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  • Open Access

Global symmetry violation from nonisometric codes

Jong-Hyun Baek*

Kang-Sin Choi†

  • Institute of Mathematical Sciences, Ewha Womans University, Seoul 03760, Korea and Scranton Honors Program, Ewha Womans University, Seoul 03760, Korea

  • *Contact author: jonghbaek@gmail.com
  • †Contact author: kangsin@ewha.ac.kr
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Phys. Rev. D 112, 126017 – Published 18 December, 2025

DOI: https://doi.org/10.1103/yr3k-vj6x

Abstract

We study the no-global-symmetry conjecture in quantum gravity by modeling black holes as nonisometric codes that encode the interior states with global charges into the fundamental states. The fluctuation in the inner products of the charged states can be larger compared to the case without charges. The nonisometric map causes states with different charges to have nonzero overlaps, signaling symmetry violation. The Renyi entropies of the radiation with global charges are found to be consistent with the quantum extremal surface formula. We compute various forms of Renyi relative entropy, as well as the fidelity, to quantify the degree of a global symmetry violation in Hawking radiation, demonstrating that global symmetries are indeed violated. We also comment on the instability of the black hole remnant.

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References (34)

  1. S. B. Giddings and A. Strominger, Loss of incoherence and determination of coupling constants in quantum gravity, Nucl. Phys. B307, 854 (1988).
  2. R. Kallosh, A. D. Linde, D. A. Linde, and L. Susskind, Gravity and global symmetries, Phys. Rev. D 52, 912 (1995).
  3. T. Banks and N. Seiberg, Symmetries and strings in field theory and gravity, Phys. Rev. D 83, 084019 (2011).
  4. D. Harlow and H. Ooguri, Constraints on symmetries from holography, Phys. Rev. Lett. 122, 191601 (2019).
  5. D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys. 383, 1669 (2021).
  6. D. Harlow and E. Shaghoulian, Global symmetry, Euclidean gravity, and the black hole information problem, J. High Energy Phys. 04 (2021) 175.
  7. J. J. Heckman, M. Hübner, and C. Murdia, On the holographic dual of a topological symmetry operator, Phys. Rev. D 110, 046007 (2024).
  8. G. Penington, Entanglement wedge reconstruction and the information paradox, J. High Energy Phys. 09 (2020) 002.
  9. 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.
  10. 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.
  11. G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, Replica wormholes and the black hole interior, J. High Energy Phys. 03 (2022) 205.
  12. 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.
  13. A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93, 035002 (2021).
  14. Y. Chen and H. W. Lin, Signatures of global symmetry violation in relative entropies and replica wormholes, J. High Energy Phys. 03 (2021) 040.
  15. P.-S. Hsin, L. V. Iliesiu, and Z. Yang, A violation of global symmetries from replica wormholes and the fate of black hole remnants, Classical Quantum Gravity 38, 194004 (2021).
  16. I. Bah, Y. Chen, and J. Maldacena, Estimating global charge violating amplitudes from wormholes, J. High Energy Phys. 04 (2023) 061.
  17. A. Almheiri, X. Dong, and D. Harlow, Bulk locality and quantum error correction in AdS/CFT, J. High Energy Phys. 04 (2015) 163.
  18. X. Dong, D. Harlow, and A. C. Wall, Reconstruction of bulk operators within the entanglement wedge in gauge-gravity duality, Phys. Rev. Lett. 117, 021601 (2016).
  19. D. Harlow, The Ryu–Takayanagi formula from quantum error correction, Commun. Math. Phys. 354, 865 (2017).
  20. C. Akers, N. Engelhardt, D. Harlow, G. Penington, and S. Vardhan, The black hole interior from non-isometric codes and complexity, J. High Energy Phys. 06 (2024) 155.
  21. S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975); 46, 206(E) (1976).
  22. P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, J. High Energy Phys. 09 (2007) 120.
  23. A. R. Brown, L. V. Iliesiu, G. Penington, and M. Usatyuk, The evaporation of charged black holes, arXiv:2411.03447.
  24. D. Petz, Quasi-entropies for finite quantum systems, Rep. Math. Phys. 23, 57 (1986).
  25. S. W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14, 2460 (1976).
  26. S. W. Hawking, The unpredictability of quantum gravity, Commun. Math. Phys. 87, 395 (1982).
  27. M. M. Wilde, A. Winter, and D. Yang, Strong converse for the classical capacity of entanglement-breaking and hadamard channels via a sandwiched Renyi relative entropy, Commun. Math. Phys. 331, 593 (2014).
  28. M. Müller-Lennert, F. Dupuis, O. Szehr, S. Fehr, and M. Tomamichel, On quantum Rényi entropies: A new generalization and some properties, J. Math. Phys. (N.Y.) 54, 122203 (2013).
  29. R. L. Frank and E. H. Lieb, Monotonicity of a relative Rényi entropy, J. Math. Phys. (N.Y.) 54, 122201 (2013).
  30. L. Susskind, Trouble for remnants, arXiv:hep-th/9501106.
  31. A. Teixeira, A. Matos, and L. Antunes, Conditional Rényi entropies, IEEE Trans. Inf. Theory 58, 4273 (2012).
  32. D. N. Page, Information in black hole radiation, Phys. Rev. Lett. 71, 3743 (1993).
  33. J. Polchinski, Monopoles, duality, and string theory, Int. J. Mod. Phys. A 19S1, 145 (2004).
  34. N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, The string landscape, black holes and gravity as the weakest force, J. High Energy Phys. 06 (2007) 060.

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Phys. Rev. D 112, 126017– Published 18 December, 2025
  • Received 16 September 2025
  • Accepted 1 December 2025
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