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Bayesian inference of the critical end point in a (2+1)-flavor system from holographic QCD

Liqiang Zhu1,*, Xun Chen1,2,3,†, Kai Zhou4,5,‡, Hanzhong Zhang1,§, and Mei Huang6,∥

  • *Contact author: zhuliqiang@mails.ccnu.edu.cn
  • †Contact author: chenxun@usc.edu.cn
  • ‡Contact author: zhoukai@cuhk.edu.cn
  • §Contact author: zhanghz@mail.ccnu.edu.cn
  • ∥Contact author: huangmei@ucas.ac.cn
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Phys. Rev. D 112, 026019 – Published 15 July, 2025

DOI: https://doi.org/10.1103/wpts-lbtr

Abstract

We present a Bayesian holographic model constructed by integrating the equation of state and baryon number susceptibility at zero chemical potential from lattice quantum chromodynamics (QCD). The model incorporates error estimates derived from lattice data. With this model, we systematically investigate the thermodynamic properties of the 2+1-flavor QCD system. Using Bayesian inference, we perform precise calibration of the model parameters and determined the critical end point (CEP) position under the maximum a posterior (MAP) estimation to be (Tc,μBc)=(0.0859  GeV,0.742  GeV). Additionally, we predict the CEP positions within 68% and 95% confidence levels, yielding (Tc,μBc)68%=(0.0820−0.0889,0.71−0.77)  GeV and (Tc,μBc)95%=(0.0816−0.0898,0.71−0.79)  GeV, respectively. Moreover, to validate the reliability and predictive power of our approach, we conduct a comprehensive comparison between our predictions and potential CEP locations proposed by other theoretical models. This work not only establishes a novel Bayesian framework for holographic modeling but also provides valuable insights and theoretical support for exploring phase transitions in strongly interacting matter under extreme conditions.

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References (124)

  1. K. Adcox et al. (PHENIX Collaboration), Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration, Nucl. Phys. A757, 184 (2005).
  2. M. M. Aggarwal et al. (STAR Collaboration), An experimental exploration of the QCD phase diagram: The search for the critical point and the onset of de-confinement, .
  3. K. Adcox et al. (PHENIX Collaboration), Suppression of hadrons with large transverse momentum in central Au+Au collisions at sNN=130-GeV, Phys. Rev. Lett. 88, 022301 (2002).
  4. J. Adams et al. (STAR Collaboration), Transverse momentum and collision energy dependence of high p(T) hadron suppression in Au+Au collisions at ultrarelativistic energies, Phys. Rev. Lett. 91, 172302 (2003).
  5. M. Xie, Q.-F. Han, E.-K. Wang, B.-W. Zhang, and H.-Z. Zhang, The medium-temperature dependence of jet transport coefficient in high-energy nucleus–nucleus collisions, Nucl. Sci. Tech. 35, 125 (2024).
  6. Y. Li, S. Shen, S. Wang, and B.-W. Zhang, Transverse momentum balance of dijets in Xe+Xe collisions at the LHC, Nucl. Sci. Tech. 35, 113 (2024).
  7. W.-j. Fu, QCD at finite temperature and density within the fRG approach: An overview, Commun. Theor. Phys. 74, 097304 (2022).
  8. J. N. Guenther, Overview of the QCD phase diagram: Recent progress from the lattice, Eur. Phys. J. A 57, 136 (2021).
  9. K. Zhou, L. Wang, L.-G. Pang, and S. Shi, Exploring QCD matter in extreme conditions with machine learning, Prog. Part. Nucl. Phys. 135, 104084 (2024).
  10. L. Du, A. Sorensen, and M. Stephanov, The QCD phase diagram and beam energy scan physics: A theory overview, Int. J. Mod. Phys. E 33, 2430008 (2024).
  11. X. Luo, S. Shi, N. Xu, and Y. Zhang, A study of the properties of the QCD phase diagram in high-energy nuclear collisions, Particles 3, 278 (2020).
  12. Y.-G. Ma, L.-G. Pang, R. Wang, and K. Zhou, Phase transition study meets machine learning, Chin. Phys. Lett. 40, 122101 (2023).
  13. H. Zhang, D. Hou, T. Kojo, and B. Qin, Functional renormalization group study of the quark-meson model with ω meson, Phys. Rev. D 96, 114029 (2017).
  14. F. Gao and Y.-x. Liu, QCD phase transitions via a refined truncation of Dyson-Schwinger equations, Phys. Rev. D 94, 076009 (2016).
  15. S.-x. Qin, L. Chang, H. Chen, Y.-x. Liu, and C. D. Roberts, Phase diagram and critical endpoint for strongly-interacting quarks, Phys. Rev. Lett. 106, 172301 (2011).
  16. C. Shi, Y.-L. Wang, Y. Jiang, Z.-F. Cui, and H.-S. Zong, Locate QCD critical end point in a continuum model study, J. High Energy Phys. 07 (2014) 014.
  17. A. M. Halasz, A. D. Jackson, R. E. Shrock, M. A. Stephanov, and J. J. M. Verbaarschot, On the phase diagram of QCD, Phys. Rev. D 58, 096007 (1998).
  18. J. Berges and K. Rajagopal, Color superconductivity and chiral symmetry restoration at nonzero baryon density and temperature, Nucl. Phys. B538, 215 (1999).
  19. M. A. Stephanov, QCD phase diagram and the critical point, Prog. Theor. Phys. Suppl. 153, 139 (2004).
  20. Z. Li, K. Xu, X. Wang, and M. Huang, The kurtosis of net baryon number fluctuations from a realistic Polyakov–Nambu–Jona-Lasinio model along the experimental freeze-out line, Eur. Phys. J. C 79, 245 (2019).
  21. F. Sun, J. Shao, R. Wen, K. Xu, and M. Huang, Chiral phase transition and spin alignment of vector mesons in the polarized-Polyakov-loop Nambu–Jona-Lasinio model under rotation, Phys. Rev. D 109, 116017 (2024).
  22. Y.-R. Bao and S.-Q. Feng, Effects of tensor spin polarization on the chiral restoration and deconfinement phase transitions, Phys. Rev. D 109, 096033 (2024).
  23. J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1998).
  24. J. Erdmenger, N. Evans, I. Kirsch, and E. Threlfall, Mesons in gauge/gravity duals—a review, Eur. Phys. J. A 35, 81 (2008).
  25. S. J. Brodsky, G. F. de Teramond, H. G. Dosch, and J. Erlich, Light-front holographic QCD and emerging confinement, Phys. Rep. 584, 1 (2015).
  26. J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, and U. A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions (Cambridge University Press, Cambridge, England, 2014).
  27. A. Adams, L. D. Carr, T. Schäfer, P. Steinberg, and J. E. Thomas, Strongly correlated quantum fluids: Ultracold quantum gases, quantum chromodynamic plasmas, and holographic duality, New J. Phys. 14, 115009 (2012).
  28. S.-w. Li and T. Jia, Dynamically flavored description of holographic QCD in the presence of a magnetic field, Phys. Rev. D 96, 066032 (2017).
  29. K. Bitaghsir Fadafan, F. Kazemian, and A. Schmitt, Towards a holographic quark-hadron continuity, J. High Energy Phys. 03 (2019) 183.
  30. R. Abt, J. Erdmenger, N. Evans, and K. S. Rigatos, Light composite fermions from holography, J. High Energy Phys. 11 (2019) 160.
  31. T. Nakas and K. S. Rigatos, Fermions and baryons as open-string states from brane junctions, J. High Energy Phys. 12 (2020) 157.
  32. D. Li and M. Huang, Dynamical holographic QCD model for glueball and light meson spectra, J. High Energy Phys. 11 (2013) 088.
  33. S. S. Gubser and A. Nellore, Mimicking the QCD equation of state with a dual black hole, Phys. Rev. D 78, 086007 (2008).
  34. O. DeWolfe, S. S. Gubser, and C. Rosen, A holographic critical point, Phys. Rev. D 83, 086005 (2011).
  35. M. Jarvinen, Holographic dense QCD in the Veneziano limit, EPJ Web Conf. 274, 08006 (2022).
  36. Y. Yang and P.-H. Yuan, Confinement-deconfinement phase transition for heavy quarks in a soft wall holographic QCD model, J. High Energy Phys. 12 (2015) 161.
  37. Y. Yang and P.-H. Yuan, A refined holographic QCD model and QCD phase structure, J. High Energy Phys. 11 (2014) 149.
  38. D. Dudal and S. Mahapatra, Thermal entropy of a quark-antiquark pair above and below deconfinement from a dynamical holographic QCD model, Phys. Rev. D 96, 126010 (2017).
  39. D. Dudal and S. Mahapatra, Interplay between the holographic QCD phase diagram and entanglement entropy, J. High Energy Phys. 07 (2018) 120.
  40. Z. Fang, S. He, and D. Li, Chiral and deconfining phase transitions from holographic QCD study, Nucl. Phys. B907, 187 (2016).
  41. X.-Y. Liu, X.-C. Peng, Y.-L. Wu, and Z. Fang, Holographic study on QCD phase transition and phase diagram with two flavors, Phys. Rev. D 109, 054032 (2024).
  42. Y.-Y. Li, X.-L. Liu, X.-Y. Liu, and Z. Fang, Correlations between the deconfining and chiral transitions in holographic QCD, Phys. Rev. D 105, 034019 (2022).
  43. R. Critelli, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Critical point in the phase diagram of primordial quark-gluon matter from black hole physics, Phys. Rev. D 96, 096026 (2017).
  44. J. Grefa, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, Hot and dense quark-gluon plasma thermodynamics from holographic black holes, Phys. Rev. D 104, 034002 (2021).
  45. I. Y. Aref’eva, A. Ermakov, and P. Slepov, Direct photons emission rate and electric conductivity in twice anisotropic QGP holographic model with first-order phase transition, Eur. Phys. J. C 82, 85 (2022).
  46. I. Y. Aref’eva, K. Rannu, and P. Slepov, Holographic model for heavy quarks in anisotropic hot dense QGP with external magnetic field, J. High Energy Phys. 07 (2021) 161.
  47. X. Chen, D. Li, and M. Huang, Criticality of QCD in a holographic QCD model with critical end point, Chin. Phys. C 43, 023105 (2019).
  48. X. Chen, S.-Q. Feng, Y.-F. Shi, and Y. Zhong, Moving heavy quarkonium entropy, effective string tension, and the QCD phase diagram, Phys. Rev. D 97, 066015 (2018).
  49. X. Chen, L. Zhang, D. Li, D. Hou, and M. Huang, Gluodynamics and deconfinement phase transition under rotation from holography, J. High Energy Phys. 07 (2021) 132.
  50. J. Zhou, X. Chen, Y.-Q. Zhao, and J. Ping, Thermodynamics of heavy quarkonium in a magnetic field background, Phys. Rev. D 102, 086020 (2020).
  51. X. Chen, D. Li, D. Hou, and M. Huang, Quarkyonic phase from quenched dynamical holographic QCD model, J. High Energy Phys. 03 (2020) 073.
  52. X. Cao, M. Baggioli, H. Liu, and D. Li, Pion dynamics in a soft-wall AdS-QCD model, J. High Energy Phys. 12 (2022) 113.
  53. M. Arcos, W. Fischler, J. F. Pedraza, and A. Svesko, Membrane nucleation rates from holography, J. High Energy Phys. 12 (2022) 141.
  54. X. Cao and H. Liu, The impact of the phase transition on quark-gluon plasma with an extremely strong magnetic field in holographic QCD, Phys. Rev. D 111, 026008 (2025).
  55. H. Bohra, D. Dudal, A. Hajilou, and S. Mahapatra, Chiral transition in the probe approximation from an Einstein-Maxwell-dilaton gravity model, Phys. Rev. D 103, 086021 (2021).
  56. I. Y. Aref’eva, A. Hajilou, K. Rannu, and P. Slepov, Magnetic catalysis in holographic model with two types of anisotropy for heavy quarks, Eur. Phys. J. C 83, 1143 (2023).
  57. H. Bohra, D. Dudal, A. Hajilou, and S. Mahapatra, Anisotropic string tensions and inversely magnetic catalyzed deconfinement from a dynamical AdS/QCD model, Phys. Lett. B 801, 135184 (2020).
  58. K. Hashimoto, S. Sugishita, A. Tanaka, and A. Tomiya, Deep learning and the AdS/CFT correspondence, Phys. Rev. D 98, 046019 (2018).
  59. K. Hashimoto, S. Sugishita, A. Tanaka, and A. Tomiya, Deep learning and holographic QCD, Phys. Rev. D 98, 106014 (2018).
  60. T. Akutagawa, K. Hashimoto, and T. Sumimoto, Deep learning and AdS/QCD, Phys. Rev. D 102, 026020 (2020).
  61. K. Hashimoto, K. Ohashi, and T. Sumimoto, Deriving the dilaton potential in improved holographic QCD from the chiral condensate, Prog. Theor. Exp. Phys. 2023, 033B01 (2023).
  62. Y.-K. Yan, S.-F. Wu, X.-H. Ge, and Y. Tian, Deep learning black hole metrics from shear viscosity, Phys. Rev. D 102, 101902 (2020).
  63. M. Song, M. S. H. Oh, Y. Ahn, and K.-Y. Kima, AdS/deep-learning made easy: Simple examples, Chin. Phys. C 45, 073111 (2021).
  64. W.-B. Chang and D.-f. Hou, Heavy quarkonium spectral function in an anisotropic background, Phys. Rev. D 109, 086010 (2024).
  65. B. Ahn, H.-S. Jeong, K.-Y. Kim, and K. Yun, Deep learning bulk spacetime from boundary optical conductivity, J. High Energy Phys. 03 (2024) 141.
  66. Z.-F. Gu, Y.-K. Yan, and S.-F. Wu, Neural ODEs for holographic transport models without translation symmetry, Eur. Phys. J. C 85, 63 (2025).
  67. K. Li, Y. Ling, P. Liu, and M.-H. Wu, Learning the black hole metric from holographic conductivity, Phys. Rev. D 107, 066021 (2023).
  68. B. Ahn, H.-S. Jeong, K.-Y. Kim, and K. Yun, Holographic reconstruction of black hole spacetime: Machine learning and entanglement entropy, J. High Energy Phys. 01 (2025) 025.
  69. X. Chen and M. Huang, Machine learning holographic black hole from lattice QCD equation of state, Phys. Rev. D 109, L051902 (2024).
  70. Y. Chen, X. Chen, D. Li, and M. Huang, Deconfinement and chiral restoration phase transition under rotation from holography in an anisotropic gravitational background, Phys. Rev. D 111, 046006 (2025).
  71. M. Xie, W. Ke, H. Zhang, and X.-N. Wang, Global constraint on the jet transport coefficient from single-hadron, dihadron, and γ-hadron spectra in high-energy heavy-ion collisions, Phys. Rev. C 109, 064917 (2024).
  72. W.-J. Xing, S. Cao, and G.-Y. Qin, Flavor hierarchy of parton energy loss in quark-gluon plasma from a Bayesian analysis, Phys. Lett. B 850, 138523 (2024).
  73. J. Wu, W. Ke, and X.-N. Wang, Bayesian inference of the path-length dependence of jet energy loss, Phys. Rev. C 108, 034911 (2023).
  74. L. Zhu, Z. Gao, W. Ke, and H. Zhang, Bayesian inference of the magnetic field and chemical potential on holographic jet quenching in heavy-ion collisions, arXiv:2506.00340.
  75. W. Fan et al. (JETSCAPE Collaboration), New metric improving Bayesian calibration of a multistage approach studying hadron and inclusive jet suppression, Phys. Rev. C 109, 064903 (2024).
  76. Y. He, L.-G. Pang, and X.-N. Wang, Bayesian extraction of jet energy loss distributions in heavy-ion collisions, Phys. Rev. Lett. 122, 252302 (2019).
  77. J. Mulligan et al. (JETSCAPE Collaboration), Determining the jet transport coefficient q^ of the quark-gluon plasma using Bayesian parameter estimation, in 55th Rencontres de Moriond on QCD and High Energy Interactions (2021), arXiv:2106.11348.
  78. J. E. Parkkila, A. Onnerstad, and D. J. Kim, Bayesian estimation of the specific shear and bulk viscosity of the quark-gluon plasma with additional flow harmonic observables, Phys. Rev. C 104, 054904 (2021).
  79. J. E. Bernhard, J. S. Moreland, and S. A. Bass, Bayesian estimation of the specific shear and bulk viscosity of quark–gluon plasma, Nat. Phys. 15, 1113 (2019).
  80. Y.-L. Cheng, S. Shi, Y.-G. Ma, H. Stöcker, and K. Zhou, Examination of nucleon distribution with Bayesian imaging for isobar collisions, Phys. Rev. C 107, 064909 (2023).
  81. S. Pratt, E. Sangaline, P. Sorensen, and H. Wang, Constraining the equation of state of super-hadronic matter from heavy-ion collisions, Phys. Rev. Lett. 114, 202301 (2015).
  82. J. E. Bernhard, J. S. Moreland, S. A. Bass, J. Liu, and U. Heinz, Applying Bayesian parameter estimation to relativistic heavy-ion collisions: Simultaneous characterization of the initial state and quark-gluon plasma medium, Phys. Rev. C 94, 024907 (2016).
  83. Y.-L. Du, K. Zhou, J. Steinheimer, L.-G. Pang, A. Motornenko, H.-S. Zong, X.-N. Wang, and H. Stöcker, Identifying the nature of the QCD transition in relativistic collision of heavy nuclei with deep learning, Eur. Phys. J. C 80, 516 (2020).
  84. M. Hippert, J. Grefa, T. A. Manning, J. Noronha, J. Noronha-Hostler, I. Portillo Vazquez, C. Ratti, R. Rougemont, and M. Trujillo, Bayesian location of the QCD critical point from a holographic perspective, Phys. Rev. D 110, 094006 (2024).
  85. X. Chen and M. Huang, Flavor dependent critical endpoint from holographic QCD through machine learning, J. High Energy Phys. 02 (2025) 123.
  86. D. Li, S. He, M. Huang, and Q.-S. Yan, Thermodynamics of deformed AdS5 model with a positive/negative quadratic correction in graviton-dilaton system, J. High Energy Phys. 09 (2011) 041.
  87. R.-G. Cai, S. He, and D. Li, A hQCD model and its phase diagram in Einstein-Maxwell-Dilaton system, J. High Energy Phys. 03 (2012) 033.
  88. S. He, S.-Y. Wu, Y. Yang, and P.-H. Yuan, Phase structure in a dynamical soft-wall holographic QCD model, J. High Energy Phys. 04 (2013) 093.
  89. S. Lin, X. Liu, X. Chen, Z. Gen-Fa, and J. Zhou, Holographic Schwinger effect in flavor-dependent systems, Phys. Rev. D 111, 046005 (2025).
  90. L. Zhang and M. Huang, Holographic cold dense matter constrained by neutron stars, Phys. Rev. D 106, 096028 (2022).
  91. B. Chen, X. Chen, X. Li, Z.-R. Zhu, and K. Zhou, Exploring transport properties of quark-gluon plasma with a machine-learning assisted holographic approach, Phys. Rev. D 111, 086033 (2025).
  92. M. Natsuume, AdS/CFT duality user guide, Lect. Notes Phys. 903, 1 (2015).
  93. M.-W. Li, Y. Yang, and P.-H. Yuan, Analytic study on chiral phase transition in holographic QCD, J. High Energy Phys. 02 (2021) 055.
  94. Y. Yang and P.-H. Yuan, Universal behaviors of speed of sound from holography, Phys. Rev. D 97, 126009 (2018).
  95. U. Gursoy, M. Jarvinen, and G. Nijs, Holographic QCD in the Veneziano limit at a finite magnetic field and chemical potential, Phys. Rev. Lett. 120, 242002 (2018).
  96. J. Novak, K. Novak, S. Pratt, J. Vredevoogd, C. Coleman-Smith, and R. Wolpert, Determining fundamental properties of matter created in ultrarelativistic heavy-ion collisions, Phys. Rev. C 89, 034917 (2014).
  97. E. Sangaline and S. Pratt, Toward a deeper understanding of how experiments constrain the underlying physics of heavy-ion collisions, Phys. Rev. C 93, 024908 (2016).
  98. J. E. Bernhard, P. W. Marcy, C. E. Coleman-Smith, S. Huzurbazar, R. L. Wolpert, and S. A. Bass, Quantifying properties of hot and dense QCD matter through systematic model-to-data comparison, Phys. Rev. C 91, 054910 (2015).
  99. M. Xie, W. Ke, H. Zhang, and X.-N. Wang, Information-field-based global Bayesian inference of the jet transport coefficient, Phys. Rev. C 108, L011901 (2023).
  100. S. Cao et al. (JETSCAPE Collaboration), Determining the jet transport coefficient qhat from inclusive hadron suppression measurements using Bayesian parameter estimation, Phys. Rev. C 104, 024905 (2021).
  101. M. Omana Kuttan, J. Steinheimer, K. Zhou, and H. Stoecker, QCD equation of state of dense nuclear matter from a Bayesian analysis of heavy-ion collision data, Phys. Rev. Lett. 131, 202303 (2023).
  102. A. Bazavov et al. (HotQCD Collaboration), Equation of state in (2+1)-flavor QCD, Phys. Rev. D 90, 094503 (2014).
  103. A. Bazavov et al., The QCD equation of state to O(μB6) from lattice QCD, Phys. Rev. D 95, 054504 (2017).
  104. D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, emcee: The MCMC hammer, Publ. Astron. Soc. Pac. 125, 306 (2013).
  105. J. Goodman and J. Weare, Ensemble samplers with affine invariance, Commun. Appl. Math. Comput. Sci. 5, 65 (2010).
  106. B. Tang, Orthogonal array-based latin hypercubes, J. Am. Stat. Assoc. 88, 1392 (1993).
  107. M. D. Morris and T. J. Mitchell, Exploratory designs for computational experiments, J. Stat. Plann. Infer. 43, 381 (1995).
  108. J. Loeppky, J. Sacks, and W. Welch, Choosing the sample size of a computer experiment: A practical guide, Technometrics 51, 366 (2009).
  109. M. E. Tipping and C. M. Bishop, Mixtures of probabilistic principal component analyzers, Neural Comput. 11, 443 (1999).
  110. C. K. Williams and C. E. Rasmussen, Gaussian Processes for Machine Learning (MIT Press Cambridge, MA, 2006), Vol. 2.
  111. L.-G. Pang, K. Zhou, N. Su, H. Petersen, H. Stöcker, and X.-N. Wang, An equation-of-state-meter of quantum chromodynamics transition from deep learning, Nat. Commun. 9, 210 (2018).
  112. M. Omana Kuttan, K. Zhou, J. Steinheimer, A. Redelbach, and H. Stoecker, An equation-of-state-meter for CBM using PointNet, J. High Energy Phys. 10 (2020) 184.
  113. L. Jiang, L. Wang, and K. Zhou, Deep learning stochastic processes with QCD phase transition, Phys. Rev. D 103, 116023 (2021).
  114. G. Aarts, K. Fukushima, T. Hatsuda, A. Ipp, S. Shi, L. Wang, and K. Zhou, Physics-driven learning for inverse problems in quantum chromodynamics, Nat. Rev. Phys. 7, 154 (2025).
  115. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21, 1087 (1953).
  116. W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika 57, 97 (1970).
  117. V. Vovchenko and H. Stoecker, thermal-fist: A package for heavy-ion collisions and hadronic equation of state, Comput. Phys. Commun. 244, 295 (2019).
  118. N. Haque, A. Bandyopadhyay, J. O. Andersen, M. G. Mustafa, M. Strickland, and N. Su, Three-loop HTLpt thermodynamics at finite temperature and chemical potential, J. High Energy Phys. 05 (2014) 027.
  119. R.-G. Cai, S. He, L. Li, and Y.-X. Wang, Probing QCD critical point and induced gravitational wave by black hole physics, Phys. Rev. D 106, L121902 (2022).
  120. Y.-Q. Zhao, S. He, D. Hou, L. Li, and Z. Li, Phase diagram of holographic thermal dense QCD matter with rotation, J. High Energy Phys. 04 (2023) 115.
  121. F. Gao and J. M. Pawlowski, QCD phase structure from functional methods, Phys. Rev. D 102, 034027 (2020).
  122. W.-j. Fu, J. M. Pawlowski, and F. Rennecke, QCD phase structure at finite temperature and density, Phys. Rev. D 101, 054032 (2020).
  123. S. Borsanyi, Z. Fodor, J. N. Guenther, P. Parotto, A. Pasztor, C. Ratti, V. Vovchenko, and C. H. Wong, Lattice QCD constraints on the critical point from an improved precision equation of state, arXiv:2502.10267.
  124. O.-Y. Luo, X. Chen, F.-P. Li, X.-H. Li, and K. Zhou, Neural network modeling of heavy-quark potential from holography, Eur. Phys. J. C 85, 637 (2025).

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Phys. Rev. D 112, 026019– Published 15 July, 2025
  • Received 7 April 2025
  • Accepted 26 June 2025
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