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Probing the factorized island branch with the capacity of entanglement in Jackiw-Teitelboim gravity

Raúl Arias* and Agustín Tamis†

  • *Contact author: rarias@fisica.unlp.edu.ar
  • †Contact author: agustin.tamis@fisica.unlp.edu.ar
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Phys. Rev. D 114, 026007 – Published 6 July, 2026

DOI: https://doi.org/10.1103/rw5x-4t3d

Abstract

Black hole islands are usually diagnosed through the von Neumann entropy, but the full replica saddle contains more information than survives in the limit n→1. In this paper we show that the capacity of entanglement can detect that extra structure already within the controlled factorized island branch of Jackiw-Teitelboim gravity coupled to a large-c bath. In the late-time high-temperature regime, the entropy plateau remains unchanged at the first nontrivial order, while the capacity acquires a definite correction. This provides a sharp semiclassical example in which nearby replica data are physically meaningful even when the entropy itself appears rigid. Our result shows that the factorized island saddle already carries finite-n information beyond the entropy, and that the capacity is a natural observable for exposing it. More broadly, it highlights that the physics of island saddles is not exhausted by the n=1 limit: the surrounding replica geometry can contain additional, and observable, information about how the semiclassical saddle is assembled.

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References (28)

  1. A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, J. High Energy Phys. 08 (2013) 090.
  2. T. Faulkner, A. Lewkowycz, and J. Maldacena, Quantum corrections to holographic entanglement entropy, J. High Energy Phys. 11 (2013) 074.
  3. N. Engelhardt and A. C. Wall, Quantum extremal surfaces: Holographic entanglement entropy beyond the classical regime, J. High Energy Phys. 01 (2015) 073.
  4. D. L. Jafferis, A. Lewkowycz, J. Maldacena, and S. J. Suh, Relative entropy equals bulk relative entropy, J. High Energy Phys. 06 (2016) 004.
  5. X. Dong, The gravity dual of Rényi entropy, Nat. Commun. 7, 12472 (2016).
  6. A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, J. High Energy Phys. 12 (2019) 063.
  7. A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, J. High Energy Phys. 03 (2020) 149.
  8. G. Penington, Entanglement wedge reconstruction and the information paradox, J. High Energy Phys. 09 (2020) 002.
  9. G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, Replica wormholes and the black hole interior, J. High Energy Phys. 03 (2022) 205.
  10. A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93, 035002 (2021).
  11. A. Almheiri, R. Mahajan, and J. Maldacena, Islands outside the horizon, arXiv:1910.11077.
  12. Y. Nakaguchi and T. Nishioka, A holographic proof of Rényi entropic inequalities, J. High Energy Phys. 12 (2016) 129.
  13. J. de Boer, J. Järvelä, and E. Keski-Vakkuri, Aspects of capacity of entanglement, Phys. Rev. D 99, 066012 (2019).
  14. K. Kawabata, T. Nishioka, Y. Okuyama, and K. Watanabe, Probing Hawking radiation through capacity of entanglement, J. High Energy Phys. 05 (2021) 062.
  15. K. Kawabata, T. Nishioka, Y. Okuyama, and K. Watanabe, Replica wormholes and capacity of entanglement, J. High Energy Phys. 10 (2021) 227.
  16. A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, Replica wormholes and the entropy of Hawking radiation, J. High Energy Phys. 05 (2020) 013.
  17. T. J. Hollowood, S. Prem Kumar, and L. C. Piper, Replica Rényi wormholes and generalised modular entropy in JT gravity, J. High Energy Phys. 10 (2024) 169.
  18. R. Arias, G. Di Giulio, E. Keski-Vakkuri, and E. Tonni, Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement, J. High Energy Phys. 03 (2023) 175.
  19. M.-H. Yu, S.-Y. Lin, and X.-H. Ge, Replica wormholes, modular entropy, and capacity of entanglement in JT gravity, Sci. China Phys. Mech. Astron. 69, 220412 (2026).
  20. R. Arias and D. Fondevila, Capacity of entanglement and replica backreaction in RST gravity, arXiv:2603.09763.
  21. C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. 126B, 41 (1983).
  22. R. Jackiw, Lower dimensional gravity, Nucl. Phys. B252, 343 (1985).
  23. A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, J. High Energy Phys. 11 (2015) 014.
  24. J. Engelsöy, T. G. Mertens, and H. Verlinde, An investigation of AdS2 backreaction and holography, J. High Energy Phys. 07 (2016) 139.
  25. J. Maldacena, D. Stanford, and Z. Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space, Prog. Theor. Exp. Phys. 2016, 12C104 (2016).
  26. T. J. Hollowood and S. Prem Kumar, Islands and Page curves for evaporating black holes in JT gravity, J. High Energy Phys. 08 (2020) 094.
  27. K. Goto, T. Hartman, and A. Tajdini, Replica wormholes for an evaporating 2D black hole, J. High Energy Phys. 04 (2021) 289.
  28. R. Arias, J. de Boer, G. Di Giulio, E. Keski-Vakkuri, and E. Tonni, Sequences of resource monotones from modular Hamiltonian polynomials, Phys. Rev. Res. 5, 043082 (2023).

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Phys. Rev. D 114, 026007– Published 6 July, 2026
  • Received 28 April 2026
  • Accepted 26 May 2026
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