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REVIEW 4 major objections 4 minor 49 references

Effects of Born-Infeld Electrodynamics on Chiral Symmetry Restoration and Meson Susceptibilities in Holographic QCD

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Born-Infeld nonlinearity in the holographic dual of QCD shifts the chiral phase boundary to higher temperatures without changing the transition order or introducing a critical endpoint.

desk verdict A standard soft-wall calculation with a new Born-Infield twist, but the scalar-sector metric uses the wrong conformal factor, so the headline beta-shift may be an artifact. read the letter →

arxiv 2608.09489 v1 pith:KTFTRG4I submitted 2026-08-10 hep-ph hep-lathep-th

Hiwa A. Ahmed , Peshwaz A. Abdoul This is my paper · ORCID
classification hep-phhep-lathep-th
keywords holographicQCDchiralsymmetryrestorationBorn-Infeldelectrodynamicssoft-wallAdS/QCDphasetransitionmesonsusceptibilitiesfinitechemicalpotentialcriticalendpoint
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

Within a soft-wall holographic QCD model built on a charged Born-Infeld black hole background, the paper tries to establish that the nonlinearity scale $\beta$ of the bulk electromagnetic sector controls the location of the chiral phase boundary without controlling its nature. The chiral condensate, extracted from the near-boundary behavior of a bulk scalar field, is the order parameter, and it gives a crossover at physical quark masses ($T_{pc}=0.1477$ GeV), a first-order transition in the chiral limit ($T_c=0.1337$ GeV), and a critical strange quark mass $m_s=37$ MeV separating first- and second-order regions at vanishing light quark mass. The genuinely new claim is that decreasing $\beta$ shifts the second-order transition line in the $T$–$\mu$ plane to higher temperatures at fixed chemical potential, so the chirally broken phase becomes harder to melt, while the transition order and the absence of a critical endpoint are unchanged. The same shift is seen in the meson-susceptibility difference $\chi_\pi-\chi_\sigma$, which melts exactly where the condensate drops. A sympathetic reader would care because this isolates a concrete parameter of the holographic model that future finite-density data could fix, and it shows that short-distance nonlinear electrodynamics can leave phase structure qualitatively intact while moving quantitative boundaries.

What carries the argument

The central object is the charged Born-Infeld black hole in five-dimensional anti-de Sitter space, used as the fixed background of the soft-wall model. Its metric function $f(z)$ (Eq. 12) and Hawking temperature (Eq. 13) carry the $\beta$ dependence that enters the scalar equations of motion, while the chiral condensate $\sigma_f$ is read off from the ultraviolet asymptotic coefficient of the bulk scalar field $\chi_f(z)$. The scalar and pseudoscalar susceptibilities are computed from the on-shell actions of the $\sigma$ and pion fluctuations; the difference $\chi_\pi-\chi_\sigma$ pinpoints where the chiral gap closes. These objects together turn the Born-Infeld scale into a predictor for the phase boundary.

What would settle it

Solve the full Einstein–dilaton–scalar system with backreaction in the Born-Infeld background and recompute the $\beta$-dependence of $T_c$; if the upward shift with decreasing $\beta$ disappears or reverses sign, the claimed stabilization is an artifact of the probe approximation. Alternatively, a lattice QCD determination of the chiral transition temperature at finite isospin density that contradicts the predicted shift would settle the matter.

Watch

Extended reading notes

Core claim

The discovery the authors report is that the Born-Infeld parameter $\beta$ acts as a tunable scale that modifies the chiral phase diagram in the soft-wall AdS/QCD model without changing the order of the transition. At zero chemical potential the critical temperature is identical ($T_c=0.1474$ GeV) for the Reissner–Nordström background and for all finite $\beta$, showing the nonlinear effect is strictly coupled to charge density. At finite density, smaller $\beta$ raises $T_c$; for example at $\mu=0.55$ GeV the critical temperature is $0.0483$ GeV in the Reissner–Nordström limit and rises to $0.0600$ GeV at $\beta=1$ GeV. Throughout the studied range the chiral transition stays second order and no critical endpoint appears. The susceptibility difference $\chi_\pi-\chi_\sigma$ decays rapidly with temperature and converges at the same $T_c$, confirming the condensate-based phase boundary.

Load-bearing premise

The finite-density result rests on evaluating the chiral sector on a fixed Born-Infeld black hole background without backreaction, and on scanning $\beta$ from 1 to 20 GeV without any QCD observable that fixes its physical value.

Editorial extensions

If this is right

  • The Born-Infeld scale becomes a physically meaningful parameter of the model: a future QCD-derived value of $\beta$ would fix the location of the chiral boundary at finite density.
  • Because $\beta$ does not change the transition order, searches for a critical endpoint in this soft-wall class should look to other mechanisms, such as backreaction or a different dilaton profile, rather than to nonlinear electrodynamics.
  • The $\beta$ effect vanishes at $\mu=0$, so distinguishing the Born-Infeld background requires finite-density data, not zero-density lattice or experiment.
  • The susceptibility difference provides a concrete holographic counterpart to lattice meson screening-mass observables, allowing a quantitative cross-check of the predicted $T_c$ shift.

Reading between the lines

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

  • The paper leaves $\beta$ unfixed by any QCD observable; fitting $\beta$ to, say, the curvature of the phase boundary at small $\mu$ or to meson spectral data would test whether values around 1–20 GeV are the physically relevant range.
  • Because the computation is probe-like, the quantitative shift of $T_c$ is conditional on the background remaining fixed; a backreacted calculation could weaken, strengthen, or reverse the shift, so the magnitude should be read as a model prediction rather than a robust QCD number.
  • Since the Born-Infeld action is the low-energy effective action of D-branes, the same $\beta$ should also appear in transport coefficients such as electrical conductivity or shear viscosity of the dual plasma, offering an independent holographic test.
  • The phase boundary flattens at high $\mu$ for small $\beta$; mapping the region of very small $\beta$ or $\mu>1.2$ GeV could reveal whether the absence of a critical endpoint is robust or just an artifact of the scanned window.
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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 manuscript constructs a soft-wall AdS/QCD model in a charged Born-Infeld (BI) black hole background and numerically solves the bulk scalar equations to obtain the chiral condensate as a function of temperature and chemical potential, for different values of the BI parameter β. It reports a crossover at physical quark masses with T_pc = 0.1477 GeV, a first-order transition in the chiral limit at T_c = 0.1337 GeV, a critical strange quark mass m_s = 37 MeV at zero light quark mass, a second-order transition line for m_l = 0, m_s = 95 MeV with T_c decreasing as μ increases, and an upward shift of the transition temperature as β decreases, with no change in transition order and no critical endpoint. The conclusions are supported by the behavior of the meson susceptibility difference (χ_π − χ_σ).

Significance. If the results were correct, the paper would provide a concrete demonstration that nonlinear Born-Infeld electrodynamics in the bulk can systematically shift the chiral phase boundary without changing its order, and the susceptibility analysis would provide an independent confirmation. The paper is written transparently: the equations of motion, boundary conditions, and numerical shooting method are stated explicitly, which is a strength. However, the central quantitative claim is currently undermined by a metric-frame inconsistency in the scalar action, and the absolute value of T_pc is largely an input of the parameter fit rather than an independent output. The qualitative framework is interesting, but the numbers in their present form cannot be considered a reliable prediction of the BI background.

major comments (4)
  1. [Section III, Eq. (22); Section II, Eq. (12)] The scalar equations of motion are not evaluated on the BI black hole metric of Section II. For the conformal metric ds^2 = e^{2A_s}(-F dt^2 + dz^2/F + dx^2) with A_s = -log z, the EOM in Eq. (22) should contain F(z) and F'(z) in place of f(z) and f'(z). Since Eq. (12) is the r-coordinate metric function expressed in z = 1/r, the correct conformal blackening factor is F(z) = z^2 f(z). Substituting f for F changes the damping coefficient from -3/z - Φ' + F'/F to -3/z - Φ' + f'/f = -5/z - Φ' + F'/F and multiplies the potential term by z^2 relative to the correct expression. The beta-dependence of the condensate is therefore computed for a different background, not the BI black hole of Section II. This is load-bearing because the central claim is precisely that decreasing β shifts the phase boundary; the numerics must be redone with F(z).
  2. [Section V] The statement that the model parameters are chosen to achieve a pseudocritical temperature of approximately 145 MeV means that the reported T_pc = 0.1477 GeV is not an independent prediction but essentially an output of the fitting procedure. This would be acceptable if the parameters were fixed by other observables, but the paper also uses the same fitted model to compute the β-shift. After the metric-frame correction, the parameters and all reported T_c values would need to be refit, so the absolute numbers in Table II and the abstract should be presented as model outputs of a fitted model, not as independent predictions.
  3. [Section VIII and Table II] Table II lists critical temperatures T_c for the RN and BI backgrounds at several chemical potentials, but these values are obtained from the susceptibility difference with a physical light quark mass m_l = 7 MeV, as stated in Section VIII, whereas the phase diagram in Fig. 8 and the T_c values quoted in Sections VI and VII are for m_l = 0. For m_l = 7 MeV the transition is a crossover, so the susceptibility difference yields a pseudocritical temperature, not the second-order critical temperature of the m_l = 0 case. The table and the text should clearly distinguish the two quantities.
  4. [Section VII, Fig. 7] The text in Section VII states that the chiral transition is second-order throughout the studied range, but the caption of Fig. 7 describes the μ = 0.6 GeV curves as a 'smooth crossover transition.' For an exactly massless light quark (m_l = 0), a continuous transition is second-order, not a crossover; the terminology should be made consistent, or the precise quark mass used in the finite-μ calculation should be stated.
minor comments (4)
  1. [Fig. 2 caption] The caption mentions m_s = 1 GeV and m_c = 3 GeV, which does not match the text description of the three-flavor system with physical quark masses (m_l = 3.5 MeV, m_s = 95 MeV); please correct the caption.
  2. [Section VI and Table II] The values T_c = 0.1475 GeV (Section VI) and 0.1474 GeV (Table II) for the same point should be unified.
  3. [Eq. (12)] The hypergeometric function 2F1 is used without being defined; please add a definition or reference.
  4. [Table I] The parameter table does not list the quark masses m_l and m_s, even though they are inputs of the calculation; please add them.

Circularity Check

2 steps flagged · score 6.0 of 10

The mu=0 pseudocritical temperature is a fit target, not an independent prediction; the Born-Infeld phase-boundary shift is not fitted and has independent model content.

  1. fitted input called prediction [Section V (parameter fixing) versus Abstract and Section VI (RN background result)]
    "The model parameters are listed in Table I. These parameters are chosen to achieve a physical mass of the rho meson and a pseudocritical temperature of approximately 145 MeV at zero chemical potential. ... At zero chemical potential, we find a chiral crossover transition for physical quark masses with a pseudocritical temperature of Tpc=0.1477 GeV."

    The pseudocritical temperature at zero chemical potential is exactly the quantity used to tune the model parameters. Section V states that the parameters were chosen to achieve a pseudocritical temperature of approximately 145 MeV at zero chemical potential; the abstract and Section VI then report Tpc=0.1477 GeV as a derived result. The reported number is therefore the residual of a fit rather than an independent prediction. The BI parameter scan is not affected, since the fit is performed in the RN limit and beta is varied afterward, but this particular headline quantity reduces by construction to its input.

  2. self citation load bearing [Section IV.A, after Eq. (40), scalar susceptibility normalization]
    "A comparison of Eq. (40) with the direct method for determining χσ, which involves differentiating the chiral condensate with respect to the light quark mass, indicates that a normalization factor (ζ2/4) must be included in Eq. (40) (see the proof in Ref. [45])."

    The proof of the normalization factor required to define the scalar susceptibility is delegated to Ref. [45], a previous paper with the same first author. The susceptibilities are then presented as an independent confirmation of the phase boundary computed from the condensate. This makes the validation partly dependent on a self-citation for a needed formula, though it is a supporting normalization for an auxiliary observable rather than the source of the beta-dependent phase-boundary shift.

full rationale

The core Born-Infeld result is not circular: after fixing parameters in the RN (large-beta) limit, the paper scans beta and finds that smaller beta shifts the second-order line to higher temperature. That shift is internally computed and is not a fit target. However, the paper explicitly tunes its model to a pseudocritical temperature of roughly 145 MeV at zero chemical potential, then reports Tpc=0.1477 GeV as a finding. That is a fitted input presented as a prediction, so one headline quantity is partially circular. The susceptibility normalization is also deferred to the same first author's earlier work, which is a minor self-citation supporting an auxiliary observable. The first-order chiral-limit temperature, the critical strange-quark mass, and the absence of a CEP are internally generated predictions and do not reduce to the fitted parameters in the same direct way. Overall, the central BI phase-boundary claim has independent content, but one fitted quantity is passed off as a prediction, giving partial circularity.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim depends on six tunable parameters: five are calibrated to hadron masses and the pseudocritical temperature, and beta is a free scan parameter. No new particles or forces are introduced. The background geometry, soft-wall action, and susceptibility formulas are all imported from prior literature.

free parameters (6)
  • lambda = 80
    Quartic scalar self-coupling, chosen together with gamma and dilaton parameters to match rho mass and a pseudocritical temperature near 145 MeV.
  • gamma = -25
    Coefficient of the determinant term, fitted to meson spectra and the chiral transition temperature.
  • mu_1 = 0.72 GeV
    Dilaton profile parameter from Refs. [28, 29], fixed to reproduce hadronic observables.
  • mu_2 = 0.176 GeV
    Dilaton profile parameter from Refs. [28, 29], fixed to match meson spectra and the chiral transition.
  • mu_g = 0.43 GeV
    Dilaton profile parameter from Refs. [28, 29], included in the profile chosen to respect IR and UV behavior.
  • beta (Born-Infeld parameter) = scanned over 1, 5, 10, 20 GeV
    Controls the strength of nonlinear electrodynamics; not fitted to data, but freely scanned and central to the main claim.
assumptions (4)
  • domain assumption The soft-wall action Eq. (17) with dilaton profile Eq. (19) is a valid holographic dual for chiral symmetry breaking and restoration.
    The entire computation rests on this bottom-up model being an adequate stand-in for QCD chiral dynamics. Invoked in Sections III and V.
  • domain assumption The Born-Infeld black hole metric Eq. (12) and chemical potential Eq. (9) correctly encode finite baryon density in the dual theory.
    The finite-density phase diagram is derived from this identification, but no QCD observable fixes the Born-Infeld scale beta.
  • domain assumption The scalar and dilaton fields do not backreact on the Born-Infeld metric.
    Section III evaluates the scalar action on the fixed BI background. If backreaction is significant, the phase boundary shift could change.
  • domain assumption The susceptibility normalization and formulas from Ref. [45] are correct.
    Section IV adopts the two-point function and normalization from a previous paper with overlapping authorship, without re-deriving the normalization in this work.

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Cite this review

Pith. "Pith review of Effects of Born-Infeld Electrodynamics on Chiral Symmetry Restoration and Meson Susceptibilities in Holographic QCD." pith.science (2026). https://pith.science/paper/KTFTRG4I

@misc{pith2026260809489,
  author       = {Pith},
  title        = {Pith review of: Effects of Born-Infeld Electrodynamics on Chiral Symmetry Restoration and Meson Susceptibilities in Holographic QCD},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KTFTRG4I}},
  note         = {Machine review of arXiv:2608.09489}
}
abstract

Within a holographic QCD framework, we numerically investigate chiral symmetry breaking and the associated phase transition at finite temperature and chemical potential. The model is constructed on a nonlinear charged Born-Infeld black hole background. The chiral condensate, extracted from the asymptotic behavior of the bulk scalar field, serves as the primary order parameter. At zero chemical potential, we find a chiral crossover transition for physical quark masses with a pseudocritical temperature of $T_{pc}=0.1477$ GeV. In the chiral limit, the transition becomes first-order with a critical temperature of $T_{c}=0.1337$ GeV. A critical strange quark mass of $m_s=37$ MeV, at zero light quark mass, separates first- and second-order transition regions. For finite chemical potential ($\mu$) and a physical strange mass ($m_s=95$ MeV) with massless light quarks, the transition remains second-order, with $T_c$ decreasing as $\mu$ increases. These results are further supported by the behavior of meson susceptibilities $(\chi_{\pi}-\chi_{\sigma})$, which exhibit a rapid thermal decay and convergence across the phase boundary. Introducing the Born-Infeld parameter $\beta$ shifts the second-order phase boundary to higher temperatures for smaller $\beta$ (stabilizing the chirally broken phase) but does not alter the transition order or introduce a critical endpoint within the studied range. Our findings are consistent with previous soft-wall model studies and highlight the significant role of nonlinear bulk electrodynamics in modifying the chiral phase diagram.

Figures

Figures reproduced from arXiv: 2608.09489 by the authors.

Figure 1
Figure 1. FIG. 1: Solutions of [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Panel (a): Temperature dependence of the light quark condensate with the large strange quark mass [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Looking for the critical strange quark mass that changes the order of the chiral phase transition from second [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The chiral condensate dependence of the temperature and chemical potential at the quark masses [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The chiral phase transition in the T- [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: The chiral condensate as a function of temperature [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: The chiral condensate as a function of temperature [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Phase diagram in the [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: The normalized difference between pseudoscalar and scalar susceptibilities ( [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: The normalized susceptibility difference ( [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

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Works this paper leans on

49 extracted references · 16 canonical work pages

  1. [1]

    Gross et al., 50 Years of Quantum Chromodynamics, Eur

    F. Gross et al., 50 Years of Quantum Chromodynamics, Eur. Phys. J. C83, 1125 (2023), arXiv:2212.11107 [hep-ph]

    arXiv 2023

  2. [2]

    Goldstone, A

    J. Goldstone, A. Salam, and S. Weinberg, Broken Symmetries, Phys. Rev.127, 965 (1962)

    1962

  3. [3]

    Baker and S

    M. Baker and S. L. Glashow, Spontaneous Breakdown of Elementary Particle Symmetries, Phys. Rev.128, 2462 (1962)

    work page 1962

  4. [4]

    F. R. Brown, F. P. Butler, H. Chen, N. H. Christ, Z.-h. Dong, W. Schaffer, L. I. Unger, and A. Vaccarino, On the existence of a phase transition for QCD with three light quarks, Phys. Rev. Lett.65, 2491 (1990)

    work page 1990

  5. [5]

    S. Aoki, H. Fukaya, and Y. Taniguchi, Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature, Phys. Rev. D86, 114512 (2012), arXiv:1209.2061 [hep-lat]

    arXiv 2012

  6. [6]

    Chiral phase transition of $N_f$=2+1 and 3 QCD at vanishing baryon chemical potential

    H.-T. Ding and P. Hegde (Bielefeld-BNL-CCNU), Chiral phase transition ofN f =2+1 and 3 QCD at vanishing baryon chemical potential, PoSLA TTICE2015, 161 (2016), arXiv:1511.00553 [hep-lat]

    work page Pith review arXiv 2016

  7. [7]

    Bazavov, H

    A. Bazavov, H. T. Ding, P. Hegde, F. Karsch, E. Laermann, S. Mukherjee, P. Petreczky, and C. Schmidt, Chiral phase structure of three flavor QCD at vanishing baryon number density, Phys. Rev. D95, 074505 (2017), arXiv:1701.03548 [hep-lat]

    arXiv 2017

  8. [8]

    H. T. Ding et al. (HotQCD), Chiral Phase Transition Temperature in ( 2+1 )-Flavor QCD, Phys. Rev. Lett.123, 062002 (2019), arXiv:1903.04801 [hep-lat]

    arXiv 2019

Show all 49 references
  1. [9]

    H.-T. Ding, P. Hegde, O. Kaczmarek, F. Karsch, A. Lahiri, S.-T. Li, S. Mukherjee, and P. Petreczky (HotQCD), Chiral phase transition in (2 + 1)-flavor QCD, PoSLA TTICE2018, 171 (2019), arXiv:1905.11610 [hep-lat]

    2019 arXiv

  2. [10]

    Kuramashi, Y

    Y. Kuramashi, Y. Nakamura, H. Ohno, and S. Takeda, Nature of the phase transition for finite temperatureN f = 3 QCD with nonperturbatively O(a) improved Wilson fermions atN t = 12, Phys. Rev. D101, 054509 (2020), arXiv:2001.04398 [hep-lat]

    2020 arXiv

  3. [11]

    L. Dini, P. Hegde, F. Karsch, A. Lahiri, C. Schmidt, and S. Sharma, Chiral phase transition in three-flavor QCD from lattice QCD, Phys. Rev. D105, 034510 (2022), arXiv:2111.12599 [hep-lat]

    2022 arXiv

  4. [12]

    Gattringer and K

    C. Gattringer and K. Langfeld, Approaches to the sign problem in lattice field theory, Int. J. Mod. Phys. A31, 1643007 (2016), arXiv:1603.09517 [hep-lat]

    2016 arXiv

  5. [13]

    J. M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2, 231 (1998), arXiv:hep-th/9711200

    1998 arXiv

  6. [14]

    Witten, Anti-de Sitter space and holography, Adv

    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2, 253 (1998), arXiv:hep-th/9802150

    1998 arXiv

  7. [15]

    Karch and E

    A. Karch and E. Katz, Adding flavor to AdS / CFT, JHEP06, 043, arXiv:hep-th/0205236

    arXiv

  8. [16]

    Sakai and S

    T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys.113, 843 (2005), arXiv:hep- th/0412141

    2005

  9. [17]

    Erlich, E

    J. Erlich, E. Katz, D. T. Son, and M. A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett.95, 261602 (2005), arXiv:hep-ph/0501128

    2005 arXiv

  10. [18]

    Da Rold and A

    L. Da Rold and A. Pomarol, Chiral symmetry breaking from five dimensional spaces, Nucl. Phys. B721, 79 (2005), arXiv:hep-ph/0501218

    2005 arXiv

  11. [19]

    Karch, E

    A. Karch, E. Katz, D. T. Son, and M. A. Stephanov, Linear confinement and AdS/QCD, Phys. Rev. D74, 015005 (2006), arXiv:hep-ph/0602229

    2006 arXiv

  12. [20]

    Ghoroku, N

    K. Ghoroku, N. Maru, M. Tachibana, and M. Yahiro, Holographic model for hadrons in deformed AdS(5) background, Phys. Lett. B633, 602 (2006), arXiv:hep-ph/0510334

    2006 arXiv

  13. [21]

    S. S. Gubser and A. Nellore, Mimicking the QCD equation of state with a dual black hole, Phys. Rev. D78, 086007 (2008), arXiv:0804.0434 [hep-th]

    2008 arXiv

  14. [22]

    S. S. Gubser, A. Nellore, S. S. Pufu, and F. D. Rocha, Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics, Phys. Rev. Lett.101, 131601 (2008), arXiv:0804.1950 [hep-th]

    2008 arXiv

  15. [23]

    Gursoy and E

    U. Gursoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP02, 032, arXiv:0707.1324 [hep-th]

    arXiv

  16. [24]

    Gursoy, E

    U. Gursoy, E. Kiritsis, and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP02, 019, arXiv:0707.1349 [hep-th]

    arXiv

  17. [25]

    Colangelo, F

    P. Colangelo, F. Giannuzzi, S. Nicotri, and V. Tangorra, Temperature and quark density effects on the chiral condensate: An AdS/QCD study, Eur. Phys. J. C72, 2096 (2012), arXiv:1112.4402 [hep-ph]

    2012 arXiv

  18. [26]

    Cui and Y.-L

    L.-X. Cui and Y.-L. Wu, Thermal Mass Spectra of Scalar and Pseudo-Scalar Mesons in IR-improved Soft-Wall AdS/QCD Model with Finite Chemical Potential, Mod. Phys. Lett. A28, 1350132 (2013), arXiv:1302.4828 [hep-ph]

    2013 arXiv

  19. [27]

    S. P. Bartz and T. Jacobson, Chiral Phase Transition and Meson Melting from AdS/QCD, Phys. Rev. D94, 075022 (2016), arXiv:1607.05751 [hep-ph]

    2016 arXiv

  20. [28]

    Chelabi, Z

    K. Chelabi, Z. Fang, M. Huang, D. Li, and Y.-L. Wu, Realization of chiral symmetry breaking and restoration in holographic QCD, Phys. Rev. D93, 101901 (2016), arXiv:1511.02721 [hep-ph]

    2016 arXiv

  21. [29]

    Chelabi, Z

    K. Chelabi, Z. Fang, M. Huang, D. Li, and Y.-L. Wu, Chiral Phase Transition in the Soft-Wall Model of AdS/QCD, JHEP 04, 036, arXiv:1512.06493 [hep-ph]

    arXiv

  22. [30]

    Z. Fang, S. He, and D. Li, Chiral and Deconfining Phase Transitions from Holographic QCD Study, Nucl. Phys. B907, 187 (2016), arXiv:1512.04062 [hep-ph]. 17

    2016 arXiv

  23. [31]

    Fang, Y.-L

    Z. Fang, Y.-L. Wu, and L. Zhang, Chiral phase transition and meson spectrum in improved soft-wall AdS/QCD, Phys. Lett. B762, 86 (2016), arXiv:1604.02571 [hep-ph]

    2016 arXiv

  24. [32]

    Li and M

    D. Li and M. Huang, Chiral phase transition of QCD withN f = 2 + 1 flavors from holography, JHEP02, 042, arXiv:1610.09814 [hep-ph]

    arXiv

  25. [33]

    S. P. Bartz and T. Jacobson, Chiral phase transition at finite chemical potential in 2+1 -flavor soft-wall anti–de Sitter space QCD, Phys. Rev. C97, 044908 (2018), arXiv:1801.00358 [hep-ph]

    2018 arXiv

  26. [34]

    H. A. Ahmed, M. Kawaguchi, and M. Huang, Effect of charm quark on chiral phase transition in Nf=2+1+1 holographic QCD, Phys. Rev. D110, 046002 (2024), arXiv:2401.04355 [hep-ph]

    2024 arXiv

  27. [35]

    R.-G. Cai, S. He, and D. Li, A hQCD model and its phase diagram in Einstein-Maxwell-Dilaton system, JHEP03, 033, arXiv:1201.0820 [hep-th]

    arXiv

  28. [36]

    Bohra, D

    H. Bohra, D. Dudal, A. Hajilou, and S. Mahapatra, Chiral transition in the probe approximation from an Einstein-Maxwell- dilaton gravity model, Phys. Rev. D103, 086021 (2021), arXiv:2010.04578 [hep-th]

    2021 arXiv

  29. [37]

    Ballon-Bayona, H

    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. D102, 126003 (2020), arXiv:2006.08810 [hep-th]

    2020 arXiv

  30. [38]

    Born and L

    M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond. A144, 425 (1934)

    1934

  31. [39]

    E. S. Fradkin and A. A. Tseytlin, Nonlinear Electrodynamics from Quantized Strings, Phys. Lett. B163, 123 (1985)

    1985

  32. [40]

    A. A. Tseytlin, Vector Field Effective Action in the Open Superstring Theory, Nucl. Phys. B276, 391 (1986), [Erratum: Nucl.Phys.B 291, 876 (1987)]

    1986

  33. [41]

    G. W. Gibbons, Aspects of Born-Infeld theory and string / M theory, AIP Conf. Proc.589, 324 (2001), arXiv:hep- th/0106059

    2001

  34. [42]

    T. K. Dey, Born-Infeld black holes in the presence of a cosmological constant, Phys. Lett. B595, 484 (2004), arXiv:hep- th/0406169

    2004

  35. [43]

    Cai, D.-W

    R.-G. Cai, D.-W. Pang, and A. Wang, Born-Infeld black holes in (A)dS spaces, Phys. Rev. D70, 124034 (2004), arXiv:hep- th/0410158

    2004

  36. [44]

    Gherghetta, J

    T. Gherghetta, J. I. Kapusta, and T. M. Kelley, Chiral symmetry breaking in the soft-wall AdS/QCD model, Phys. Rev. D79, 076003 (2009), arXiv:0902.1998 [hep-ph]

    2009 arXiv

  37. [45]

    H. A. Ahmed, D. Li, M. Kawaguchi, and M. Huang, Probing the chiral and U(1) axial symmetry restoration via meson susceptibilities in holographic QCD, Phys. Rev. D114, 026032 (2026), arXiv:2603.12911 [hep-ph]

    2026 arXiv

  38. [46]

    Kawaguchi, S

    M. Kawaguchi, S. Matsuzaki, and A. Tomiya, Analysis of nonperturbative flavor violation at chiral crossover criticality in QCD, Phys. Rev. D103, 054034 (2021), arXiv:2005.07003 [hep-ph]

    2021 arXiv

  39. [47]

    X. Cao, S. Qiu, H. Liu, and D. Li, Thermal properties of light mesons from holography, JHEP08, 005, arXiv:2102.10946 [hep-ph]

    arXiv

  40. [48]

    X. Cao, H. Liu, and D. Li, Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography, Phys. Rev. D102, 126014 (2020), arXiv:2009.00289 [hep-ph]

    2020 arXiv

  41. [49]

    Cuteri, O

    F. Cuteri, O. Philipsen, and A. Sciarra, On the order of the QCD chiral phase transition for different numbers of quark flavours, JHEP11, 141, arXiv:2107.12739 [hep-lat]

    arXiv

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Reviewed August 11, 2026 · model on record in the stance chip above.