Built on

De Boer, Jan and Van Breukelen, Rik and Lokhande, Sagar F. and Papadodimas, Kyriakos and Verlinde, Erik, “Probing typical black hole microstates,” JHEP
Original
1901
Earlier work this paper cites.
Romero-Bermúdez, Aurelio and Schalm, Koenraad and Scopelliti, Vincenzo, “Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?,” JHEP
Original
1903
Earlier work this paper cites.
Bernamonti, Alice and Galli, Federico and Hernandez, Juan and Myers, Robert C. and Ruan, Shan-Ming and Simón, Joan, “First Law of Holographic Complexity,” Phys. Rev. Lett
Original
1903
Earlier work this paper cites.
Czech, Bartlomiej and De Boer, Jan and Ge, Dongsheng and Lamprou, Lampros, “A modular sewing kit for entanglement wedges,” JHEP
Original
1903
Earlier work this paper cites.
Lin, Henry W. and Maldacena, Juan and Zhao, Ying, “Symmetries Near the Horizon,” JHEP
Original
1904
Earlier work this paper cites.
Barbón, J. L. F. and Rabinovici, E. and Shir, R. and Sinha, R., “On The Evolution Of Operator Complexity Beyond Scrambling,” JHEP
Original
1907
Earlier work this paper cites.
Bueno, Pablo and Magan, Javier M. and Shahbazi, C. S., “Complexity measures in QFT and constrained geometric actions,” arXiv:1908.03577 [hep-th]
Original
1908
Earlier work this paper cites.
Lucas, Andrew, “Non-perturbative dynamics of the operator size distribution in the Sachdev-Ye-Kitaev model,” arXiv:1910.09539 [hep-th]
Original
1910
Earlier work this paper cites.
Berenstein, David and Simón, Joan, “Localized states in global AdS,” arXiv:1910.10227 [hep-th]
Original
1910
Earlier work this paper cites.
Streicher, Alexandre, “SYK Correlators for All Energies,” arXiv:1911.10171 [hep-th]
Original
1911
Earlier work this paper cites.
Mousatov, Alexandros, “Operator Size for Holographic Field Theories,” arXiv:1911.05089 [hep-th]
Original
1911
Earlier work this paper cites.
Barbón, José L. F. and Martín-García, Javier and Sasieta, Martin, “Momentum/Complexity Duality and the Black Hole Interior,” arXiv:1912.05996 [hep-th]
Original
1912
Earlier work this paper cites.
de Boer, Jan and Lamprou, Lampros, “Holographic Order from Modular Chaos,” arXiv:1912.02810 [hep-th]
Original
1912
Earlier work this paper cites.
I. Gelfand and M. Neumark, “On the imbedding of normed rings into the ring of operators in hilbert space,” Rec. Math. [Mat. Sbornik] N.S
1943
Earlier work this paper cites.
Segal, I. E., “Irreducible representations of operator algebras,” Bull. Amer. Math. Soc
1947
Earlier work this paper cites.
Larkin, A. I. and Ovchinnikov, Y. N., “Quasiclassical Method in the Theory of Superconductivity,” Soviet Journal of Experimental and Theoretical Physics
1969
Earlier work this paper cites.
’t Hooft, Gerard, “A Planar Diagram Theory for Strong Interactions,” Nucl. Phys
1973
Earlier work this paper cites.
Unruh, W. G., “Notes on black hole evaporation,” Phys. Rev
1976
Earlier work this paper cites.

Similar

Sachdev, Subir and Ye, Jinwu, “Gapless spin fluid ground state in a random, quantum Heisenberg magnet,” Phys. Rev. Lett
1993
Cited alongside, same era.
Srednicki, Mark, “Chaos and quantum thermalization,” Phys. Rev. E
1994
Cited alongside, same era.
Maldacena, Juan Martin, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys
1998
Cited alongside, same era.
Gubser, S. S. and Klebanov, Igor R. and Polyakov, Alexander M., “Gauge theory correlators from noncritical string theory,” Phys. Lett
1998
Cited alongside, same era.
Witten, Edward, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys
1998
Cited alongside, same era.
Witten, Edward, “Anti-de Sitter space, thermal phase transition, and confinement in gauge theories,” Adv. Theor. Math. Phys

Then

Nozaki, Masahiro and Numasawa, Tokiro and Takayanagi, Tadashi, “Holographic Local Quenches and Entanglement Density,” JHEP
Original
2013
Later among the works it cites.
Papadodimas, Kyriakos and Raju, Suvrat, “Black Hole Interior in the Holographic Correspondence and the Information Paradox,” Phys. Rev. Lett
Original
2014
Later among the works it cites.
Papadodimas, Kyriakos and Raju, Suvrat, “State-Dependent Bulk-Boundary Maps and Black Hole Complementarity,” Phys. Rev
Original
2014
Later among the works it cites.
A. Kitaev, “A simple model of quantum holography,” Talks at KITP, April 7, 2015 and May 27, 2015
2015
Later among the works it cites.
Shenker, Stephen H. and Stanford, Douglas, “Stringy effects in scrambling,” JHEP
Original

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2020

On operator growth and emergent Poincar\'e symmetries

Magan, Javier M., Simon, Joan

Understand

We consider operator growth for generic large-N gauge theories at finite temperature.

Our analysis is performed in terms of Fourier modes, which do not mix with other operators as time evolves, and whose correlation functions are determined by their two-point functions alone, at leading order in the large-N limit.
The algebra of these modes allows for a simple analysis of the operators with whom the initial operator mixes over time, and guarantees the existence of boundary CFT operators closing the bulk Poincar\'e algebra, describing the experience of infalling observers.
We discuss several existing approaches to operator growth, such as number operators, proper energies, the many-body recursion method, quantum circuit complexity, and comment on its relation to classical chaos in black hole dynamics.

Built on

De Boer, Jan and Van Breukelen, Rik and Lokhande, Sagar F. and Papadodimas, Kyriakos and Verlinde, Erik, “Probing typical black hole microstates,” JHEP
Original
1901
Earlier work this paper cites.
Romero-Bermúdez, Aurelio and Schalm, Koenraad and Scopelliti, Vincenzo, “Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?,” JHEP
Original
1903
Earlier work this paper cites.
Bernamonti, Alice and Galli, Federico and Hernandez, Juan and Myers, Robert C. and Ruan, Shan-Ming and Simón, Joan, “First Law of Holographic Complexity,” Phys. Rev. Lett
Original
1903
Earlier work this paper cites.
Czech, Bartlomiej and De Boer, Jan and Ge, Dongsheng and Lamprou, Lampros, “A modular sewing kit for entanglement wedges,” JHEP
Original
1903
Earlier work this paper cites.
Lin, Henry W. and Maldacena, Juan and Zhao, Ying, “Symmetries Near the Horizon,” JHEP
Original
1904
Earlier work this paper cites.
Barbón, J. L. F. and Rabinovici, E. and Shir, R. and Sinha, R., “On The Evolution Of Operator Complexity Beyond Scrambling,” JHEP
Original
1907
Earlier work this paper cites.
Bueno, Pablo and Magan, Javier M. and Shahbazi, C. S., “Complexity measures in QFT and constrained geometric actions,” arXiv:1908.03577 [hep-th]
Original
1908
Earlier work this paper cites.
Lucas, Andrew, “Non-perturbative dynamics of the operator size distribution in the Sachdev-Ye-Kitaev model,” arXiv:1910.09539 [hep-th]
Original
1910
Earlier work this paper cites.
Berenstein, David and Simón, Joan, “Localized states in global AdS,” arXiv:1910.10227 [hep-th]
Original
1910
Earlier work this paper cites.
Streicher, Alexandre, “SYK Correlators for All Energies,” arXiv:1911.10171 [hep-th]
Original
1911
Earlier work this paper cites.
Mousatov, Alexandros, “Operator Size for Holographic Field Theories,” arXiv:1911.05089 [hep-th]
Original
1911
Earlier work this paper cites.
Barbón, José L. F. and Martín-García, Javier and Sasieta, Martin, “Momentum/Complexity Duality and the Black Hole Interior,” arXiv:1912.05996 [hep-th]
Original
1912
Earlier work this paper cites.
de Boer, Jan and Lamprou, Lampros, “Holographic Order from Modular Chaos,” arXiv:1912.02810 [hep-th]
Original
1912
Earlier work this paper cites.
I. Gelfand and M. Neumark, “On the imbedding of normed rings into the ring of operators in hilbert space,” Rec. Math. [Mat. Sbornik] N.S
1943
Earlier work this paper cites.
Segal, I. E., “Irreducible representations of operator algebras,” Bull. Amer. Math. Soc
1947
Earlier work this paper cites.
Larkin, A. I. and Ovchinnikov, Y. N., “Quasiclassical Method in the Theory of Superconductivity,” Soviet Journal of Experimental and Theoretical Physics
1969
Earlier work this paper cites.
’t Hooft, Gerard, “A Planar Diagram Theory for Strong Interactions,” Nucl. Phys
1973
Earlier work this paper cites.
Unruh, W. G., “Notes on black hole evaporation,” Phys. Rev
1976
Earlier work this paper cites.

Similar

Sachdev, Subir and Ye, Jinwu, “Gapless spin fluid ground state in a random, quantum Heisenberg magnet,” Phys. Rev. Lett
1993
Cited alongside, same era.
Srednicki, Mark, “Chaos and quantum thermalization,” Phys. Rev. E
1994
Cited alongside, same era.
Maldacena, Juan Martin, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys
1998
Cited alongside, same era.
Gubser, S. S. and Klebanov, Igor R. and Polyakov, Alexander M., “Gauge theory correlators from noncritical string theory,” Phys. Lett
1998
Cited alongside, same era.
Witten, Edward, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys
1998
Cited alongside, same era.
Witten, Edward, “Anti-de Sitter space, thermal phase transition, and confinement in gauge theories,” Adv. Theor. Math. Phys