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REVIEW 2 major objections 4 minor 46 references

Holographic QCD phase diagram for a rotating plasma in the Hawking-Page approach

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read In the hard-wall and soft-wall AdS/QCD models, rotation and quark chemical potential both lower the deconfinement temperature, and rotation shrinks the zero-temperature critical chemical potential.

desk verdict Hard wall result is solid, but the soft wall's μ0(ω) conclusion is probably an artifact of the small-z gauge field approximation. read the letter →

arxiv 2501.16446 v3 pith:OM6NDQOS submitted 2025-01-27 hep-th

Nelson R. F. Braga , Octavio C. Junqueira This is my paper · ORCID
classification hep-th
keywords holographicQCDHawking-Pagetransitionrotatingquark-gluonplasmaconfinement/deconfinementquarkchemicalpotentialAdS/QCDReissner-Nordströmblackhole
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 aims to establish how plasma rotation and quark chemical potential jointly shape the boundary between confined hadronic matter and the quark-gluon plasma. Using the Hawking–Page transition — the gravitational switch between a black-hole geometry (the plasma) and thermal anti-de Sitter space (the hadron phase) — in two holographic AdS/QCD models, the authors derive that the critical deconfinement temperature $T_c$ decreases both as the rotational velocity increases and as the quark chemical potential $\mu$ increases. They also find that the zero-temperature critical chemical potential, the value beyond which matter stays deconfined for all temperatures, decreases with rotation. If correct, this gives a holographic prediction for the rotating, dense phase diagram of strongly interacting matter that goes beyond existing zero-rotation and zero-density results.

What carries the argument

The central object is the rotating Reissner–Nordström AdS$_5$ black hole with cylindrical symmetry, obtained by a Lorentz boost in the $(t,\phi)$ plane, whose horizon temperature $T = (1/\pi z_h)(1 - q^2 z_h^6/2)\sqrt{1-\omega^2 l^2}$ and whose regularized free-energy difference against thermal AdS determine the transition. The quark chemical potential is read off the boundary value of the temporal gauge field, and rotation rescales it as $\mu' = \mu/\gamma$. The hard-wall and soft-wall models are two prescriptions for the infrared scale that defines the confined phase, and the comparison between them tests how robust the conclusion is to the cutoff scheme.

What would settle it

Recompute the soft-wall phase boundary using the exact vector-field solution from Ref. [46] and check whether $T_c$ still decreases with $\omega l$ at fixed $\mu$; if the slope reverses or the $\mu_0$ curve bends upward, the central claim is falsified.

Watch

Extended reading notes

Core claim

The central claim is that a rotating, dense quark-gluon plasma has a lower deconfinement temperature than a static plasma at the same chemical potential, and that the chemical potential at which the transition temperature vanishes decreases with rotation. This is shown by embedding a charged, rotating AdS black hole in a five-dimensional geometry with an infrared cutoff — a hard wall at $z=z_0$ or a soft-wall dilaton $e^{-cz^2}$ — and computing the Hawking–Page free-energy difference between the black-hole geometry and thermal AdS. The phase transition is first order in both models. The rotating chemical potential enters as $\mu' = \mu / \gamma(\omega l)$, and the results reduce to the known finite-density, zero-rotation limit.

Load-bearing premise

The soft-wall calculation uses the approximate gauge-field solution $A_0(z)=i(\mu - \eta q z^2)$, valid only for small $z$, while the phase-boundary horizons found in Tables 1 and 3 reach values where the soft-wall dilaton is not close to one.

Editorial extensions

If this is right

  • In both hard-wall and soft-wall models, $T_c(\mu,\omega l)$ decreases monotonically as either the quark chemical potential or the rotational velocity grows.
  • The zero-temperature critical chemical potential $\mu_0$ falls with rotation: in dimensionless units, the hard-wall value drops from 1.6429 at $\omega l=0$ to 1.5336 at $\omega l=0.45$, and the soft-wall value from about 1.435 to 0.905 as $\omega l$ goes from 0 to 0.6.
  • With infrared scales fixed by rho-meson masses, the non-rotating, zero-density deconfinement temperature is 191 MeV in the soft-wall model (consistent with lattice QCD) and 122 MeV in the hard-wall model.
  • The transition remains first order for all investigated $\mu$ and $\omega$, in contrast to the crossover found in Polyakov-loop EMD models, because the Hawking–Page criterion compares two distinct geometries.

Reading between the lines

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

  • If the trend at low angular velocity persists to the vorticity values reached in non-central heavy-ion collisions, deconfinement should set in at lower beam energies for more central-vorticity events; centrality-resolved freeze-out measurements could test this.
  • The $\mu/\gamma$ rescaling suggests a general mechanism: any Lorentz-like transformation that reduces the effective chemical potential will push the phase boundary down, so analogous effects may appear for magnetic-field or strain counterparts.
  • The disagreement with rotating-gluodynamics lattice results, which find $T_c$ increasing with rotation, means the claim is not settled by existing simulations; a lattice study with dynamical quarks at real angular velocity could decide between the two pictures.
  • The quantitative gap between hard-wall ($\mu_0\approx1.64$) and soft-wall ($\mu_0\approx1.44$) values at zero rotation shows the infrared cutoff scheme matters at the ten-percent level; matching both to a single physical $\mu_0$ would constrain the cutoff prescription.
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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

2 major / 4 minor

Summary. The manuscript computes the Hawking-Page deconfinement temperature for a rotating, finite-density holographic plasma by comparing the on-shell actions of a rotating charged AdS black hole and thermal AdS in the hard-wall and soft-wall AdS/QCD models. Using the identification \mu = \eta q z_h^2 for the quark chemical potential and a cylindrically boosted Reissner-Nordstrom metric, it obtains critical temperature surfaces T_c(\mu,\omega l) and zero-temperature critical chemical potentials \mu_0(\omega l). The hard-wall calculation is analytic, reduces to known limits, and predicts that T_c decreases with increasing \mu and increasing rotation. The soft-wall calculation is numerical and reports the same qualitative behavior, with \mu_0 also decreasing with rotation. The central claim is that in both models rotation lowers the deconfinement temperature and the zero-temperature critical chemical potential.

Significance. The hard-wall part is a clean, internally consistent extension of earlier Hawking-Page calculations and gives explicit, falsifiable phase-diagram surfaces with the IR scale fixed by rho-meson phenomenology. The paper is transparent about its assumptions and provides numerical tables and comparisons with the lattice and holographic literature. However, the soft-wall part, which is essential to the two-model claim, relies on a small-\bar z expansion whose validity is contradicted by the paper's own tables. Until the soft-wall calculation is redone with the exact gauge-field solution, the claimed soft-wall \mu_0(\omega l) trend is not established. The hard-wall branch remains a useful result, but the significance of the paper as a two-model prediction is currently limited.

major comments (2)
  1. [§2 and §3.2, Eqs. (2.5)-(2.9), (3.23); Tables 1 and 3] The soft-wall analysis is built on the small-z expansion A_0(z)=i(\mu-\eta q z^2) and on \mu=\eta q z_h^2. In the soft-wall dilaton background the exact Maxwell solution is A_t(z)=\mu[1-(e^{c z^2}-1)/(e^{c z_h^2}-1)], so the charge-potential relation is \eta q=\mu c/(e^{c z_h^2}-1), not \mu/z_h^2. The critical horizons in Tables 1 and 3 reach \bar z_h=1.43 and 1.72, where e^{\bar z_h^2}-1 is not close to \bar z_h^2. The statement in Section 4 that the tabulated horizons legitimize Eq. (2.5) is therefore not supported by the paper's own data. Using the exact relation in the T=0 condition q^2 z_h^6/2=1 gives \bar\mu=\sqrt{2}(e^{\bar z_h^2}-1)/\bar z_h^3, which is increasing over the tabulated range, whereas the approximate relation gives \bar\mu=\sqrt{2}/\bar z_h, which is decreasing. Since rotation moves the zero-temperature critical horizon to larger \bar z_h, the claimed decrease of \mu_0 with \omega l can be reversed. The soft-wall free energies, Tables 2 and 4, and Figs. 6-8 should therefore be recomputed with the exact gauge field.
  2. [§4, Eqs. (4.6)-(4.7) and Abstract] The conclusion that 'in both models, the effect is the same' and the soft-wall values \bar\mu_0^{sw}(0.4)\approx1.030, \bar\mu_0^{sw}(0.5)\approx0.975, and \bar\mu_0^{sw}(0.6)\approx0.905 are inferred from the approximate equations described in the previous comment. These numerical outputs are not reliable until the exact soft-wall gauge solution is implemented. The hard-wall results in Eqs. (4.4)-(4.5) are unaffected and support the qualitative trend, but the two-model central claim is currently established only for the hard-wall model. The soft-wall computation should either be repeated with the exact solution or the conclusions should be restricted to the hard-wall case.
minor comments (4)
  1. [Introduction and Section 4] There are several typographical errors: 'hidrodynamic' in the Introduction, and 'ploted', 'criterea', and 'happpens' in Section 4.
  2. [Eq. (3.18)] This equation is labeled as the non-rotating case but still contains \gamma(\omega l); since \gamma(0)=1 this is harmless, but it would be clearer to write the factor explicitly as unity.
  3. [Table 2, row \bar\mu=0.650] The \omega l=0.4 entry (0.174746) is identical to the \omega l=0.5 entry; recomputing from Table 1 gives approximately 0.217 for \omega l=0.4, so one of the entries is a typographical error.
  4. [Eq. (3.15)] The term written as 34\omega^4 z_h^4 inside \bar h_1 should use the barred horizon \bar z_h^4 to be dimensionally consistent with the other dimensionless quantities.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Tc(mu, omega) and mu0(omega) results are genuine outputs of an explicit Hawking-Page free-energy calculation.

full rationale

The claimed Tc(mu, omega) and mu0(omega) are outputs of an explicit Hawking-Page calculation: the regularized free-energy difference Delta E (Eqs. 3.7-3.9) is computed from the two competing geometries, the transition is fixed by Delta E = 0, and the physical IR scales (1/z0 = 323 MeV, sqrt(c) = 338 MeV) are pinned by rho-meson spectroscopy (Ref. [42]), not by any value of the target phase boundary. The rotation dependence enters through the coordinate-transformed metric and gauge field and the standard surface-gravity temperature (2.23); no step inserts the desired Tc(mu, omega) or mu0(omega) as an input. The omega=0 and mu=0 limits reproduce the authors' earlier results ([44] and [21]), and the non-rotating finite-density hard-wall solution is given in closed form (3.19)-(3.20), which shows the result is computed rather than assumed. The only methodological caveat is the soft-wall use of the small-z RN gauge solution (2.5) and the statement in Section 4 that the tabulated horizons legitimize that approximation; since those horizons are themselves obtained with the same approximation, this is a self-consistency check and a numerical-accuracy concern, not a circular derivation of the phase diagram. Self-citations are consistency checks, not load-bearing. No circular step found.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The model uses two IR energy scales fixed by hadron phenomenology and one normalization factor eta that sets the physical chemical potential scale. The main unvalidated input is the small-z approximation for the gauge field in the soft wall.

free parameters (3)
  • z0 (hard wall IR cutoff) = 1/z0 = 323 MeV
    Fixed by the rho meson mass (Ref [42]); converts dimensionless hard wall results to physical temperatures.
  • sqrt(c) (soft wall IR scale) = 338 MeV
    Fit to lightest rho meson masses (Ref [42]); sets the soft wall temperature and chemical potential units.
  • eta = 1 in plots; sqrt(3/4) ~ 0.866 for physical results
    The gauge field normalization in Eq. (2.7); set to 1 for simplicity and rescaled at the end using N_c=3, N_f=6 from Eq. (4.12). The choice N_f=6 is a modeling input.
assumptions (5)
  • domain assumption AdS/CFT duality and the identification of the black hole phase with the deconfined quark-gluon plasma
    The entire holographic setup, used throughout Sections 2 and 3.
  • domain assumption Hawking-Page transition between thermal AdS and black hole AdS represents the confinement/deconfinement transition
    Inherited from Refs [42,43], used in Section 3.
  • domain assumption The rotating plasma is described by the boosted static RN-AdS metric plus the transformed gauge field
    Coordinate transformation in Eqs. (2.11)-(2.12), following Refs [15,16,39,40].
  • domain assumption The chemical potential of the rotating plasma is mu' = mu / gamma
    Defined from the invariant coupling A'_M J'^M in Section 2, Eq. (2.18), in agreement with Refs [15,25].
  • ad hoc to paper The soft wall gauge field is approximated by the small-z RN solution A0(z) = i(mu - eta q z^2) up to the horizon
    Used in Eq. (3.4) and the soft wall action; the paper acknowledges it is only valid for small z, but the critical horizons in Tables 1 and 3 are not small.

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Pith. "Pith review of Holographic QCD phase diagram for a rotating plasma in the Hawking-Page approach." pith.science (2026). https://pith.science/paper/OM6NDQOS

@misc{pith2026250116446,
  author       = {Pith},
  title        = {Pith review of: Holographic QCD phase diagram for a rotating plasma in the Hawking-Page approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OM6NDQOS}},
  note         = {Machine review of arXiv:2501.16446}
}
abstract

We investigate the combined effect of rotation and finite chemical potential in the confinement/deconfinement transition of strongly interacting matter. The holographic description consists of a five-dimensional geometry that contains a black hole (BH) in the deconfined (plasma) phase. The geometry is equipped with some cut-off that introduces an infrared energy scale. We consider two possibilities: the so-called hard wall and soft wall AdS/QCD models. The transition between the plasma and hadronic phases is represented holographically as a Hawking-Page transition between geometries with and without a black hole. The gravitational dual of the rotating plasma at finite density is given by a Reissner-Nordstr\"om (RN) charged anti-de Sitter (AdS) BH with non-zero angular momentum. This analysis provides the critical temperature of deconfinement as a function of the quark chemical potential and the plasma rotational velocity. For the case of very low temperatures, the dependence of the critical values of the chemical potential for the transition to occur at $ T \to 0 $ on the rotation is found.

Figures

Figures reproduced from arXiv: 2501.16446 by the authors.

Figure 1
Figure 1. Regularized action density for the hard wall model at (ωl = 0.5), with µ¯ = 1.20 (blue), µ¯ = 1.25 (yellow), ¯µ = 1.30 (green), and ¯µ = 1.35 (red). The critical horizons are defined by △E = 0. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Critical temperature T¯ c versus quark chemical potential for a non-rotating plasma in the hard wall model. In the limit ω → 0, one recovers the result for the system at finite density without rotation of Ref. [44]. Considering additionally q → 0, one obtains the result for a static system at zero quark chemical potential [42]. There is no transition if z0 < zh, since △E is always positive in this case, according to… view at source ↗
Figure 3
Figure 3. Critical temperatures of deconfinement as a function of quark chemical potential µ¯ in the hard wall AdS/QCD model, at fixed values of plasma rotational velocity. see Eq. (3.14). In the physical region with positive temperature, the domain of the horizon position is defined by zh ≤ √ 2/µ¯, with △E → ∞ ¯ when zh → √ 2/µ¯. For the case with zero chemical potential, such divergencies do not appear since the pole in Eq.… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Critical temperatures versus QGP rotational velocity, for HP transitions at fixed quark chemical potentials ¯µ in the hard wall AdS/QCD model. For a non-rotating system with zero quark density, we recover the expression for the critical temperature obtained in [42], Tc…
Figure 5
Figure 5. Figure 5: Extended QCD phase diagram. Critical temperature as a function of the quark chemical potential and plasma rotational velocity, T¯ c(¯µ, ωl), in the hard wall AdS/QCD model. 3.2. Soft wall model In the soft wall AdS/QCD model [31] one takes z0 → ∞, while c ̸= 0, in equa…
Figure 6
Figure 6. Figure 6: Action density of regularized rotating BH at finite density versus horizon position in the soft wall model, at a fixed rotational velocity (ωl = 0.5), and different quark chemical potentials. From the values of z¯hc of TABLES 1 and 3 in the appendix, we compute the cri…
Figure 7
Figure 7. Figure 7: Critical temperatures of deconfinement as a function of quark chemical potential in the soft wall model, at fixed values of plasma rotational velocity [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Critical temperatures versus QGP rotational velocities, for HP transitions at fixed quark chemical potentials in the soft wall AdS/QCD model. 4. Final remarks and conclusions Our results demonstrate that rotation decreases the critical temperatures of deconfinement for…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.