- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

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
  • Access by Xinjiang University

Holographic Krylov complexity in N=4 SYM theory

Ali Fatemiabhari1,*, Horatiu Nastase2,†, and Dibakar Roychowdhury3,‡

  • *Contact author: alifatemiabhari@gmail.com
  • †Contact author: horatiu.nastase@unesp.br
  • ‡Contact author: dibakar.roychowdhury@ph.iitr.ac.in
PDF

Phys. Rev. D 113, 106033 – Published 28 May, 2026

DOI: https://doi.org/10.1103/6999-p31b

Abstract

We propose and calculate a holographic Krylov complexity in N=4 SYM theory via the proper momentum for motion in AdS5 sliced by AdS3. The motion in an AdS3 subgroup corresponds to the Krylov complexity of the Sl(2) subsector. The general motion corresponds to the Krylov complexity of the N=4 SYM.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (30)

  1. M. A. Nielsen, A geometric approach to quantum circuit lower bounds, Quantum Inf. Comput. 6, 213 (2006).
  2. D. Stanford and L. Susskind, Complexity and shock wave geometries, Phys. Rev. D 90, 126007 (2014).
  3. A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle, and Y. Zhao, Holographic complexity equals bulk action?, Phys. Rev. Lett. 116, 191301 (2016).
  4. A. Belin, R. C. Myers, S.-M. Ruan, G. Sárosi, and A. J. Speranza, Does complexity equal anything?, Phys. Rev. Lett. 128, 081602 (2022).
  5. R. Jefferson and R. C. Myers, Circuit complexity in quantum field theory, J. High Energy Phys. 10 (2017) 107.
  6. D. E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi, and E. Altman, A universal operator growth hypothesis, Phys. Rev. X 9, 041017 (2019).
  7. P. Nandy, A. S. Matsoukas-Roubeas, P. Martínez-Azcona, A. Dymarsky, and A. del Campo, Quantum dynamics in Krylov space: Methods and applications, Phys. Rep. 1125, 1 (2025).
  8. E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, Krylov complexity, arXiv:2507.06286.
  9. S. Baiguera, V. Balasubramanian, P. Caputa, S. Chapman, J. Haferkamp, M. P. Heller, and N. Y. Halpern, Quantum complexity in gravity, quantum field theory, and quantum information science, Phys. Rep. 1159, 1 (2026).
  10. V. Balasubramanian, P. Caputa, J. M. Magan, and Q. Wu, Quantum chaos and the complexity of spread of states, Phys. Rev. D 106, 046007 (2022).
  11. E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, A bulk manifestation of Krylov complexity, J. High Energy Phys. 08 (2023) 213.
  12. M. Ambrosini, E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, Operator K-complexity in DSSYK: Krylov complexity equals bulk length, J. High Energy Phys. 08 (2025) 059.
  13. P. Caputa, B. Chen, R. W. McDonald, J. Simón, and B. Strittmatter, Spread complexity rate as proper momentum, Phys. Rev. D 113, L041901 (2026).
  14. J. L. F. Barbon, J. Martin-Garcia, and M. Sasieta, A generalized momentum/complexity correspondence, J. High Energy Phys. 04 (2021) 250.
  15. R. N. Das, S. Demulder, J. Erdmenger, and C. Northe, Spread complexity for the planar limit of holography, J. High Energy Phys. 06 (2025) 166.
  16. A. Anabalon and S. F. Ross, Supersymmetric solitons and a degeneracy of solutions in AdS/CFT, J. High Energy Phys. 07 (2021) 015.
  17. A. Anabalón, H. Nastase, and M. Oyarzo, Supersymmetric AdS solitons and the interconnection of different vacua of N=4 Super Yang-Mills, J. High Energy Phys. 05 (2024) 217.
  18. G. T. Horowitz and R. C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D 59, 026005 (1998).
  19. Y. Lozano, N. T. Macpherson, C. Nunez, and A. Ramirez, AdS3 solutions in massive IIA with small N=(4,0) supersymmetry, J. High Energy Phys. 01 (2020) 129.
  20. Y. Lozano, N. T. Macpherson, C. Nunez, and A. Ramirez, 1/4 BPS solutions and the AdS3/CFT2 correspondence, Phys. Rev. D 101, 026014 (2020).
  21. Y. Lozano, N. T. Macpherson, C. Nunez, and A. Ramirez, Two dimensional N=(0,4) quivers dual to AdS3 solutions in massive IIA, J. High Energy Phys. 01 (2020) 140.
  22. Y. Lozano, N. T. Macpherson, C. Nunez, and A. Ramirez, AdS3 solutions in massive IIA, defect CFTs and T-duality, J. High Energy Phys. 12 (2019) 013.
  23. Y. Lozano, C. Nunez, A. Ramirez, and S. Speziali, M-strings and AdS3 solutions to M-theory with small N=(0,4) supersymmetry, J. High Energy Phys. 08 (2020) 118.
  24. Y. Lozano, C. Nunez, A. Ramirez, and S. Speziali, New AdS2 backgrounds and N=4 conformal quantum mechanics, J. High Energy Phys. 03 (2021) 277.
  25. Y. Lozano, C. Nunez, A. Ramirez, and S. Speziali, AdS2 duals to ADHM quivers with Wilson lines, J. High Energy Phys. 03 (2021) 145.
  26. Y. Lozano, C. Nunez, and A. Ramirez, AdS2×S2×CY2 solutions in type IIB with 8 supersymmetries, J. High Energy Phys. 04 (2021) 110.
  27. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, A semiclassical limit of the gauge/string correspondence, Nucl. Phys. B636, 99 (2002).
  28. V. A. Kazakov and K. Zarembo, Classical/quantum integrability in non-compact sector of AdS/CFT, J. High Energy Phys. 10 (2004) 060.
  29. N. Beisert, The complete one loop dilatation operator of N=4 superYang-Mills theory, Nucl. Phys. B676, 3 (2004).
  30. D. E. Berenstein, J. M. Maldacena, and H. S. Nastase, Strings in flat space and pp waves from N=4 superYang-Mills, J. High Energy Phys. 04 (2002) 013.

Outline

Information

Phys. Rev. D 113, 106033– Published 28 May, 2026
  • Received 6 February 2026
  • Accepted 17 April 2026
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