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Topological charges and confined-deconfined phase transition in holography

Nelson R. F. Braga* and William S. Cunha†

  • *Contact author: braga@if.ufrj.br
  • †Contact author: wscunha@pos.if.ufrj.br
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Phys. Rev. D 114, 046007 – Published 5 August, 2026

DOI: https://doi.org/10.1103/n5bn-2ph2

Abstract

In recent years, many interesting works providing a topological description for black hole (BH) properties have appeared in the literature. In particular, in this framework BHs correspond to topological defects in an enlarged (off shell) parameter space, with an associated total topological charge. In gauge/gravity duality the transition from the confined to the deconfined phase is mapped into the dominance of a BH phase on the gravity side. Here we show, using a holographic anti–de Sitter (AdS)/QCD model, that the introduction of an energy scale in AdS space results in a change in the topological class. Such a modification corresponds to the existence of confined and deconfined phases, separated by a Hawking-Page transition at a finite critical temperature.

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References (35)

  1. D. Dudal, D. R. Granado, and T. G. Mertens, No inverse magnetic catalysis in the QCD hard and soft wall models, Phys. Rev. D 93, 125004 (2016).
  2. N. R. F. Braga and L. F. Ferreira, Bottomonium dissociation in a finite density plasma, Phys. Lett. B 773, 313 (2017).
  3. N. R. F. Braga and L. F. Ferreira, Quasinormal modes for quarkonium in a plasma with magnetic fields, Phys. Lett. B 795, 462 (2019).
  4. N. R. F. Braga and R. Da Mata, Quasinormal modes for heavy vector mesons in a finite density plasma, Phys. Lett. B 804, 135381 (2020).
  5. N. R. F. Braga, Y. F. Ferreira, and L. F. Ferreira, Configuration entropy and stability of bottomonium radial excitations in a plasma with magnetic fields, Phys. Rev. D 105, 114044 (2022).
  6. A. Ballon-Bayona and A. S. d. S. Junior, Nucleons and vector mesons in a confining holographic QCD model, Phys. Rev. D 109, 094050 (2024).
  7. A. Nascimento and H. Boschi-Filho, Mechanical properties of the proton from a deformed AdS holographic model, Phys. Rev. D 113, 106020 (2026).
  8. E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2, 505 (1998).
  9. S. W. Hawking and D. N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. 87, 577 (1983).
  10. C. P. Herzog, A holographic prediction of the deconfinement temperature, Phys. Rev. Lett. 98, 091601 (2007).
  11. C. A. Ballon Bayona, H. Boschi-Filho, N. R. F. Braga, and L. A. Pando Zayas, On a holographic model for confinement/deconfinement, Phys. Rev. D 77, 046002 (2008).
  12. N. R. F. Braga, L. F. Faulhaber, and O. C. Junqueira, Confinement-deconfinement temperature for a rotating quark-gluon plasma, Phys. Rev. D 105, 106003 (2022).
  13. N. R. F. Braga and O. C. Junqueira, Hawking-Page transition in holographic QCD at finite density, Phys. Lett. B 855, 138813 (2024).
  14. N. R. F. Braga, W. S. Cunha, and Y. F. Ferreira, Holography and charmonium structure in a finite density plasma, Phys. Lett. B 868, 139798 (2025).
  15. Y.-S. Duan and M.-L. Ge, SU(2) gauge theory and electrodynamics with N magnetic monopoles, Sci. Sin. 9, 11 (1979).
  16. Y. Duan, The structure of the topological current, SLAC-PUB-3301, 1984.
  17. S.-W. Wei, Topological charge and black hole photon spheres, Phys. Rev. D 102, 064039 (2020).
  18. S.-W. Wei and Y.-X. Liu, Topology of black hole thermodynamics, Phys. Rev. D 105, 104003 (2022).
  19. S.-W. Wei, Y.-X. Liu, and R. B. Mann, Black hole solutions as topological thermodynamic defects, Phys. Rev. Lett. 129, 191101 (2022).
  20. S.-W. Wei, Y.-X. Liu, and R. B. Mann, Universal topological classifications of black hole thermodynamics, Phys. Rev. D 110, L081501 (2024).
  21. D. Wu, W. Liu, S.-Q. Wu, and R. B. Mann, Novel topological classes in black hole thermodynamics, Phys. Rev. D 111, L061501 (2025).
  22. D. Wu, S.-Y. Gu, X.-D. Zhu, Q.-Q. Jiang, and S.-Z. Yang, Topological classes of thermodynamics of the static multi-charge AdS black holes in gauged supergravities: Novel temperature-dependent thermodynamic topological phase transition, J. High Energy Phys. 06 (2024) 213.
  23. S.-P. Wu, S.-J. Yang, and S.-W. Wei, Extended thermodynamical topology of black hole, Eur. Phys. J. C 85, 1372 (2025).
  24. P. K. Yerra, C. Bhamidipati, and S. Mukherji, Topology of critical points and Hawking-Page transition, Phys. Rev. D 106, 064059 (2022).
  25. H. Babaei-Aghbolagh, H. Esmaili, S. He, and H. Mohammadzadeh, Thermodynamic topology of Einstein-Maxwell-Dilaton Theories, Eur. Phys. J. C 86, 78 (2026).
  26. S.-J. Yang, S.-P. Wu, S.-W. Wei, and Y.-X. Liu, A topological perspective on bulk boundary thermodynamic equivalence, Eur. Phys. J. C 86, 498 (2026).
  27. P. Colangelo, F. Giannuzzi, and S. Nicotri, Holography, heavy-quark free energy, and the QCD phase diagram, Phys. Rev. D 83, 035015 (2011).
  28. P. Colangelo, F. Giannuzzi, and S. Nicotri, In-medium hadronic spectral functions through the soft-wall holographic model of QCD, J. High Energy Phys. 05 (2012) 076.
  29. B.-H. Lee, C. Park, and S.-J. Sin, A dual geometry of the hadron in dense matter, J. High Energy Phys. 07 (2009) 087.
  30. A. Karch, E. Katz, D. T. Son, and M. A. Stephanov, Linear confinement and AdS/QCD, Phys. Rev. D 74, 015005 (2006).
  31. The Physics of the Quark-Gluon Plasma: Introductory Lectures, edited by S. Sarkar, H. Satz, and B. Sinha (Springer, Berlin, Heidelberg, 2009), Vol. 785.
  32. U. Gursoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, J. High Energy Phys. 02 (2008) 032.
  33. U. Gursoy, E. Kiritsis, and F. Nitti, Exploring improved holographic theories for QCD: Part II, J. High Energy Phys. 02 (2008) 019.
  34. A. Ballon-Bayona, L. A. H. Mamani, A. S. Miranda, and V. T. Zanchin, Effective holographic models for QCD: Thermodynamics and viscosity coefficients, Phys. Rev. D 104, 046013 (2021).
  35. T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113, 843 (2005).

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Phys. Rev. D 114, 046007– Published 5 August, 2026
  • Received 6 May 2026
  • Accepted 26 June 2026
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