

A covariant holographic entanglement entropy proposal journal, July 2007

Generalized gravitational entropy journal, August 2013

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

Holographic entanglement entropy for general higher derivative gravity journal, January 2014

Black hole entropy is the Noether charge journal, October 1993

Particle creation by black holes journal, August 1975

Generalized entropy and higher derivative gravity journal, March 2014

Comparison of the Noether charge and Euclidean methods for computing the entropy of stationary black holes journal, October 1995

Aspects of holographic entanglement entropy journal, August 2006

Quantum corrections to holographic entanglement entropy journal, November 2013

Some properties of the Noether charge and a proposal for dynamical black hole entropy journal, July 1994

Relative entropy equals bulk relative entropy journal, June 2016

Gravitation from entanglement in holographic CFTs journal, March 2014

Some results on the shape dependence of entanglement and Rényi entropies journal, February 2015

Entanglement entropy: a perturbative calculation journal, December 2014

Particle creation by black holes journal, June 1976

A Covariant Holographic Entanglement Entropy Proposal text, January 2007

Generalized gravitational entropy text, January 2013

Entanglement Temperature and Entanglement Entropy of Excited States text, January 2013

Quantum corrections to holographic entanglement entropy text, January 2013

Holographic Entanglement Entropy for General Higher Derivative Gravity text, January 2013

Entanglement Entropy: A Perturbative Calculation text, January 2014

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

Causality & holographic entanglement entropy text, January 2014

Holographic Entanglement Entropy for the Most General Higher Derivative Gravity text, January 2014

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

The Gravity Duals of Modular Hamiltonians preprint, January 2014

Universal Terms of Entanglement Entropy for 6d CFTs preprint, January 2015

Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition text, January 2016

Gravity duals of boundary cones text, January 2016

State-Dependent Divergences in the Entanglement Entropy text, January 2016

The Ryu-Takayanagi Formula from Quantum Error Correction text, January 2016

Deriving covariant holographic entanglement text, January 2016

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

Black Hole Entropy is Noether Charge text, January 1993

Aspects of Holographic Entanglement Entropy text, January 2006

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

Anti De Sitter Space And Holography text, January 1998

Universality in the geometric dependence of Rényi entropy journal, January 2015

Generalized gravitational entropy text, January 2013

Quantum corrections to holographic entanglement entropy text, January 2013

Entanglement Entropy: A Perturbative Calculation text, January 2014

The Endpoint of Hawking Evaporation text, January 1992

Superselection sectors of gravitational subregions journal, January 2019

On actions for (entangling) surfaces and DCFTs journal, April 2018

Losing the IR: a holographic framework for area theorems journal, January 2019

Entanglement entropy and subregion complexity in thermal perturbations around pure AdS spacetime journal, December 2019

Complete Einstein equations from the generalized First Law of Entanglement journal, July 2018

Bulk entanglement entropy in perturbative excited states journal, January 2018

Local phase space and edge modes for diffeomorphism-invariant theories text, January 2017

Complete Einstein equation from the generalized First Law of Entanglement text, January 2017

Learning the Alpha-bits of Black Holes text, January 2018

Holographic Renyi Entropy from Quantum Error Correction text, January 2018

Flat entanglement spectra in fixed-area states of quantum gravity text, January 2018

Entanglement Wedge Reconstruction using the Petz Map text, January 2019

Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole text, January 2019

The four laws of black hole mechanics
journal, June 1973

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

The gravity dual of a density matrix
journal, July 2012

Nonlinear gravity from entanglement in conformal field theories
journal, August 2017

The gravity dual of Rényi entropy
journal, August 2016

The gravity duals of modular Hamiltonians
journal, September 2016

Relative entropy and holography
journal, August 2013

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

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

The Ryu–Takayanagi Formula from Quantum Error Correction
journal, May 2017

Entanglement Entropy of Electromagnetic Edge Modes
journal, March 2015

Deriving covariant holographic entanglement
journal, November 2016

Holographic entanglement entropy and gravitational anomalies
journal, July 2014

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

Causality & holographic entanglement entropy
journal, December 2014

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

Anti de Sitter space and holography
journal, January 1998

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
journal, November 2014

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
journal, September 2016

Bulk locality from modular flow
journal, July 2017

A covariant holographic entanglement entropy proposal
journal, July 2007

Generalized gravitational entropy
journal, August 2013

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

Holographic entanglement entropy for general higher derivative gravity
journal, January 2014

Black hole entropy is the Noether charge
journal, October 1993

Particle creation by black holes
journal, August 1975

Generalized entropy and higher derivative gravity
journal, March 2014

Comparison of the Noether charge and Euclidean methods for computing the entropy of stationary black holes
journal, October 1995

Aspects of holographic entanglement entropy
journal, August 2006

Quantum corrections to holographic entanglement entropy
journal, November 2013

Some properties of the Noether charge and a proposal for dynamical black hole entropy
journal, July 1994

Relative entropy equals bulk relative entropy
journal, June 2016

Gravitation from entanglement in holographic CFTs
journal, March 2014

Some results on the shape dependence of entanglement and Rényi entropies
journal, February 2015

Entanglement entropy: a perturbative calculation
journal, December 2014

Particle creation by black holes
journal, June 1976

A Covariant Holographic Entanglement Entropy Proposal
text, January 2007

Generalized gravitational entropy
text, January 2013

Entanglement Temperature and Entanglement Entropy of Excited States
text, January 2013

Quantum corrections to holographic entanglement entropy
text, January 2013

Holographic Entanglement Entropy for General Higher Derivative Gravity
text, January 2013

Entanglement Entropy: A Perturbative Calculation
text, January 2014

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

Causality & holographic entanglement entropy
text, January 2014

Holographic Entanglement Entropy for the Most General Higher Derivative Gravity
text, January 2014

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

The Gravity Duals of Modular Hamiltonians
preprint, January 2014

Universal Terms of Entanglement Entropy for 6d CFTs
preprint, January 2015

Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
text, January 2016

Gravity duals of boundary cones
text, January 2016

State-Dependent Divergences in the Entanglement Entropy
text, January 2016

The Ryu-Takayanagi Formula from Quantum Error Correction
text, January 2016

Deriving covariant holographic entanglement
text, January 2016

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

Black Hole Entropy is Noether Charge
text, January 1993

Aspects of Holographic Entanglement Entropy
text, January 2006

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

Anti De Sitter Space And Holography
text, January 1998

Universality in the geometric dependence of Rényi entropy
journal, January 2015

Generalized gravitational entropy
text, January 2013

Quantum corrections to holographic entanglement entropy
text, January 2013

Entanglement Entropy: A Perturbative Calculation
text, January 2014

The Endpoint of Hawking Evaporation
text, January 1992

Superselection sectors of gravitational subregions
journal, January 2019

On actions for (entangling) surfaces and DCFTs
journal, April 2018

Losing the IR: a holographic framework for area theorems
journal, January 2019

Entanglement entropy and subregion complexity in thermal perturbations around pure AdS spacetime
journal, December 2019

Complete Einstein equations from the generalized First Law of Entanglement
journal, July 2018

Bulk entanglement entropy in perturbative excited states
journal, January 2018

Local phase space and edge modes for diffeomorphism-invariant theories
text, January 2017

Complete Einstein equation from the generalized First Law of Entanglement
text, January 2017

Learning the Alpha-bits of Black Holes
text, January 2018

Holographic Renyi Entropy from Quantum Error Correction
text, January 2018

Flat entanglement spectra in fixed-area states of quantum gravity
text, January 2018

Entanglement Wedge Reconstruction using the Petz Map
text, January 2019

Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole
text, January 2019

Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
text, January 2019

Escaping the interiors of pure boundary-state black holes
journal, February 2023

Petz reconstruction in random tensor networks
journal, October 2020