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REVIEW 5 major objections 6 minor 1 cited by

Transport coefficients and quasinormal modes in Einstein-dilaton holographic QCD

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper argues that a bottom-up holographic QCD model with a quadratic dilaton reproduces the universal shear viscosity ratio η/s = 1/(4π) and yields a bulk viscosity that, for a chosen dilaton strength, falls inside the band of values…

desk verdict Solid shear-sector result and new QNM tables, but the bulk-viscosity comparison to JETSCAPE rests on an underdocumented normalization constant; needs a revision, not a desk reject. read the letter →

arxiv 2507.04165 v2 pith:ZFER4HU6 submitted 2025-07-05 hep-th

Nairy A. Villarreal , Luis A. H. Mamani , Alfonso Ballon-Bayona , Alex S. Miranda , Vilson T. Zanchin This is my paper
classification hep-th PACS 11.25.Tq12.38.Mh
keywords holographicQCDEinstein-dilatongravityquadraticdilatonshearviscositybulkquasinormalmodesKuboformulaspeedofsound
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

The paper tries to show that a simple holographic model of the quark-gluon plasma—a five-dimensional Einstein-dilaton gravity theory with a quadratic scalar profile—can describe both the thermodynamics and the transport properties of the deconfined plasma. Working in the hydrodynamic limit, it derives the dispersion relation of the vector-sector perturbations and extracts the shear viscosity ratio η/s = 1/(4π), the universal value found in many strongly coupled theories. In the scalar sector it applies the Kubo formula with a numerically computed normalization factor to obtain the bulk viscosity to entropy density ratio ζ/s, which stays within the range deduced from heavy-ion collision data when the dilaton parameter c lies between 0.4 and 1.0 GeV². It also shows that the speed of sound approaches lattice QCD results at high temperatures for c around 0.22–0.4 GeV². A sympathetic reader would care because these are parameter-controlled predictions from a model built to reproduce confinement, testable against existing QGP measurements.

What carries the argument

The machinery is the set of gauge-invariant master equations for tensor, vector, and scalar perturbations of the Einstein-dilaton black hole, together with the potential-reconstruction solution of the background. The vector-sector dispersion relation ω = −i q²/(4πT) is the object from which the shear viscosity is read off; its coefficient γη = 1/(4πT) yields η/s = 1/(4π). For the bulk viscosity the load-bearing object is the scalar master equation at q = 0, whose conserved flux F = (2f/3ζ1)(φ′/ζ1′)² Im(Z_φ* Z_φ′) is combined with the Kubo formula ζ = (2/9κ²) lim_{ω→0} F/ω; the normalization constant Cφ, extracted numerically from the near-horizon expansion Z_φ ≈ Cφ(1−u)^{iw/f′_h}, controls the final value of ζ/s.

What would settle it

Compute the q = 0 scalar master equation by a second, independent method (for example, direct second-order expansion of the action) and check whether the conserved flux F is independent of the holographic coordinate; if the flux varies with u, or if a high-precision lattice QCD calculation of ζ/s at T ≈ 200–300 MeV falls outside the band that c ∈ [0.4, 1.0] GeV² produces, the central claim fails.

Watch

Extended reading notes

Core claim

The central claim is that the quadratic-dilaton Einstein background, with warp factor ζ1(z) = z ₀F₁(5/4; c²z⁴/9) and horizon function f(z) = 1 − C_h ∫₀ᶻ ζ1³, is quantitatively viable for transport in the deconfined phase. The vector master equation yields the hydrodynamic mode ω = −i q²/(4πT), which fixes γη = η/(sT) = 1/(4πT) and therefore the ratio η/s = 1/(4π). In the scalar sector at zero momentum, the master equation with the conserved flux from Abel's identity gives the bulk-viscosity formula ζ/s = (8/27)(ζ1h²/4π)[(φ′/ζ1′)²|_{u=1}]|Cφ|²; with the normalization Cφ computed numerically from a near-horizon expansion, the resulting ζ/s curve sits inside the heavy-ion data band for c ∈ [0.4, 1.0] GeV², while the alternative fluid/gravity version (Cφ = 1) matches the same band for c ∈ [0.22, 1.0] GeV². The quasinormal mode spectra in the tensor and vector sectors are computed with a pseudospectral method and show that the dilaton modifies the imaginary parts most strongly at small wavenumber, tending to the conformal limit as q grows.

Load-bearing premise

The bulk-viscosity comparison with heavy-ion data depends on the zero-momentum scalar perturbation equation being derived correctly and on the numerical constant Cφ being accurate; if either is off, the claimed match changes.

Editorial extensions

If this is right

  • The shear viscosity to entropy density ratio of this holographic QCD plasma is exactly η/s = 1/(4π), independent of the dilaton strength, so the plasma saturates the universal holographic bound.
  • The bulk viscosity to entropy density ratio is a nontrivial function of temperature; for large black holes it grows toward T_min and falls to zero at high temperature, and for c between 0.4 and 1.0 GeV² it lies inside the band inferred from heavy-ion data.
  • For c ≈ 0.22 GeV², whose minimum temperature is near 178 MeV, the model's speed of sound agrees with lattice QCD in the deconfined phase down to temperatures close to 150 MeV.
  • The quasinormal mode spectrum shows that the dilaton slows the decay (makes Im ω less negative) most strongly at small wavenumber, with a return to conformal behavior at large q; the hydrodynamic vector mode obeys ω = −i q²/(4πT) at small q.
  • Large black holes are thermodynamically stable with positive specific heat and positive v_s², while small black holes have negative specific heat and negative v_s², so only the large-black-hole branch is physical for plasma description.

Reading between the lines

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

  • The same flux/Kubo machinery could be applied at finite baryon density once a gauge field is added; the model's parameter c would then be fit simultaneously to ζ/s and v_s² data, which may break the current degeneracy between the Cφ and Cφ = 1 variants.
  • The good match of the fluid/gravity version (Cφ = 1) over a wider c range suggests that the near-horizon normalization Cφ may be a proxy for higher-order hydrodynamic corrections; checking whether Cφ deviates from 1 at large black hole temperatures would discriminate between the two extraction procedures.
  • Because the model's ζ/s diverges as v_s² → 0 on the small-black-hole branch, a lattice or experimental determination of ζ/s near the minimum temperature could test whether the divergence is physical or an artifact of the master equation truncation at q = 0.
  • If extended to finite baryon density, the same model predicts a temperature-dependent speed of sound that could be compared with neutron-star merger constraints, where the conformal value 1/3 is known to be violated.
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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

5 major / 6 minor

Summary. The paper studies a five-dimensional Einstein-dilaton holographic model with a quadratic dilaton profile phi(z) = c z^2, a reconstructed potential, and an AdS black hole at finite temperature. It computes the black hole thermodynamics, including the minimum temperature T_min and the large/small black hole branches, the speed of sound, and the quasinormal modes of the tensor and vector sectors. In the hydrodynamic limit of the vector sector it obtains the shear dispersion relation and recovers the universal ratio eta/s = 1/(4 pi). In the scalar sector it computes the bulk viscosity from a Kubo formula combined with a numerically determined normalization constant C_phi, and compares zeta/s with the JETSCAPE band and v_s^2 with lattice QCD data. The paper presents the model as a phenomenological bottom-up holographic description of the QCD plasma.

Significance. If the bulk-viscosity calculation is valid, the paper provides a useful bottom-up benchmark that connects an Einstein-dilaton model with data-driven estimates from JETSCAPE and lattice QCD. The vector-sector derivation is clean and reproduces the standard eta/s = 1/(4 pi) result without additional assumptions, and the QNM spectra for tensor and vector sectors are cross-checked against the conformal case and against two independent numerical implementations. The main significance is therefore conditional on the scalar-sector normalization constant C_phi: the value of zeta/s scales as |C_phi|^2, and the paper does not currently provide enough information to assess the reliability of that constant.

major comments (5)
  1. [Section VI.A, Eq. (70), and Fig. 9] The central quantitative claim, that the GPR formula with the numerically computed C_phi places zeta/s inside the JETSCAPE band for 0.4 <= c <= 1.0 GeV^2, is not supported by the information given. The paper reports no numerical values of C_phi, no dependence on T or c, and no convergence test in the near-horizon parameter delta (fixed at 10^-4) or in the iterative normalization procedure. Since Eq. (70) is proportional to |C_phi|^2, a 20% error in C_phi changes zeta/s by about 44%, which is comparable to the width of the JETSCAPE band shown in Fig. 9. The authors should provide a table of C_phi values, a delta-convergence study, and a quantitative comparison of the resulting zeta/s with the EO formula before the agreement in Fig. 9 can be assessed.
  2. [Section VI.B, Eqs. (70) and (75)] The consistency check with the Eling-Oz formula is not independent validation of the numerical normalization. Eq. (75) is exactly Eq. (70) with |C_phi|^2 = 1, so it verifies only the algebraic prefactor of the flux formula, not the value of C_phi produced by the shooting procedure. The sentence in Section VIII claiming confirmation of consistency between near-horizon dynamics and hydrodynamic transport coefficients overstates what the comparison establishes; the agreement with JETSCAPE for the lower curves in Fig. 9 depends entirely on the unvalidated value of C_phi.
  3. [Section V.A, Eq. (61)] The statement that the dilaton 'modifies the diffusion coefficient gamma_eta' is incorrect if gamma_eta denotes the physical quantity eta/(sT). From Eq. (58), omega = -i q^2/(4 pi T), so gamma_eta = 1/(4 pi T) is independent of the dilaton. Eq. (61), w = -i (1/4 - phi_h^2/30) q^2, is the same dispersion relation expressed in dimensionless variables using f'_h(phi_h); the apparent dependence on phi_h is a normalization effect of q = z_h q and w = z_h omega. The text should be rephrased to avoid contradicting the universal result stated immediately above.
  4. [Appendix B.3 and Eq. (64)] The scalar master equation is the basis of the bulk-viscosity computation, but it is not derived in the paper. Appendix B.3 lists the perturbation equations and describes the elimination procedure verbally, but the intermediate algebra leading to Eq. (64) is omitted. Because a sign or factor error in this equation would change C_phi and hence Fig. 9, the derivation should be included, or a precise step-by-step mapping to the corresponding derivation in Ref. [24] should be provided.
  5. [Section VII, Figs. 9 and 10] The comparison with data is a calibration rather than an independent prediction: the dilaton parameter c is the model's free parameter, and the values used are selected because they place the curves inside the JETSCAPE and lattice bands. The paper should state this explicitly and show a continuous scan over c, with the data band overlaid, so the sensitivity to c is visible. It should also address the tension that the value of c that best matches the lattice sound speed (approximately 0.22 GeV^2) lies at the edge of the range needed for the GPR lower curves in Fig. 9 (0.4 to 1.0 GeV^2); the claim of simultaneous description should be quantified.
minor comments (6)
  1. [Section III.B, Eq. (35) and Eq. (58)] The notation for q is inconsistent: in Eq. (35) q denotes the dimensionless quantity z_h q, while in the second equality of Eq. (58) q is the physical wavenumber. Please use different symbols, e.g., q_bar, to avoid ambiguity.
  2. [Section VIII, last paragraph] The sentence 'The bulk viscosity eta/s is sensitive to non-conformal symmetry effects' should refer to zeta/s, not eta/s.
  3. [Figure 9 caption] The caption should specify which line style and color correspond to c = 0.22 GeV^2 versus c = 0.4 GeV^2, and which curves use the numerically computed C_phi versus C_phi = 1; currently the reader must infer this from the main text.
  4. [Section VI.A] The description of the iterative procedure for C_phi is only verbal ('in an iterative way that ensures the solution remains consistent'). A concrete algorithm or pseudo-code would be needed to reproduce the result.
  5. [Figure 4 caption] The phrase 'Large (Small) black hole solutions correspond to solid (dashed) blue (red) line' is confusing; it should read 'solid blue (large black holes) and dashed red (small black holes)'.
  6. [General] No data repository or code is provided. For a paper whose central new result depends on numerical integration and spectral methods, depositing the tables of C_phi and the QNM frequencies would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: transport coefficient derivations are self-contained given the stated Einstein-dilaton model; the JETSCAPE comparison varies a free model parameter rather than presenting a fitted quantity as a prediction.

full rationale

The paper's derivation chain is not circular. The shear viscosity ratio eta/s = 1/(4 pi) follows from solving the vector-sector master equation in the hydrodynamic limit and identifying the diffusion constant in Eq. (58); this is a standard two-derivative Einstein-gravity result and is derived rather than assumed. The bulk viscosity is computed via the Kubo formula using the scalar-sector master equation (64), conserved flux (66), and the boundary condition Z_phi(0)=1, with C_phi obtained by solving the same boundary value problem. The comparison with JETSCAPE data scans the model's free parameter c, which is an input of the model, not a fitted output; a successful comparison with data for a range of c is a benchmark, not a circular prediction. The equality between the EO formula (75) and the GPR formula (70) at |C_phi|^2=1 is an explicit algebraic identity, correctly labeled as such, and is not used as independent evidence for the numerical value of C_phi. While the numerical reliability of C_phi is a legitimate concern—it is reported without convergence checks or explicit values—that is a robustness issue, not circularity. No load-bearing step reduces to its own input by construction, and no self-citation carries the derivation.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The model has one genuinely free parameter, the dilaton strength c, which is tuned to match the JETSCAPE and lattice data sets. The other inputs are standard holographic dictionary assumptions (AdS/CFT, Kubo formula, fluid/gravity) from the cited literature. No new particles or fields are introduced. The dependence of the headline comparison on the fitted c is the main circularity burden.

free parameters (1)
  • dilaton strength c = 0.22 to 1.0 GeV^2 (used values c=0.22, 0.4, 1.0 GeV^2)
    The quadratic dilaton profile parameter in Eq. (10). It sets the scale of conformal symmetry breaking and determines Tmin, vs², and ζ/s. The paper selects c so that ζ/s falls in the JETSCAPE band and vs² approaches lattice QCD data (Section VII).
assumptions (5)
  • ad hoc to paper The five-dimensional Einstein-dilaton action with the quadratic dilaton profile ϕ(z)=c z², with ζ1=ζ2 and a potential reconstructed from the Einstein equations, is a valid holographic dual of a QCD-like plasma.
    This is the model input, stated in Section II.B (Eqs. 9-10). The dilaton profile is chosen by hand to produce linear confinement at zero temperature; its parameter c is later tuned to data.
  • domain assumption AdS/CFT duality and the Lorentzian prescription: retarded Green's functions of the boundary theory are obtained from the ratio B/A of the near-boundary solution coefficients (Eq. 34), and QNM poles correspond to poles of the correlators.
    Used throughout Sections III-V, based on Refs. [7-9]. The paper does not derive or justify the duality; it assumes its validity.
  • domain assumption The Kubo formula for bulk viscosity in the form ζ = (2/(9κ²)) lim_{ω→0} (1/ω) F, with the conserved flux F computed from Abel's identity, is applicable to this Einstein-dilaton model.
    Adopted from Refs. [23,24] and used in Section VI and Appendix C. The applicability is assumed, not independently derived.
  • domain assumption The Eling-Oz fluid/gravity formula, ζ/s = (8/(12π)) (dϕ_h/d ln s)², is equivalent to the Kubo-formula result when |Cϕ|²=1.
    Used in Section VI.B, Eq. (71), referencing Ref. [28]. The paper shows this equivalence algebraically in Eqs. (73)-(75).
  • domain assumption The hydrodynamic expansion in small frequency and wavenumber (λ ≪ 1) truncates at first order for the vector sector, giving the shear diffusion pole.
    Standard hydrodynamic limit of holographic QNMs, used in Section V.A. The truncation at first order is valid for ω, q ≪ T.

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Cite this review

Pith. "Pith review of Transport coefficients and quasinormal modes in Einstein-dilaton holographic QCD." pith.science (2026). https://pith.science/paper/ZFER4HU6

@misc{pith2026250704165,
  author       = {Pith},
  title        = {Pith review of: Transport coefficients and quasinormal modes in Einstein-dilaton holographic QCD},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZFER4HU6}},
  note         = {Machine review of arXiv:2507.04165}
}
abstract

In this paper, we investigate the transport coefficients of a strongly coupled plasma in the context of holographic QCD models based on Einstein-dilaton gravity that are compatible with linear confinement at zero temperature. At finite temperature, the holographic model is characterized by an asymptotically anti-de Sitter (AdS) black hole coupled to a scalar field, the dilaton, which is quadratic in the radial direction. The inclusion of the scalar field results in an explicit breaking of the conformal symmetry in the dual field theory. In such systems, the Hawking temperature of the black hole corresponds to the plasma temperature in the dual field theory. We confirm the existence of a minimum temperature $T_{\min}$, above which two distinct classes of black hole solutions emerge: one corresponding to large black holes and the other to small black holes. We calculate some thermodynamic quantities -- such as entropy, specific heat, and speed of sound -- and find results that are consistent with similar holographic models. We calculate the quasinormal modes (QNM) of the tensor and vector sectors using the pseudospectral method. In the hydrodynamic regime, we derive the dispersion relation for the vector sector, from which we extract the shear viscosity and the ratio $\eta/s=1/4 \pi$. The bulk viscosity is calculated using the Kubo formula in the scalar sector. Finally, our results for the speed of sound are compared with the Lattice QCD predictions, and our results for the bulk viscosity are compared with those reported by the JETSCAPE collaboration.

Figures

Figures reproduced from arXiv: 2507.04165 by the authors.

Figure 1
Figure 1. FIG. 1. Temperature as a function of the horizon position [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The speed of sound squared as a function of the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The real and imaginary parts of the first three fre [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The shear viscosity normalized by [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The imaginary part of the frequency of the hydro [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The imaginary part of the frequency of the hydro [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Bulk viscosity to entropy density ratio versus [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Speed of sound comparison between Lattice QCD [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Bulk viscosity to entropy density ratio obtained using [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Hydrodynamical transports in generic AdS Gauss-Bonnet-scalar Gravity

    hep-th 2025-07 conditional novelty 6.0 of 10

    Analytic shear and bulk viscosity formulas are derived for a five-dimensional Einstein-Scalar-Maxwell-Gauss-Bonnet holographic model, with the shear viscosity cross-checked by Kubo methods.

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