- Letter
- Open Access
Toward a holographic realization of the -flavor QCD phase structure
Phys. Rev. D 112, L111504 – Published 12 December, 2025
DOI: https://doi.org/10.1103/3plt-wlt7
Abstract
We present a fully backreacted Einstein-Maxwell-Dilaton–flavor model with dynamical light and strange sectors, calibrated to lattice QCD using a machine-learning–assisted spectral method. The model reproduces the -flavor equation of state and chiral dynamics with quantitative accuracy, and maps the Columbia plot with a tricritical point at and a critical mass , consistent with lattice results. At finite density, it yields a crossover-to-first-order transition and predicts a critical endpoint at and , within the reach of heavy-ion experiments. These findings establish a unified holographic framework for the QCD phase structure across quark masses and baryon density, providing the first consistent and quantitative description of both deconfinement and chiral transitions within a single holographic model.
Physics Subject Headings (PhySH)
Article Text
References (64)
- Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, Nature (London) 443, 675 (2006).
- K. Fukushima, J. Subatomic Part. Cosmol. 3, 100066 (2025).
- F. R. Brown, F. P. Butler, H. Chen, N. H. Christ, Z.-h. Dong, W. Schaffer, L. I. Unger, and A. Vaccarino, Phys. Rev. Lett. 65, 2491 (1990).
- E. Laermann and O. Philipsen, Annu. Rev. Nucl. Part. Sci. 53, 163 (2003).
- R. D. Pisarski and F. Wilczek, Phys. Rev. D 29, 338 (1984).
- S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Phys. Lett. B 730, 99 (2014).
- A. Bazavov et al. (HotQCD Collaboration), Phys. Rev. D 90, 094503 (2014).
- E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
- S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998).
- J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998).
- S. S. Gubser, A. Nellore, S. S. Pufu, and F. D. Rocha, Phys. Rev. Lett. 101, 131601 (2008).
- O. DeWolfe, S. S. Gubser, and C. Rosen, Phys. Rev. D 83, 086005 (2011).
- M. Jarvinen and E. Kiritsis, J. High Energy Phys. 03 (2012) 002.
- K. Chelabi, Z. Fang, M. Huang, D. Li, and Y.-L. Wu, Phys. Rev. D 93, 101901 (2016).
- D. Li and M. Huang, J. High Energy Phys. 02 (2017) 042.
- I. Y. Aref’eva, A. Ermakov, K. Rannu, and P. Slepov, Eur. Phys. J. C 83, 79 (2023).
- R. Critelli, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Phys. Rev. D 96, 096026 (2017).
- D. Li, M. Huang, and Q.-S. Yan, Eur. Phys. J. C 73, 2615 (2013).
- Z. Fang and Y.-L. Wu, Chin. Phys. C 44, 103101 (2020).
- H. Bohra, D. Dudal, A. Hajilou, and S. Mahapatra, Phys. Rev. D 103, 086021 (2021).
- X. Chen, D. Li, D. Hou, and M. Huang, J. High Energy Phys. 03 (2020) 073.
- T. Alho, M. Järvinen, K. Kajantie, E. Kiritsis, and K. Tuominen, J. High Energy Phys. 01 (2013) 093.
- A. Alfano, N. Evans, and W. Fan, arXiv:2506.09456.
- D. Li, J. Liao, and M. Huang, Phys. Rev. D 89, 126006 (2014).
- T. Alho, M. Järvinen, K. Kajantie, E. Kiritsis, C. Rosen, and K. Tuominen, J. High Energy Phys. 04 (2014) 124.
- Q. Fu, S. He, L. Li, and Z. Li, J. High Energy Phys. 06 (2025) 221.
- R.-G. Cai, S. He, and D. Li, J. High Energy Phys. 03 (2012) 033.
- R.-G. Cai, S. He, L. Li, and H.-A. Zeng, arXiv:2406.12772.
- Z. Zhang, D. Li, L. Yu, Z. Li, and X. Wang, arXiv:2507.22724.
- J. Grefa, M. Hippert, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Phys. Rev. D 106, 034024 (2022).
- Y.-Q. Zhao, S. He, D. Hou, L. Li, and Z. Li, J. High Energy Phys. 04 (2023) 115.
- Z. Li and F. Wang, arXiv:2507.09113.
- T. Demircik, N. Jokela, M. Jarvinen, and A. Piispa, arXiv:2405.02392.
- C. Ecker, N. Jokela, and M. Järvinen, arXiv:2506.10065.
- X.-Y. Liu, X.-C. Peng, Y.-L. Wu, and Z. Fang, Phys. Rev. D 109, 054032 (2024).
- Z. Fang, Y.-L. Wu, and L. Zhang, Phys. Rev. D 98, 114003 (2018).
- P. Gubler and D. Satow, Prog. Part. Nucl. Phys. 106, 1 (2019).
- S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo (Wuppertal-Budapest Collaboration), J. High Energy Phys. 09 (2010) 073.
- S. Borsányi, Z. Fodor, J. N. Guenther, R. Kara, S. D. Katz, P. Parotto, A. Pásztor, C. Ratti, and K. K. Szabó, Phys. Rev. Lett. 126, 232001 (2021).
- A. Bazavov et al., Phys. Rev. D 95, 054504 (2017).
- X. Cao, H. Liu, and D. Li, Phys. Rev. D 102, 126014 (2020).
- Y. Chen, X. Chen, D. Li, and M. Huang, Phys. Rev. D 111, 046006 (2025).
- S. P. Bartz and T. Jacobson, Phys. Rev. D 94, 075022 (2016).
- A. Bazavov et al. (HotQCD Collaboration), Phys. Lett. B 795, 15 (2019).
- A. Bazavov et al., Phys. Rev. D 80, 014504 (2009).
- A. Bazavov, N. Brambilla, H. T. Ding, P. Petreczky, H. P. Schadler, A. Vairo, and J. H. Weber, Phys. Rev. D 93, 114502 (2016).
- S. Borsanyi, K. R., Z. Fodor, D. A. Godzieba, P. Parotto, and D. Sexty, Phys. Rev. D 105, 074513 (2022).
- L. Giusti, M. Hirasawa, M. Pepe, and L. Virzì, Phys. Lett. B 868, 139775 (2025).
- T. D. Cohen and L. Y. Glozman, Eur. Phys. J. A 60, 171 (2024).
- Y. Fujimoto, K. Fukushima, Y. Hidaka, and L. McLerran, Phys. Rev. D 112, 074006 (2025).
- H.-T. Ding, F. Karsch, and S. Mukherjee, Int. J. Mod. Phys. E 24, 1530007 (2015).
- G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, Proc. Sci., LATTICE2007 (2007) 182.
- H. T. Ding, A. Bazavov, P. Hegde, F. Karsch, S. Mukherjee, and P. Petreczky, Proc. Sci., LATTICE2011 (2011) 191.
- R.-G. Cai, S. He, L. Li, and Y.-X. Wang, Phys. Rev. D 106, L121902 (2022).
- F. Gao and J. M. Pawlowski, Phys. Rev. D 102, 034027 (2020).
- Z. Li, K. Xu, X. Wang, and M. Huang, Eur. Phys. J. C 79, 245 (2019).
- H. Zhang, D. Hou, T. Kojo, and B. Qin, Phys. Rev. D 96, 114029 (2017).
- D. A. Clarke, P. Dimopoulos, F. Di Renzo, J. Goswami, C. Schmidt, S. Singh, and K. Zambello, arXiv:2405.10196.
- H. Shah, M. Hippert, J. Noronha, C. Ratti, and V. Vovchenko, arXiv:2410.16206.
- J. Grefa, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Phys. Rev. D 104, 034002 (2021).
- M. Hippert, J. Grefa, T. A. Manning, J. Noronha, J. Noronha-Hostler, I. Portillo Vazquez, C. Ratti, R. Rougemont, and M. Trujillo, Phys. Rev. D 110, 094006 (2024).
- N. Jokela, M. Järvinen, and A. Piispa, Phys. Rev. D 110, 126013 (2024).
- A. Lysenko, M. I. Gorenstein, R. Poberezhniuk, and V. Vovchenko, Phys. Rev. C 111, 054903 (2025).
- X. Luo, S. Shi, N. Xu, and Y. Zhang, Particles 3, 278 (2020).