- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Lindblad dynamics in holography

Takanori Ishii1,*,† and Daichi Takeda2,†,‡

  • 1Theoretical Particle Physics Group Department of Physics, Kyoto University, Kitashirakawa, Kyoto 606-8502, Japan
  • 2iTHEMS, RIKEN, Wako, Saitama 351-0198, Japan

  • *Contact author: ishiit@gauge.scphys.kyoto-u.ac.jp
  • †These authors contributed equally to this work.
  • ‡Contact author: daichi.takeda@riken.jp
PDF

Phys. Rev. D 112, 046020 – Published 26 August, 2025

DOI: https://doi.org/10.1103/l2rx-t9dd

Abstract

We develop, in the AdS/CFT correspondence, a method to compute correlation functions when the conformal field theory (CFT) is governed by the Lindblad equation for open quantum systems, via the anti–de Sitter (AdS) theory. Using a simple example in AdS3/CFT2, we demonstrate that the predictions of the AdS theory based on our method match the direct computations in the dual CFT. We also briefly discuss the relaxation problem and the holographic entropy in this example.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (43)

  1. Juan Martin Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998).
  2. S. S. Gubser, Igor R. Klebanov, and Alexander M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428, 105 (1998).
  3. Edward Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
  4. Dam T. Son and Andrei O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, J. High Energy Phys. 09 (2002) 042.
  5. C. P. Herzog and D. T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, J. High Energy Phys. 03 (2003) 046.
  6. Kostas Skenderis and Balt C. van Rees, Real-time gauge/gravity duality, Phys. Rev. Lett. 101, 081601 (2008).
  7. Kostas Skenderis and Balt C. van Rees, Real-time gauge/gravity duality: Prescription, renormalization and examples, J. High Energy Phys. 05 (2009) 085.
  8. Balt C. van Rees, Real-time gauge/gravity duality and ingoing boundary conditions, Nucl. Phys. B, Proc. Suppl. 192–193, 193 (2009).
  9. Paolo Glorioso, Michael Crossley, and Hong Liu, A prescription for holographic Schwinger-Keldysh contour in non-equilibrium systems, arXiv:1812.08785.
  10. Dam T. Son and Derek Teaney, Thermal noise and stochastic strings in AdS/CFT, J. High Energy Phys. 07 (2009) 021.
  11. Jan de Boer, Veronika E. Hubeny, Mukund Rangamani, and Masaki Shigemori, Brownian motion in AdS/CFT, J. High Energy Phys. 07 (2009) 094.
  12. Chandan Jana, R. Loganayagam, and Mukund Rangamani, Open quantum systems and Schwinger-Keldysh holograms, J. High Energy Phys. 07 (2020) 242.
  13. Ofer Aharony, Adam B. Clark, and Andreas Karch, The CFT/AdS correspondence, massive gravitons and a connectivity index conjecture, Phys. Rev. D 74, 086006 (2006).
  14. Andreas Karch, Mianqi Wang, and Merna Youssef, AdS Higgs mechanism from double trace deformed CFT, J. High Energy Phys. 02 (2024) 044.
  15. Hao Geng, Open AdS/CFT via a double-trace deformation, J. High Energy Phys. 09 (2024) 012.
  16. Vittorio Gorini, Andrzej Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N level systems, J. Math. Phys. (N.Y.) 17, 821 (1976).
  17. Goran Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  18. Sean A. Hartnoll, Lectures on holographic methods for condensed matter physics, Classical Quantum Gravity 26, 224002 (2009).
  19. Christopher P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42, 343001 (2009).
  20. John McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010, 723105 (2010).
  21. Gary T. Horowitz, Introduction to holographic superconductors, Lect. Notes Phys. 828, 313 (2011).
  22. Subir Sachdev, Condensed matter and AdS/CFT, Lect. Notes Phys. 828, 273 (2011).
  23. Jorge V. Rocha, Evaporation of large black holes in AdS: Coupling to the evaporon, J. High Energy Phys. 08 (2008) 075.
  24. Ahmed Almheiri, Netta Engelhardt, Donald Marolf, and Henry Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, J. High Energy Phys. 12 (2019) 063.
  25. Geoffrey Penington, Entanglement wedge reconstruction and the information paradox, J. High Energy Phys. 09 (2020) 002.
  26. Ahmed Almheiri, Thomas Hartman, Juan Maldacena, Edgar Shaghoulian, and Amirhossein Tajdini, Replica wormholes and the entropy of Hawking radiation, J. High Energy Phys. 05 (2020) 013.
  27. Jonas Glatthard, Thermodynamics of the Page curve in Markovian open quantum systems, arXiv:2501.09082.
  28. N Lo Gullo, I Sinayskiy, Th Busch, and F Petruccione, Non-Markovianity criteria for open system dynamics, arXiv:1401.1126.
  29. Walter T Strunz, Path integral, semiclassical and stochastic propagators for markovian open quantum systems, J. Phys. A 30, 4053 (1997).
  30. Xiangyi Meng, Double-trace deformation in open quantum field theory, Phys. Rev. D 104, 016016 (2021).
  31. Ofer Aharony, Micha Berkooz, and Eva Silverstein, Multiple trace operators and nonlocal string theories, J. High Energy Phys. 08 (2001) 006.
  32. Edward Witten, Multitrace operators, boundary conditions, and AdS/CFT correspondence, arXiv:hep-th/0112258.
  33. Micha Berkooz, Amit Sever, and Assaf Shomer, ‘Double trace’ deformations, boundary conditions and space-time singularities, J. High Energy Phys. 05 (2002) 034.
  34. Amit Sever and Assaf Shomer, A note on multitrace deformations and AdS/CFT, J. High Energy Phys. 07 (2002) 027.
  35. Ofer Aharony, Micha Berkooz, and Boaz Katz, Non-local effects of multi-trace deformations in the AdS/CFT correspondence, J. High Energy Phys. 10 (2005) 097.
  36. Aurelia Chenu, Mathieu Beau, Jianshu Cao, and Adolfo del Campo, Quantum simulation of generic many-body open system dynamics using classical noise, Phys. Rev. Lett. 118, 140403 (2017).
  37. Sebastian de Haro, Sergey N. Solodukhin, and Kostas Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217, 595 (2001).
  38. Sean A. Hartnoll, Christopher P. Herzog, and Gary T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101, 031601 (2008).
  39. Sean A. Hartnoll, Christopher P. Herzog, and Gary T. Horowitz, Holographic superconductors, J. High Energy Phys. 12 (2008) 015.
  40. Don N. Page, Information in black hole radiation, Phys. Rev. Lett. 71, 3743 (1993).
  41. Daichi Takeda, Coarse-graining black holes out of equilibrium with boundary observables on time slice, J. High Energy Phys. 05 (2024) 319; 10 (2024) 154(E).
  42. Tomohiro Shigemura, Keito Shimizu, Sotaro Sugishita, Daichi Takeda, and Takuya Yoda, Heat and work in black hole thermodynamics via holography, J. High Energy Phys. 05 (2025) 069.
  43. Ronnie Kosloff, Quantum thermodynamics: A dynamical viewpoint, Entropy 15, 2100 (2013).

Outline

Information

Phys. Rev. D 112, 046020– Published 26 August, 2025
  • Received 30 April 2025
  • Accepted 1 August 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation