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Phase transition of hot dense QCD Matter from a refined holographic EMD model

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A refined holographic EMD model, calibrated to lattice QCD, predicts a QCD critical end point at $T = 102.25$ MeV and $\mu_B = 590.5$ MeV and a corresponding peak in $\kappa\sigma^2$ in the 3–5 GeV collision-energy window.

desk verdict A competent holographic model with a concrete but fragile conditional prediction: the 3–5 GeV kappa sigma^2 peak is worth a referee's time, but it is an extrapolation between two unquantified curves. read the letter →

arxiv 2507.09113 v1 pith:UOOF5Y6E submitted 2025-07-12 hep-ph

Zhibin Li , Fei Wang This is my paper
classification hep-ph
keywords holographicQCDEinstein-Maxwell-dilatonmodelcriticalendpointbaryonnumbersusceptibilitieschemicalfreeze-outlinefinite-densityequationofstateGauss-Bonnetgravity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper constructs a five-dimensional holographic model of quark–gluon matter—an Einstein–Maxwell–dilaton system with a refined dilaton potential and a non-unit gauge kinetic coupling—and shows that, after calibration to zero-density lattice QCD data, it reproduces the equation of state and baryon-number susceptibilities at finite baryon density. Using that model, the authors locate the QCD critical end point at temperature $T \approx 102$ MeV and baryon chemical potential $\mu_B \approx 590$ MeV, and they trace the baryon-number susceptibility ratio $\kappa\sigma^2$ along empirical chemical freeze-out lines. Their central prediction is conditional: if the freeze-out line passes below and to the left of the first-order transition line, $\kappa\sigma^2$ should first dip near 6 GeV and then form a peak in the 3–5 GeV collision-energy range, which is precisely the window that current heavy-ion data do not yet cover. The point is that this turns a contested phase-structure question into a specific, checkable beam-energy prediction.

What carries the argument

The load-bearing objects are the five-dimensional Einstein–Maxwell–dilaton action with dilaton potential $V(\phi) = -12\cosh[c_1\phi] + (6c_1^2 - \tfrac{3}{2})\phi^2 + c_2\phi^6 + c_3\phi^8$ and gauge kinetic function $Z(\phi) = c_4\,\mathrm{sech}(c_5\phi^3)$, solved as a black hole with metric $ds^2 = -e^{-w(r)}f(r)\,dt^2 + f(r)^{-1}dr^2 + r^2 d\vec{x}^2$. Holographic renormalization of the on-shell action gives the boundary pressure, energy density, and free energy, while the Wald Noether-charge method yields the first law $\delta E = \mu_B\,\delta\rho_B + T\,\delta s$ and, at first order in metric perturbation, the shear-viscosity result $\eta/s = 1/(4\pi) - \lambda_{GB} T/r_h$. The second load-bearing mechanism is the chemical freeze-out line, Eq. (5.2) with the parameters in Table 2: it converts each collision energy $\sqrt{s_{NN}}$ into a curve in the $T$\u2013$\mu_B$ plane, and the predicted $\kappa\sigma^2$ peak appears only for the lines FR-2 and FR-3, which pass below and to the left of the critical end point, rather than for FR-1, which crosses the first-order line. The refined ansatz treats $Z(0)$ as a free parameter rather than forcing $Z(0)=1$, which avoids the high-temperature $\chi_2^B$ overshoot of earlier models.

What would settle it

In a high-statistics fixed-target beam-energy scan, measure the net-proton kurtosis\u2013variance product $\kappa\sigma^2$ at collision energies between 3 and 5 GeV while independently extracting temperature and baryon chemical potential at freeze-out from hadron yields: if no peak appears while the extracted freeze-out points lie on FR-2 or FR-3, the central prediction is falsified. An independent lattice or functional calculation that rules out a first-order transition or critical point near $\mu_B \approx 590$ MeV and $T \approx 102$ MeV would also do so.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central result is that one refined holographic EMD model can do three things at once. Calibrated to zero-density lattice QCD equation-of-state and baryon-number-susceptibility data, it reproduces lattice results at finite baryon density, including higher-order susceptibilities $\chi_4^B$, $\chi_6^B$, $\chi_8^B$. Extrapolated to high density, it yields a critical end point at $T = 102.25$ MeV and $\mu_B = 590.5$ MeV with a first-order transition line at higher chemical potential, located by minimizing free energy. Evaluated along chemical freeze-out lines fitted to measured hadron yields, the susceptibility ratio $\kappa\sigma^2 = \chi_4^B/\chi_2^B$ matches the downward trend of the data between 200 and 7.7 GeV and then, for the two freeze-out lines that stay left of the first-order line, produces a minimum near 6 GeV and a peak near 3–5 GeV. The model thus converts the open question of the critical point's location into a concrete energy window: if freeze-out does not cross the first-order line, the peak should be seen there.

Load-bearing premise

The 3–5 GeV prediction is carried by the empirical chemical freeze-out line fitted to hadron-production data, not by the holographic model itself; if the real freeze-out path crosses the first-order transition line, the predicted $\kappa\sigma^2$ peak disappears.

Editorial extensions

If this is right

  • A first-order phase transition line exists for $\mu_B > 590$ MeV, so the transition sharpens with increasing baryon density, with the critical end point at $T = 102.25$ MeV, $\mu_B = 590.5$ MeV.
  • Along freeze-out lines that match available hadron data, $\kappa\sigma^2$ should dip near 6 GeV and then form a peak in the 3–5 GeV window; this peak is the paper's concrete experimental fingerprint for the critical end point.
  • The model quantitatively reproduces lattice QCD results for pressure, baryon density, and $\chi_2^B$ at $\mu_B/T$ up to 2.5 and for higher-order susceptibilities near the phase boundary, giving a finite-density equation of state usable for other heavy-ion observables.
  • The Wald-formalism calculation fixes the shear-viscosity ratio in Gauss–Bonnet gravity as $\eta/s = 1/(4\pi) - \lambda_{GB} T/r_h$, connecting the critical-point thermodynamics to transport properties within the same framework.
  • If the real freeze-out line behaves like FR-1 and crosses the first-order line, the predicted peak disappears; this conditional structure explains why current data showing no non-monotonic signal above 7.7 GeV do not contradict the model.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If a peak is found in the 3–5 GeV window, it would confirm a critical point near the predicted location only insofar as the freeze-out line is independently known; measuring freeze-out temperatures and baryon chemical potentials in the same collisions would be needed to separate the critical point's position from the path through the phase diagram.
  • The sensitivity of the peak to the freeze-out line can be inverted: the observed absence of a peak above 7.7 GeV, combined with the model's susceptibility ratios, could be used to rule out freeze-out paths that cross the first-order line even before the critical point itself is located.
  • The model is calibrated at zero density and checked at $\mu_B/T \le 2.5$, so its prediction at $\mu_B \approx 590$ MeV involves extrapolation; future lattice data on higher-order baryon susceptibilities at moderate $\mu_B/T$ would directly test that extrapolated region.
  • The same Wald $n-2$ form could be applied to compute bulk viscosity or charge conductivities in the EMD model, extending the framework from equilibrium phase structure to dynamical signatures that may also be critical-point sensitive.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper constructs a refined holographic Einstein-Maxwell-Dilaton (EMD) model for hot and dense QCD matter. It derives thermodynamic quantities via holographic renormalization, proves the first law of thermodynamics using the Wald formalism, and computes the shear viscosity in Gauss-Bonnet gravity. The model is calibrated to lattice QCD data at zero baryon density (equation of state and second-order baryon number susceptibility) and compared with finite-density lattice data for mu_B/T up to 2.5. The central phenomenological claim is that the model places the QCD critical end point at (T, mu_B) = (102.25, 590.5) MeV and, if the chemical freeze-out line does not intersect the first-order transition line, predicts a peak-like structure in kappa sigma^2 (identified with chi_4^B/chi_2^B) in the sqrt(s_NN) = 3-5 GeV range.

Significance. If the CEP prediction and the associated freeze-out-line projection are quantitatively reliable, the paper would provide a specific, falsifiable energy window for the QCD critical end point, which is a central goal of the RHIC beam energy scan program. The model also demonstrates a useful improvement over earlier EMD constructions by allowing a non-unit UV limit of the gauge kinetic function and by achieving good quantitative agreement with lattice data at finite mu_B/T. The derivations in Sections 3 and 4 are detailed and are benchmarked against known results, which is a strength of the manuscript. However, the significance is substantially tempered by the lack of uncertainty propagation and by the fact that the headline prediction is an extrapolation far outside the calibrated region, combined with an externally fitted freeze-out curve.

major comments (4)
  1. [Section 5, Figs. 1-3 and 6] The CEP at (T, mu_B) = (102.25, 590.5) MeV is obtained by extrapolating a model calibrated to lattice data in the region T ~ 130-280 MeV and mu_B/T <= 2.5 to a point with mu_B/T ~ 5.8 and T ~ 102 MeV. No test, cross-validation, or uncertainty estimate is provided for this extrapolation, so the quoted CEP position is not established by the fits shown. Because the 3-5 GeV peak is a projection of this single CEP point onto the freeze-out line, this unsupported extrapolation is load-bearing for the central claim.
  2. [Section 5, Table 1] Table 1 lists eight parameters, but the text only explains how c1 through c5 are fixed by fitting the lattice EoS and chi_2^B. The values of kappa_2^5 = 3.36 pi, b = -0.27435, and phi_s = 1085 MeV are not derived or discussed, even though they control the entropy/energy normalization and the dilaton potential. Without a description of how these parameters are determined or varied, the model is not fully reproducible and the sensitivity of the CEP location to them cannot be assessed.
  3. [Eq. (5.2), Table 2, Figs. 6-8] The predicted peak in chi_4^B/chi_2^B arises only for the empirical freeze-out lines FR-2 and FR-3; FR-1, which is also a representative fit to the hadrochemistry data [73,74], intersects the first-order line and yields no peak. Since the freeze-out parameters in Eq. (5.2) have no quoted uncertainties, the relative placement of the freeze-out curve and the CEP, and therefore the existence and 3-5 GeV location of the peak, is not robust. The paper demonstrates sensitivity to the freeze-out choice but does not quantify it.
  4. [Section 6, Conclusions] The abstract and the body of the paper condition the peak prediction on the chemical freeze-out line not intersecting the first-order transition line, yet the Conclusions state that 'there is a high probability of observing a peak in kappa sigma^2' in the 3-5 GeV range. No probability estimate or uncertainty quantification is given, so this overstatement is not supported by the preceding analysis. The conclusion should preserve the conditional and exploratory nature of the prediction.
minor comments (4)
  1. [Figure 4 and Section 5 text] The text and figure caption contain inconsistent notation: the left panel is described as chi_4^B/chi_4^B in the text but the caption and data are for chi_4^B/chi_2^B; the right panel is labeled chi_6^B/chi_4^B in the text but should be chi_6^B/chi_2^B according to the caption.
  2. [References] References [57] and [68] are the same work (both cite arXiv:2404.12109) and should be merged to avoid duplication.
  3. [Section 5, Fig. 6] The mapping between collision energy sqrt(s_NN) and (T, mu_B) from [69] is used to produce the red holographic points in Fig. 6, but no explicit formula or tabulated values are provided, which makes the conversion difficult to reproduce independently.
  4. [Section 5, Fig. 5] In the paragraph discussing Figure 5, the text refers to 'the chi_4^B' panel but the left panel of the figure is labeled chi_4^B; please clarify whether the mention of 'chi_4' is intended as chi_4^B or a typo.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the refined EMD model is calibrated to zero-density lattice QCD data, and the CEP and kappa-sigma-squared peak are computed outputs rather than refitted inputs.

full rationale

The model parameters in Table 1 are fixed by fitting the zero-density lattice QCD equation of state and chi2_B; the CEP at (T=102.25 MeV, mu_B=590.5 MeV) and the higher-order susceptibility ratios are then obtained by solving the model, not by fitting the quantities they are used to predict. The freeze-out curves FR-1/2/3 are fitted to external hadrochemistry data from Refs. [73,74], and the 3-5 GeV peak in chi4/chi2 appears only when one of these external freeze-out curves passes near the computed CEP; the abstract explicitly conditions the peak on the freeze-out line not intersecting the first-order line. This is a contingent extrapolation, not a fit renamed as a prediction. References [16,39] are benchmarks or extensions of the same potential family, but the central derivation does not reduce to those citations; the first-law and shear-viscosity results are derived in the paper and checked against independent results [54,67]. No equation is defined in terms of the quantity it is used to predict, and no load-bearing uniqueness claim is imported from self-citation. The absence of uncertainty propagation on the CEP and freeze-out line, and the 'high probability' wording in the conclusions, are robustness concerns rather than circularity.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The central claims rest on nine fitted parameter groups (eight for the gravity action plus freeze-out lines) and on the holographic duality premise. The model's predictive power is therefore conditional on the fitted ansatz; the CEP and peak predictions inherit all this fit uncertainty.

free parameters (9)
  • c1 = 0.71
    Controls dilaton potential V(phi); fitted to zero-density lattice EoS (Table 1, Section 5).
  • c2 = 3.7e-3
    Coefficient of phi^6 term in V(phi); fitted to lattice EoS.
  • c3 = 2.8e-5
    New phi^8 coefficient added to improve EoS fit; fitted to lattice EoS.
  • c4 (Z(0)) = 0.35
    UV limit of gauge kinetic function; fitted to chi2_B at zero density; chosen to keep chi2_B below the Stefan-Boltzmann limit.
  • c5 = 0.0925
    Shape parameter of Z(phi)=c4 sech(c5 phi^3); fitted to chi2_B.
  • kappa2_5 = 3.36 pi
    Five-dimensional gravitational constant; sets overall normalization of thermodynamic quantities; fitted.
  • b = -0.27435
    Holographic counterterm coefficient in Eq (2.14); appears in renormalized action; fitted.
  • phi_s = 1085 MeV
    Source of dilaton field, related to QCD scale; fitted.
  • Freeze-out line parameters (T0,d1,d2) = FR-1: 157,60,-2.85; FR-2: 153,100,-2.75; FR-3: 149,135,-2.75
    Parameters in Eq (5.2) fit to empirical T-sqrt(s_NN) and mu_B-sqrt(s_NN) relations [73,74]; FR-2 is best fit, FR-1 and FR-3 are variants to test sensitivity.
assumptions (5)
  • domain assumption Gauge/gravity duality is a valid description of strongly coupled QCD at finite temperature and baryon density.
    The entire EMD holographic construction assumes the 5D gravity theory encodes the boundary field theory; no derivation from QCD is given (Sections 1-2).
  • ad hoc to paper The chosen dilaton potential V(phi) and gauge kinetic function Z(phi) in Eq (5.1) capture the relevant QCD dynamics.
    The functional forms are selected to fit lattice data, not derived from first principles; c3 phi^8 and Z(0)=c4 are new choices.
  • domain assumption The empirical freeze-out parameterization Eq (5.2) correctly connects collision energy to (T, mu_B).
    The kappa sigma squared prediction along collision energy depends on this bridge; parameters are fit to empirical data [73,74] but the mapping is not derived from the holographic model.
  • standard math The in-going boundary condition Eq (4.2) and Noether charge/Wald formalism correctly give shear viscosity.
    These are standard results from [55,65,66]; the paper applies them and checks against [54,67].
  • standard math The minimum of free energy density determines the phase transition and CEP location.
    Standard thermodynamic criterion used to draw the first-order line and CEP in Figure 6; no independent check.

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Cite this review

Pith. "Pith review of Phase transition of hot dense QCD Matter from a refined holographic EMD model." pith.science (2026). https://pith.science/paper/UOOF5Y6E

@misc{pith2026250709113,
  author       = {Pith},
  title        = {Pith review of: Phase transition of hot dense QCD Matter from a refined holographic EMD model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UOOF5Y6E}},
  note         = {Machine review of arXiv:2507.09113}
}
abstract

In this study, we begin by delineating the Einstein-Maxwell-Dilaton (EMD) model within the holographic QCD framework and deriving the equation of state through holographic renormalization. Subsequently, we utilize the Wald method to determine the first law of thermodynamics for a five-dimensional black hole, thereby confirming the alignment of our EMD model with the thermodynamics of the grand canonical ensemble in the boundary field theory. By employing the $n-2$ form in the Wald method, we proceed to calculate the shear viscosity in Gauss-Bonnet gravity. The results we obtain demonstrate consistency with those from first-order metric perturbation. Furthermore, we construct a refined EMD model that attains quantitative agreement with the lattice QCD equation of state and baryon number susceptibility data at finite density. Using this enhanced model, we delve into the investigation of signals related to the QCD phase transition critical endpoint. At present, no non-monotonic changes in $\kappa\sigma^2$ have been observed within the 7$\sim$200 GeV collision energy range at STAR. However, our theoretical analysis suggests that if the chemical freeze-out line does not intersect the first-order phase transition line, a peak-like structure in $\kappa\sigma^2$ is anticipated within the 3$\sim$5 GeV range.

Figures

Figures reproduced from arXiv: 2507.09113 by the authors.

Figure 1
Figure 1. A comparison of the equation of state from our holographic model (red solid curves) [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. The temperature dependence of P/T4 (Left panel) and ϵ/T4 (Right panel) along lines with different µB/T ratios compared with lattice QCD data [61]. The bands show lattice QCD re￾sults, with red solid lines representing holographic QCD predictions. For µB/T = 0, 1, 2, and 2.5 , the holographic model aligns well with lattice QCD between T = 130 ∼ 280 MeV. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. A comparison of the temperature dependence of ∆ [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Baryon number susceptibility χ B 4 /χB 2 (Left panel) and χ B 6 /χB 2 (Right panel) at µB = 0. The red solid line shows the holographic QCD results. Orange and blue data points with error bars respectively represent lattice QCD data for Nτ = 6 and Nτ = 8 and the green …
Figure 5
Figure 5. Figure 5: Comparisons of holographic results (red solid lines) and lattice QCD data. From left [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: The phase diagram (Top-left panel), χ B 2 /χB 1 (Top-right panel), χ B 3 /χB 2 (Bottom-left panel) and χ B 4 /χB 2 (Bottom-right panel) in holographic QCD model. The green dot represents the CEP (T = 102.25 MeV, µB = 590.5 MeV) and the green line stands for the first o…
Figure 7
Figure 7. Figure 7: The red, cyan, and orange lines indicate the three fitted chemical freeze-out lines. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Behavior of χ B 4 /χB 2 with collision energy √ SNN along the three fitted chemical freeze￾out lines. Blue data points with error bars represent STAR data [63]. Gray and green bands represent lattice QCD [3, 70] and UrQMD results [71, 72], respectively. In [PITH_FULL_…

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Reference graph

Works this paper leans on

73 extracted references · 18 canonical work pages · cited by 1 Pith paper

  1. [16]

    Holographic study of higher-order baryon number susceptibilities at finite temperature and density,

    Z. Li, J. Liang, S. He, and L. Li, “Holographic study of higher-order baryon number susceptibilities at finite temperature and density,” Phys. Rev. D 108 no. 4, (2023) 046008, arXiv:2305.13874 [hep-ph]

    arXiv 2023

  2. [1]

    Cluster Expansion Model for QCD Baryon Number Fluctuations: No Phase Transition at µB/T < π,

    V. Vovchenko, J. Steinheimer, O. Philipsen, and H. Stoecker, “Cluster Expansion Model for QCD Baryon Number Fluctuations: No Phase Transition at µB/T < π,” Phys. Rev. D 97 no. 11, (2018) 114030, arXiv:1711.01261 [hep-ph]

    arXiv 2018

  3. [2]

    QCD Crossover at Finite Chemical Potential from Lattice Simulations,

    S. Borsanyi, Z. Fodor, J. N. Guenther, R. Kara, S. D. Katz, P. Parotto, A. Pasztor, C. Ratti, and K. K. Szabo, “QCD Crossover at Finite Chemical Potential from Lattice Simulations,” Phys. Rev. Lett. 125 no. 5, (2020) 052001, arXiv:2002.02821 [hep-lat]

    arXiv 2020

  4. [3]

    Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data,

    A. Bazavov et al., “Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data,” Phys. Rev. D 101 no. 7, (2020) 074502, arXiv:2001.08530 [hep-lat]

    arXiv 2020

  5. [4]

    Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme,

    S. Bors´ anyi, Z. Fodor, J. N. Guenther, R. Kara, S. D. Katz, P. Parotto, A. P´ asztor, C. Ratti, and K. K. Szab´ o, “Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme,” Phys. Rev. Lett. 126 no. 23, (2021) 232001, arXiv:2102.06660 [hep-lat]

    arXiv 2021

  6. [5]

    Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at non-vanishing net baryon-number density,

    D. Bollweg, D. A. Clarke, J. Goswami, O. Kaczmarek, F. Karsch, S. Mukherjee, P. Petreczky, C. Schmidt, and S. Sharma, “Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at non-vanishing net baryon-number density,” arXiv:2212.09043 [hep-lat]

    arXiv

  7. [6]

    Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density,

    O. Philipsen, “Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density,” Symmetry 13 no. 11, (2021) 2079, arXiv:2111.03590 [hep-lat]. 19

    arXiv 2021

  8. [7]

    Third moments of conserved charges as probes of QCD phase structure,

    M. Asakawa, S. Ejiri, and M. Kitazawa, “Third moments of conserved charges as probes of QCD phase structure,” Phys. Rev. Lett. 103 (2009) 262301, arXiv:0904.2089 [nucl-th]

    arXiv 2009

Show all 73 references
  1. [8]

    QCD critical region and higher moments for three flavor models,

    B. J. Schaefer and M. Wagner, “QCD critical region and higher moments for three flavor models,” Phys. Rev. D 85 (2012) 034027, arXiv:1111.6871 [hep-ph]

    2012 arXiv

  2. [9]

    Mapping the QCD phase diagram with susceptibilities of conserved charges within Nambu–Jona-Lasinio model,

    W. Fan, X. Luo, and H.-S. Zong, “Mapping the QCD phase diagram with susceptibilities of conserved charges within Nambu–Jona-Lasinio model,” Int. J. Mod. Phys. A 32 no. 11, (2017) 1750061, arXiv:1608.07903 [hep-ph]

    2017 arXiv

  3. [10]

    Susceptibilities from a black hole engineered EoS with a critical point,

    I. Portillo, “Susceptibilities from a black hole engineered EoS with a critical point,” J. Phys. Conf. Ser. 832 no. 1, (2017) 012041, arXiv:1610.09981 [nucl-th]

    2017 arXiv

  4. [11]

    Probing the QCD phase structure with higher order baryon number susceptibilities within the NJL model,

    W. Fan, X. Luo, and H. Zong, “Probing the QCD phase structure with higher order baryon number susceptibilities within the NJL model,” Chin. Phys. C 43 no. 3, (2019) 033103, arXiv:1702.08674 [hep-ph]

    2019 arXiv

  5. [12]

    Locating the QCD critical end point through the peaked baryon number susceptibilities along the freeze-out line,

    Z. Li, Y. Chen, D. Li, and M. Huang, “Locating the QCD critical end point through the peaked baryon number susceptibilities along the freeze-out line,” Chin. Phys. C 42 no. 1, (2018) 013103, arXiv:1706.02238 [hep-ph]

    2018 arXiv

  6. [13]

    The kurtosis of net baryon number fluctuations from a realistic Polyakov–Nambu–Jona-Lasinio model along the experimental freeze-out line,

    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 no. 3, (2019) 245, arXiv:1801.09215 [hep-ph]

    2019 arXiv

  7. [14]

    Hyper-order baryon number fluctuations at finite temperature and density,

    W.-j. Fu, X. Luo, J. M. Pawlowski, F. Rennecke, R. Wen, and S. Yin, “Hyper-order baryon number fluctuations at finite temperature and density,” Phys. Rev. D 104 no. 9, (2021) 094047, arXiv:2101.06035 [hep-ph]

    2021 arXiv

  8. [15]

    Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model*,

    Y.-P. Zhao, C.-Y. Wang, S.-Y. Zuo, and C.-M. Li, “Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model*,” Chin. Phys. C 47 no. 5, (2023) 053103, arXiv:2302.12010 [hep-ph]

    2023 arXiv

  9. [17]

    On the sign of kurtosis near the QCD critical point,

    M. A. Stephanov, “On the sign of kurtosis near the QCD critical point,” Phys. Rev. Lett. 107 (2011) 052301, arXiv:1104.1627 [hep-ph]

    2011 arXiv

  10. [18]

    Bulk Properties of the Medium Produced in Relativistic Heavy-Ion Collisions from the Beam Energy Scan Program,

    STAR Collaboration, L. Adamczyk et al., “Bulk Properties of the Medium Produced in Relativistic Heavy-Ion Collisions from the Beam Energy Scan Program,” Phys. Rev. C 96 no. 4, (2017) 044904, arXiv:1701.07065 [nucl-ex]. 20

    2017 arXiv

  11. [19]

    Baryon susceptibilities from a holographic equation of state,

    I. Portillo, “Baryon susceptibilities from a holographic equation of state,” Nucl. Phys. A 967 (2017) 916–919, arXiv:1705.01021 [nucl-th]

    2017 arXiv

  12. [20]

    Quark matter under rotation in the NJL model with vector interaction,

    X. Wang, M. Wei, Z. Li, and M. Huang, “Quark matter under rotation in the NJL model with vector interaction,” Phys. Rev. D 99 no. 1, (2019) 016018, arXiv:1808.01931 [hep-ph]

    2019 arXiv

  13. [21]

    QCD Matter and Phase Transitions under Extreme Conditions,

    M. Huang and P. Zhuang, “QCD Matter and Phase Transitions under Extreme Conditions,” Symmetry 15 no. 2, (2023) 541

    2023

  14. [22]

    Precision Measurement of (Net-)proton Number Fluctuations in Au+Au Collisions at RHIC,

    STAR Collaboration, “Precision Measurement of (Net-)proton Number Fluctuations in Au+Au Collisions at RHIC,” arXiv:2504.00817 [nucl-ex]

    arXiv

  15. [23]

    A holographic critical point,

    O. DeWolfe, S. S. Gubser, and C. Rosen, “A holographic critical point,” Phys. Rev. D 83 (2011) 086005, arXiv:1012.1864 [hep-th]

    2011 arXiv

  16. [24]

    Dynamic critical phenomena at a holographic critical point,

    O. DeWolfe, S. S. Gubser, and C. Rosen, “Dynamic critical phenomena at a holographic critical point,” Phys. Rev. D 84 (2011) 126014, arXiv:1108.2029 [hep-th]

    2011 arXiv

  17. [25]

    A hQCD model and its phase diagram in Einstein-Maxwell-Dilaton system,

    R.-G. Cai, S. He, and D. Li, “A hQCD model and its phase diagram in Einstein-Maxwell-Dilaton system,” JHEP 03 (2012) 033, arXiv:1201.0820 [hep-th]

    2012 arXiv

  18. [26]

    Some aspects of QGP phase in a hQCD model,

    R.-G. Cai, S. Chakrabortty, S. He, and L. Li, “Some aspects of QGP phase in a hQCD model,” JHEP 02 (2013) 068, arXiv:1209.4512 [hep-th]

    2013 arXiv

  19. [27]

    Holographic calculation of the electric conductivity of the strongly coupled quark-gluon plasma near the deconfinement transition,

    S. I. Finazzo and J. Noronha, “Holographic calculation of the electric conductivity of the strongly coupled quark-gluon plasma near the deconfinement transition,” Phys. Rev. D 89 no. 10, (2014) 106008, arXiv:1311.6675 [hep-th]

    2014 arXiv

  20. [28]

    A Refined Holographic QCD Model and QCD Phase Structure,

    Y. Yang and P.-H. Yuan, “A Refined Holographic QCD Model and QCD Phase Structure,” JHEP 11 (2014) 149, arXiv:1406.1865 [hep-th]

    2014 arXiv

  21. [29]

    Critical point in the phase diagram of primordial quark-gluon matter from black hole physics,

    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 no. 9, (2017) 096026, arXiv:1706.00455 [nucl-th]

    2017 arXiv

  22. [30]

    Gravitation waves from QCD and electroweak phase transitions,

    Y. Chen, M. Huang, and Q.-S. Yan, “Gravitation waves from QCD and electroweak phase transitions,” JHEP 05 (2018) 178, arXiv:1712.03470 [hep-ph]

    2018 arXiv

  23. [31]

    Holographic QCD phase diagram with critical point from Einstein–Maxwell-dilaton dynamics,

    J. Knaute, R. Yaresko, and B. K¨ ampfer, “Holographic QCD phase diagram with critical point from Einstein–Maxwell-dilaton dynamics,” Phys. Lett. B 778 (2018) 419–425, arXiv:1702.06731 [hep-ph]

    2018 arXiv

  24. [32]

    Chiral phase transition and QCD phase diagram from AdS/QCD,

    Z. Fang, Y.-L. Wu, and L. Zhang, “Chiral phase transition and QCD phase diagram from AdS/QCD,” Phys. Rev. D 99 no. 3, (2019) 034028, arXiv:1810.12525 [hep-ph]. 21

    2019 arXiv

  25. [33]

    Criticality from Einstein-Maxwell-dilaton holography at finite temperature and density,

    A. Ballon-Bayona, H. Boschi-Filho, E. F. Capossoli, and D. M. Rodrigues, “Criticality from Einstein-Maxwell-dilaton holography at finite temperature and density,” Phys. Rev. D 102 no. 12, (2020) 126003, arXiv:2006.08810 [hep-th]

    2020 arXiv

  26. [34]

    Analytic Study on Chiral Phase Transition in Holographic QCD,

    M.-W. Li, Y. Yang, and P.-H. Yuan, “Analytic Study on Chiral Phase Transition in Holographic QCD,” JHEP 02 (2021) 055, arXiv:2009.05694 [hep-th]

    2021 arXiv

  27. [35]

    Hot and dense quark-gluon plasma thermodynamics from holographic black holes,

    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 no. 3, (2021) 034002, arXiv:2102.12042 [nucl-th]

    2021 arXiv

  28. [36]

    Gravitational waves and primordial black hole productions from gluodynamics by holography,

    S. He, L. Li, Z. Li, and S.-J. Wang, “Gravitational waves and primordial black hole productions from gluodynamics by holography,” Sci. China Phys. Mech. Astron. 67 no. 4, (2024) 240411, arXiv:2210.14094 [hep-ph]

    2024 arXiv

  29. [37]

    QCD Equilibrium and Dynamical Properties from Holographic Black Holes,

    J. Grefa, M. Hippert, J. Noronha, J. Noronha-Hostler, I. Portillo, C. Ratti, and R. Rougemont, “QCD Equilibrium and Dynamical Properties from Holographic Black Holes,” Rev. Mex. Fis. Suppl. 3 no. 4, (2022) 040910, arXiv:2207.12564 [nucl-th]

    2022 arXiv

  30. [38]

    Machine learning holographic black hole from lattice QCD equation of state,

    X. Chen and M. Huang, “Machine learning holographic black hole from lattice QCD equation of state,” Phys. Rev. D 109 no. 5, (2024) L051902, arXiv:2401.06417 [hep-ph]

    2024 arXiv

  31. [39]

    Probing QCD critical point and induced gravitational wave by black hole physics,

    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 no. 12, (2022) L121902, arXiv:2201.02004 [hep-th]

    2022 arXiv

  32. [40]

    Bayesian location of the QCD critical point from a holographic perspective,

    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 no. 9, (2024) 094006, arXiv:2309.00579 [nucl-th]

    2024 arXiv

  33. [41]

    Neural network modeling of heavy-quark potential from holography,

    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 no. 6, (2025) 637, arXiv:2408.03784 [hep-ph]

    2025 arXiv

  34. [42]

    Bayesian Inference of the Critical Endpoint in 2+1-Flavor System from Holographic QCD,

    L. Zhu, X. Chen, K. Zhou, H. Zhang, and M. Huang, “Bayesian Inference of the Critical Endpoint in 2+1-Flavor System from Holographic QCD,” arXiv:2501.17763 [hep-ph]

    arXiv

  35. [43]

    High-precise determination of critical exponents in holographic QCD,

    F. Sun, X. Chen, S. Li, and A. Watanabe, “High-precise determination of critical exponents in holographic QCD,” arXiv:2503.17642 [hep-ph]

    arXiv

  36. [44]

    Holographic entanglement properties in the QCD phase diagram from Einstein-Maxwell-dilaton models,

    Z. Li, “Holographic entanglement properties in the QCD phase diagram from Einstein-Maxwell-dilaton models,” Phys. Rev. D 110 no. 4, (2024) 046012, arXiv:2402.02944 [hep-th]. 22

    2024 arXiv

  37. [45]

    Jet quenching and quark energy loss from holographic QCD,

    Z. Li, D. Li, and M. Huang, “Jet quenching and quark energy loss from holographic QCD,” Phys. Rev. D 111 no. 12, (2025) 126019, arXiv:2504.04147 [hep-ph]

    2025 arXiv

  38. [46]

    Black hole entropy is the Noether charge,

    R. M. Wald, “Black hole entropy is the Noether charge,” Phys. Rev. D 48 no. 8, (1993) R3427–R3431, arXiv:gr-qc/9307038

    1993 arXiv

  39. [47]

    Some properties of Noether charge and a proposal for dynamical black hole entropy,

    V. Iyer and R. M. Wald, “Some properties of Noether charge and a proposal for dynamical black hole entropy,” Phys. Rev. D 50 (1994) 846–864, arXiv:gr-qc/9403028

    1994 arXiv

  40. [48]

    Scalar Charges in Asymptotic AdS Geometries,

    H.-S. Liu and H. L¨ u, “Scalar Charges in Asymptotic AdS Geometries,” Phys. Lett. B 730 (2014) 267–270, arXiv:1401.0010 [hep-th]

    2014 arXiv

  41. [49]

    Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity,

    H. Lu, C. N. Pope, and Q. Wen, “Thermodynamics of AdS Black Holes in Einstein-Scalar Gravity,” JHEP 03 (2015) 165, arXiv:1408.1514 [hep-th]

    2015 arXiv

  42. [50]

    Holographic Heat Current as Noether Current,

    H.-S. Liu, H. Lu, and C. N. Pope, “Holographic Heat Current as Noether Current,” JHEP 09 (2017) 146, arXiv:1708.02329 [hep-th]

    2017 arXiv

  43. [51]

    On Thermodynamics of AdS Black Holes with Scalar Hair,

    L. Li, “On Thermodynamics of AdS Black Holes with Scalar Hair,” Phys. Lett. B 815 (2021) 136123, arXiv:2008.05597 [gr-qc]

    2021 arXiv

  44. [52]

    Strongly coupled quark-gluon plasma in heavy ion collisions,

    E. Shuryak, “Strongly coupled quark-gluon plasma in heavy ion collisions,” Rev. Mod. Phys. 89 (2017) 035001, arXiv:1412.8393 [hep-ph]

    2017 arXiv

  45. [53]

    Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant,

    X.-H. Ge and S.-J. Sin, “Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant,” JHEP 05 (2009) 051, arXiv:0903.2527 [hep-th]

    2009 arXiv

  46. [54]

    Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography,

    C. Charmousis, B. Gouteraux, and E. Kiritsis, “Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography,” JHEP 09 (2012) 011, arXiv:1206.1499 [hep-th]

    2012 arXiv

  47. [55]

    Note on the Noether charge and holographic transports,

    Z.-Y. Fan, “Note on the Noether charge and holographic transports,” Phys. Rev. D 97 no. 6, (2018) 066013, arXiv:1801.07870 [hep-th]

    2018 arXiv

  48. [56]

    Hot QCD Phase Diagram From Holographic Einstein-Maxwell-Dilaton Models,

    R. Rougemont, J. Grefa, M. Hippert, J. Noronha, J. Noronha-Hostler, I. Portillo, and C. Ratti, “Hot QCD Phase Diagram From Holographic Einstein-Maxwell-Dilaton Models,” arXiv:2307.03885 [nucl-th]

    arXiv

  49. [58]

    Refining holographic models of the quark-gluon plasma,

    N. Jokela, M. J¨ arvinen, and A. Piispa, “Refining holographic models of the quark-gluon plasma,” Phys. Rev. D 110 no. 12, (2024) 126013, arXiv:2405.02394 [hep-th]

    2024 arXiv

  50. [59]

    Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the 23 hadron resonance gas model,

    HotQCD Collaboration, A. Bazavov et al., “Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the 23 hadron resonance gas model,” Phys. Rev. D 86 (2012) 034509, arXiv:1203.0784 [hep-lat]

    2012 arXiv

  51. [60]

    Equation of state in ( 2+1 )-flavor QCD,

    HotQCD Collaboration, A. Bazavov et al., “Equation of state in ( 2+1 )-flavor QCD,” Phys. Rev. D 90 (2014) 094503, arXiv:1407.6387 [hep-lat]

    2014 arXiv

  52. [61]

    The QCD Equation of State to O(µ6 B) from Lattice QCD,

    A. Bazavov et al., “The QCD Equation of State to O(µ6 B) from Lattice QCD,” Phys. Rev. D 95 no. 5, (2017) 054504, arXiv:1701.04325 [hep-lat]

    2017 arXiv

  53. [62]

    Taylor expansions and Pad´ e approximants for cumulants of conserved charge fluctuations at nonvanishing chemical potentials,

    HotQCD Collaboration, D. Bollweg, J. Goswami, O. Kaczmarek, F. Karsch, S. Mukherjee, P. Petreczky, C. Schmidt, and P. Scior, “Taylor expansions and Pad´ e approximants for cumulants of conserved charge fluctuations at nonvanishing chemical potentials,” Phys. Rev. D 105 no. 7, ...

    2022 arXiv

  54. [63]

    Energy Dependence of Moments of Net-Proton, Net-Kaon, and Net-Charge Multiplicity Distributions at STAR,

    J. Xu, “Energy Dependence of Moments of Net-Proton, Net-Kaon, and Net-Charge Multiplicity Distributions at STAR,” J. Phys. Conf. Ser. 736 no. 1, (2016) 012002, arXiv:1611.07134 [hep-ex]

    2016 arXiv

  55. [64]

    Measurements of Proton High Order Cumulants in √sNN = 3 GeV Au+Au Collisions and Implications for the QCD Critical Point,

    STAR Collaboration, M. S. Abdallah et al., “Measurements of Proton High Order Cumulants in √sNN = 3 GeV Au+Au Collisions and Implications for the QCD Critical Point,” Phys. Rev. Lett. 128 no. 20, (2022) 202303, arXiv:2112.00240 [nucl-ex]

    2022

  56. [65]

    Thermodynamical First Laws of Black Holes in Quadratically-Extended Gravities,

    Z.-Y. Fan and H. Lu, “Thermodynamical First Laws of Black Holes in Quadratically-Extended Gravities,” Phys. Rev. D 91 no. 6, (2015) 064009, arXiv:1501.00006 [hep-th]

    2015 arXiv

  57. [66]

    AdS and Lifshitz Scalar Hairy Black Holes in Gauss-Bonnet Gravity,

    B. Chen, Z.-Y. Fan, and L.-Y. Zhu, “AdS and Lifshitz Scalar Hairy Black Holes in Gauss-Bonnet Gravity,” Phys. Rev. D 94 no. 6, (2016) 064005, arXiv:1604.08282 [hep-th]

    2016 arXiv

  58. [67]

    Viscosity Bound Violation in Higher Derivative Gravity,

    M. Brigante, H. Liu, R. C. Myers, S. Shenker, and S. Yaida, “Viscosity Bound Violation in Higher Derivative Gravity,” Phys. Rev. D 77 (2008) 126006, arXiv:0712.0805 [hep-th]

    2008 arXiv

  59. [68]

    Revisiting holographic model for thermal and dense QCD with a critical point,

    Q. Fu, S. He, L. Li, and Z. Li, “Revisiting holographic model for thermal and dense QCD with a critical point,” arXiv:2404.12109 [hep-ph]

    arXiv

  60. [69]

    Freeze-out and thermalization in relativistic heavy ion collisions,

    S. Gupta, D. Mallick, D. K. Mishra, B. Mohanty, and N. Xu, “Freeze-out and thermalization in relativistic heavy ion collisions,” arXiv:2004.04681 [hep-ph]

    2004 arXiv

  61. [70]

    Strangeness-correlations on the pseudocritical line in (2+1)-flavor QCD,

    D. Bollweg, H. T. Ding, J. Goswami, F. Karsch, S. Mukherjee, P. Petreczky, and C. Schmidt, “Strangeness-correlations on the pseudocritical line in (2+1)-flavor QCD,” Phys. Rev. D 110 no. 5, (2024) 054519, arXiv:2407.09335 [hep-lat]

    2024 arXiv

  62. [71]

    Microscopic models for ultrarelativistic heavy ion collisions,

    S. A. Bass et al., “Microscopic models for ultrarelativistic heavy ion collisions,” Prog. Part. Nucl. Phys. 41 (1998) 255–369, arXiv:nucl-th/9803035. 24

    1998 arXiv

  63. [72]

    Relativistic hadron hadron collisions in the ultrarelativistic quantum molecular dynamics model,

    M. Bleicher et al., “Relativistic hadron hadron collisions in the ultrarelativistic quantum molecular dynamics model,” J. Phys. G 25 (1999) 1859–1896, arXiv:hep-ph/9909407

    1999 arXiv

  64. [73]

    The Horn, the hadron mass spectrum and the QCD phase diagram: The Statistical model of hadron production in central nucleus-nucleus collisions,

    A. Andronic, P. Braun-Munzinger, and J. Stachel, “The Horn, the hadron mass spectrum and the QCD phase diagram: The Statistical model of hadron production in central nucleus-nucleus collisions,” Nucl. Phys. A 834 (2010) 237C–240C, arXiv:0911.4931 [nucl-th]

    2010 arXiv

  65. [74]

    Decoding the phase structure of QCD via particle production at high energy,

    A. Andronic, P. Braun-Munzinger, K. Redlich, and J. Stachel, “Decoding the phase structure of QCD via particle production at high energy,” Nature 561 no. 7723, (2018) 321–330, arXiv:1710.09425 [nucl-th]. 25

    2018 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.