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  • Open Access

From confinement to chaos in AdS/CFT via nonequilibrium local states

Dmitry S. Ageev* and Vladimir A. Bykov†

  • *Contact author: ageev@mi-ras.ru
  • †Contact author: bykov.va20@physics.msu.ru
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Phys. Rev. D 113, 046014 – Published 18 February, 2026

DOI: https://doi.org/10.1103/x8r7-sbrt

Abstract

In this paper, we study excited states in anti–de Sitter (AdS) space prepared by local operator insertions of a massive scalar field, corresponding to local operator quenches in a free bulk scalar theory. Using the AdS/CFT correspondence, we compute the time evolution of boundary observables in the dual conformal field theory states. We then introduce a hard wall in AdS Poincare coordinates to impose an infrared cutoff (“hard wall”), thereby creating a confining deformation of the dual conformal field theory, and analyze the dynamics of excited states in this confining background. By comparing the evolution of boundary two-point correlation functions in the deformed theory with the statistics of Gaussian random matrix ensembles, we show that for sufficiently heavy operators, the spacing-ratio statistics of peaks in the temporal dynamics are closest to those of the Gaussian symplectic ensemble. Finally, we extend the analysis to the compact Bañados-Teitelboim-Zanelli black hole and to its hard-wall deformation, where we find qualitatively similar trends.

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References (65)

  1. J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998).
  2. E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
  3. S. A. Hartnoll, A. Lucas, and S. Sachdev, Holographic Quantum Matter (MIT Press, Cambridge, MA, 2018), ISBN [Amazon][WorldCat].
  4. J. Zaanen, Y. W. Sun, Y. Liu, and K. Schalm, Holographic Duality in Condensed Matter Physics (Cambridge University Press, Cambridge, England, 2015), ISBN [Amazon][WorldCat].
  5. Y. Sekino and L. Susskind, Fast scramblers, J. High Energy Phys. 10 (2008) 065.
  6. S. H. Shenker and D. Stanford, Black holes and the butterfly effect, J. High Energy Phys. 03 (2014) 067.
  7. D. S. Ageev, A. A. Bagrov, and A. A. Iliasov, Deterministic chaos and fractal entropy scaling in Floquet conformal field theories, Phys. Rev. B 103, L100302 (2021).
  8. V. Rosenhaus, Chaos in the quantum field theory S-matrix, Phys. Rev. Lett. 127, 021601 (2021).
  9. D. S. Ageev, Chaotic nature of holographic QCD, Phys. Rev. D 104, 126013 (2021).
  10. D. J. Gross and V. Rosenhaus, Chaotic scattering of highly excited strings, J. High Energy Phys. 05 (2021) 048.
  11. J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys. 08 (2016) 106.
  12. G. P. Brandino, R. M. Konik, and G. Mussardo, Energy level distribution of perturbed conformal field theories, J. Stat. Mech. (2010) P07013.
  13. J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, Black holes and random matrices, J. High Energy Phys. 05 (2017) 118; 09 (2018) 2.
  14. M. Srdinšek, T. Prosen, and S. Sotiriadis, Signatures of chaos in nonintegrable models of quantum field theories, Phys. Rev. Lett. 126, 121602 (2021).
  15. M. Bianchi, M. Firrotta, J. Sonnenschein, and D. Weissman, Measure for chaotic scattering amplitudes, Phys. Rev. Lett. 129, 261601 (2022).
  16. M. Bianchi, M. Firrotta, J. Sonnenschein, and D. Weissman, Measuring chaos in string scattering processes, Phys. Rev. D 108, 066006 (2023).
  17. J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94, 106002 (2016).
  18. H. Liu and J. Sonner, Quantum many-body physics from a gravitational lens, Nat. Rev. Phys. 2, 615 (2020).
  19. Y. M. Bunkov and G. E. Volovik, Spin superfluidity and magnon Bose-Einstein condensation, Phys. Usp. 53, 848 (2010).
  20. A. Milekhin and N. Sukhov, All holographic systems have scar states, Phys. Rev. D 110, 046023 (2024).
  21. P. Calabrese and J. L. Cardy, Time-dependence of correlation functions following a quantum quench, Phys. Rev. Lett. 96, 136801 (2006).
  22. P. Calabrese and J. Cardy, Quantum quenches in extended systems, J. Stat. Mech. (2007) P06008.
  23. P. Calabrese and J. Cardy, Entanglement and correlation functions following a local quench: A conformal field theory approach, J. Stat. Mech. (2007) P10004.
  24. S. R. Das, D. A. Galante, and R. C. Myers, Universal scaling in fast quantum quenches in conformal field theories, Phys. Rev. Lett. 112, 171601 (2014).
  25. S. R. Das, D. A. Galante, and R. C. Myers, Universality in fast quantum quenches, J. High Energy Phys. 02 (2015) 167.
  26. P. Calabrese and J. Cardy, Quantum quenches in 1+1 dimensional conformal field theories, J. Stat. Mech. (2016) 064003.
  27. S. Sotiriadis, P. Calabrese, and J. Cardy, Quantum quench from a thermal initial state, Europhys. Lett. 87, 20002 (2009).
  28. M. Nozaki, T. Numasawa, and T. Takayanagi, Quantum entanglement of local operators in conformal field theories, Phys. Rev. Lett. 112, 111602 (2014).
  29. D. S. Ageev and V. V. Pushkarev, Quantum quenches in fractonic field theories, arXiv:2306.14951.
  30. D. S. Ageev, A. A. Bagrov, A. I. Belokon, A. Iliasov, V. V. Pushkarev, and F. Verheijen, Local quenches in fracton field theory: Lieb-Robinson bound, noncausal dynamics and fractal excitation patterns, Phys. Rev. D 110, 065011 (2024).
  31. D. S. Ageev and I. Y. Aref’eva, Holographic non-equilibrium heating, J. High Energy Phys. 03 (2018) 103.
  32. D. S. Ageev, I. Y. Aref’eva, A. A. Bagrov, and M. I. Katsnelson, Holographic local quench and effective complexity, J. High Energy Phys. 08 (2018) 071.
  33. D. S. Ageev, Holography, quantum complexity and quantum chaos in different models, EPJ Web Conf. 191, 06006 (2018).
  34. D. S. Ageev, A. I. Belokon, and V. V. Pushkarev, From locality to irregularity: Introducing local quenches in massive scalar field theory, J. High Energy Phys. 05 (2023) 188; 12 (2023) 184(E).
  35. D. S. Ageev and V. V. Pushkarev, Chaotic signatures in free field theory, arXiv:2507.18746.
  36. J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. Achim Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions (Cambridge University Press, Cambridge, England, 2014), ISBN [Amazon][WorldCat], [Amazon][WorldCat], [Amazon][WorldCat], [Amazon][WorldCat].
  37. I. Y. Aref’eva, Holographic approach to quark–gluon plasma in heavy ion collisions, Phys. Usp. 57, 527 (2014).
  38. O. DeWolfe, S. S. Gubser, C. Rosen, and D. Teaney, Heavy ions and string theory, Prog. Part. Nucl. Phys. 75, 86 (2014).
  39. J. Polchinski and M. J. Strassler, The string dual of a confining four-dimensional gauge theory, arXiv:hep-th/0003136.
  40. J. Erlich, E. Katz, D. T. Son, and M. A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett. 95, 261602 (2005).
  41. N. Savić and M. Čubrović, Weak chaos and mixed dynamics in the string S-matrix, J. High Energy Phys. 03 (2024) 101.
  42. M. Ghodrati, String scattering amplitudes and mutual information in confining backgrounds: The partonic behavior, Phys. Rev. D 112, 046011 (2025).
  43. D. Das, S. Mandal, and A. Sarkar, Chaotic and thermal aspects in the highly excited string S-matrix, J. High Energy Phys. 08 (2024) 200.
  44. A. Bhattacharya and A. Jana, Quantum chaos and complexity from string scattering amplitudes, arXiv:2408.11096.
  45. I. Pesando, No “chaos” in bosonic string massive scalar amplitudes, arXiv:2502.03539.
  46. B. Allen and T. Jacobson, Vector two point functions in maximally symmetric spaces, Commun. Math. Phys. 103, 669 (1986).
  47. T. Banks, M. R. Douglas, G. T. Horowitz, and E. J. Martinec, AdS dynamics from conformal field theory, arXiv:hep-th/9808016.
  48. V. Keranen and P. Kleinert, Non-equilibrium scalar two point functions in AdS/CFT, J. High Energy Phys. 04 (2015) 119.
  49. V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75, 155111 (2007).
  50. Y. Y. Atas, E. Bogomolny, O. Giraud, and G. Roux, Distribution of the ratio of consecutive level spacings in random matrix ensembles, Phys. Rev. Lett. 110, 084101 (2013).
  51. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papić, Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations, Phys. Rev. B 98, 155134 (2018).
  52. C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papic, Weak ergodicity breaking from quantum many-body scars, Nat. Phys. 14, 745 (2018).
  53. M. Serbyn, D. A. Abanin, and Z. Papić, Quantum many-body scars and weak breaking of ergodicity, Nat. Phys. 17, 675 (2021).
  54. L. Ebner, A. Schäfer, C. Seidl, B. Müller, and X. Yao, Entanglement entropy of (2+1)-dimensional SU(2) lattice gauge theory on plaquette chains, Phys. Rev. D 110, 014505 (2024).
  55. L. Ebner, B. Müller, A. Schäfer, C. Seidl, and X. Yao, Eigenstate thermalization in (2+1)-dimensional SU(2) lattice gauge theory, Phys. Rev. D 109, 014504 (2024).
  56. A. Chandran, M. D. Schulz, and F. J. Burnell, The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains, Phys. Rev. B 94, 235122 (2016).
  57. R. Mélin, Level spacing statistics of bidimensional Fermi liquids. II. Landau fixed point and quantum chaos, J. Phys. I 5, 787 (1995).
  58. A. Khudorozhkov, A. Tiwari, C. Chamon, and T. Neupert, Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries, SciPost Phys. 13, 098 (2022).
  59. S. Trebst, M. Troyer, Z. Wang, and A. W. Ludwig, A short introduction to Fibonacci anyon models. Prog. Theor. Phys. Suppl. 176, 384 (2008).
  60. H. A. Weidenmuller and G. E. Mitchell, Random matrices and chaos in nuclear physics. Part 1. Nuclear structure, Rev. Mod. Phys. 81, 539 (2009).
  61. K. M. Frahm, L. Ermann, and D. L. Shepelyansky, Dynamical thermalization of interacting fermionic atoms in a Sinai oscillator trap, Condens. Mat. 4, 76 (2019).
  62. T. Guhr, A. Muller-Groeling, and H. A. Weidenmuller, Random matrix theories in quantum physics: Common concepts, Phys. Rep. 299, 189 (1998).
  63. S. Das, S. K. Garg, C. Krishnan, and A. Kundu, Fuzzballs and random matrices, J. High Energy Phys. 10 (2023) 031.
  64. D. S. Ageev, V. V. Pushkarev, and A. N. Zueva, Spectral form factors for curved spacetimes with a horizon, Phys. Rev. D 112, 086012 (2025).
  65. M. Bianchi, M. Firrotta, J. Sonnenschein, and D. Weissman, Multi-dimensional chaos I: Classical and quantum mechanics, arXiv:2510.03007.

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Phys. Rev. D 113, 046014– Published 18 February, 2026
  • Received 23 October 2025
  • Accepted 5 December 2025
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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.

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