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Frame-dependency of the confinement temperature in a strongly-coupled plasma under rotation: a holographic description

T0 review · 1 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The co-rotating confinement temperature of a rotating strongly coupled plasma depends on angular position and can rise, fall, or turn over as rotation grows.

desk verdict A solid holographic extension to unequal-rotation Myers-Perry black holes: the co-rotating critical temperature acquires real angular dependence, and the main caveat is interpretive, not mathematical. read the letter →

arxiv 2608.13301 v1 pith:2G74GRHQ submitted 2026-08-13 hep-th hep-ph

Nelson R. F. Braga , Alexsandre L. Ferreira Jr This is my paper · ORCID
classification hep-thhep-ph
keywords quark-gluonplasmaconfinement/deconfinementMyers-PerryblackholeholographicQCDTolman-EhrenfestlawrotatingHawking-Pagetransitionframedependence
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 aims to resolve how rotation changes the temperature at which a strongly coupled plasma confines, by extending a holographic model of the quark-gluon plasma to a black hole with two independent angular momenta. It claims that the disagreement between lattice and holographic results is a frame effect: a static observer sees the confinement temperature fall as rotation grows, while a co-rotating observer can see it rise. With two unequal rotation axes, the co-rotating temperature also acquires an angular dependence, so at a fixed rotation speed different points on the plasma sphere can move toward or away from confinement. The result matters because heavy-ion collisions produce rapidly rotating droplets of plasma, and knowing which frame and which position a prediction refers to is essential for comparing theory with experiment.

What carries the argument

The central object is the Myers-Perry black hole in five-dimensional anti-de Sitter space with two independent angular momenta, characterized by rotation parameters $a$ and $b$; its holographic dual is a strongly coupled plasma on $\mathbb{R}\times S^3$. Unequal parameters break the spherical symmetry of the equal-rotation case, which is why the local temperature can depend on the angular coordinate $\theta$ locating points between the two rotation axes. The argument runs through three steps: the regularized on-shell free energy of the black hole relative to thermal AdS (computed with a change of variables that turns the radial/angular integral into a triangle), the Hawking-Page condition that fixes the critical horizon radius at $r_+=l$, and the Tolman-Ehrenfest law $T_{\mathrm{loc}}\sqrt{-g_{tt}}=T$ applied to the static and co-rotating boundary frames. The co-rotating metric supplies the combined Lorentz factor $\gamma$, and it is this factor that turns the frame-independent reference temperature into an angle-dependent local critical temperature.

What would settle it

At small angular velocity and a single rotation axis ($w=0$), equations (4.6)-(4.7) predict $T_c^{\mathrm{rot}}/T_c(0)=1+\frac16(2-3\cos^2\theta)\,v_\phi^2+\cdots$, so near the rotation axis ($\theta\approx0$) the local critical temperature falls while at the equator ($\theta=\pi/2$) it rises. A lattice simulation of rotating gluodynamics in the co-rotating frame that measures the local Polyakov-loop transition temperature as a function of distance from the rotation axis at small angular velocity would confirm or falsify this dichotomy.

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Extended reading notes

Core claim

The central claim is that for the most general five-dimensional Myers-Perry black hole, with two independent rotation parameters $a$ and $b$, the local confinement temperature measured by a co-rotating observer at angular position $\theta$ is $$$T^{{\mathrm{rot}}$}_c(v_\phi,v_\psi,\$\theta$)=\frac{\gamma}{3}\left(1+\frac{1}{\gamma_\phi}+\frac{1}{\gamma_\psi}\right)T_c(0,0),\qquad \gamma=\left(1-v_\$phi^{2}$\$sin^{2}$\$\theta$-v_\$psi^{2}$\$cos^{2}$\$\theta$\right)^{-1/2}.$$ In the equal-rotation limit $v_\phi=v_\psi$ the angular dependence drops out and the co-rotating temperature always grows with rotation. For unequal rotations the angular dependence is genuine: depending on $\theta$ and on the ratio $w=v_\psi/v_\phi$, the co-rotating critical temperature can decrease, increase, or first increase and then fall as the rotation grows, while the static-frame critical temperature $T_c(v_\phi,v_\psi)=\frac13(1+1/\gamma_\phi+1/\gamma_\psi)T_c(0,0)$ always decreases. The paper concludes that the lattice and holographic results are both correct and differ only because they refer to different observers.

Load-bearing premise

The argument rests on treating the global Hawking-Page critical temperature as a local, observer-dependent quantity via $T_{\mathrm{rot}}=\gamma T_{\mathrm{BH}}$; if a global phase transition cannot be assigned a local critical temperature in this way, the angular dependence loses its meaning.

Editorial extensions

If this is right

  • In a static frame, the deconfinement temperature always falls with rotation, falling faster when the second angular velocity is larger, i.e. for larger $w=v_\psi/v_\phi$.
  • In a co-rotating frame with unequal rotations, the local critical temperature can rise, fall, or be non-monotonic in the angular velocity; monotonic growth survives only for equal angular momenta ($w=1$) or at the equator $\theta=\pi/2$.
  • For $w>1/\sqrt{2}$, even a small rotation raises the local critical temperature at every angle, reproducing the qualitative behavior seen in lattice QCD.
  • Near-luminal rotation pushes the co-rotating critical temperature back down except for $w=1$ or $\theta=\pi/2$, so a peak in the temperature as a function of angular velocity is generic for unequal rotations.
  • The small-velocity coefficient $B_2=\frac16[1-(1-w^2)(3\cos^2\theta-1)]$ gives a concrete signature that distinguishes the unequal-spinning model from the spherically symmetric one.

Reading between the lines

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

  • If the angular dependence is real, a rapidly rotating plasma should not deconfine uniformly: regions at different distances from the two rotation axes can cross the transition at different angular velocities, so rotation may drive spatially inhomogeneous confinement inside a single fireball.
  • The same Tolman-Ehrenfest conversion applied here to the Hawking-Page temperature could be applied to other observer-dependent quantities in rotating plasmas, such as the chiral transition temperature or transport coefficients, producing a family of frame-corrected predictions.
  • A lattice test of the predicted dichotomy near the rotation axis versus the equator at small angular velocity would be a sharper discriminator than comparing only global average temperatures.
  • The stereographic projection mentioned in the paper suggests the angle $\theta$ may map to a spatial coordinate in a flat-space plasma; if so, the predicted angular dependence could be measured as a radial or azimuthal temperature profile in heavy-ion collisions.
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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

1 major / 6 minor

Summary. This paper studies the Hawking-Page transition of the five-dimensional Myers-Perry-AdS black hole with two independent rotation parameters a and b. The authors compute the regularized on-shell free energy, find the critical horizon radius r_+ = l, express the critical temperature in terms of the linear velocities (v_phi, v_psi), and then apply the Tolman-Ehrenfest law to obtain local critical temperatures for static and co-rotating observers. For a != b, the co-rotating critical temperature T_rot_c acquires an angular dependence, so that, depending on the angle theta and the velocity ratio w = v_psi/v_phi, it can decrease, increase, or become non-monotonic with rotation, while the static-frame critical temperature always decreases. The equal-rotation limit reproduces Ref. [31] and the non-rotating limit gives T_c = 3/(2 pi l).

Significance. The result is a concrete, parameter-free holographic prediction for the frame dependence of the deconfinement temperature in a rotating strongly coupled plasma with two unequal angular momenta. The analytic formulas (3.17), (3.19), and (4.5)-(4.9) are internally consistent and reduce correctly to known limits; the small-velocity expansion (4.6)-(4.7) is explicit and the near-luminal behavior is analyzed. The new integration trick for the on-shell action in Sec. 3.1 is a useful technical contribution. If the Tolman-Ehrenfest identification is accepted, the model provides a qualitative resolution of the apparent contradiction between holographic and lattice results for rotating QGP and makes a falsifiable prediction about the angular profile of the local critical temperature.

major comments (1)
  1. [Sec. 4.2, Eq. (4.5)] The identification of T_rot_c = gamma T_c as the local confinement temperature of a co-rotating observer is the load-bearing step for the paper's central angular-dependence claim, but the derivation is kinematic: it states what a local thermometer reads when the global system sits at the Hawking-Page transition. The manuscript itself acknowledges (Secs. 1 and 5) that the system is globally either in a plasma or a hadronic state and that the model cannot describe inhomogeneous mixed phases. Because the angular profile of T_rot_c is entirely controlled by gamma(theta), the physical interpretation of this profile as a spatially varying confinement temperature would require an independent check, e.g., a local Polyakov-loop calculation or a position-dependent saddle point. I recommend adding a paragraph that clarifies the precise status of T_rot_c and softens the comparison with lattice results; the free-energy computation and Eq. (4.5) itself can stand as they are.
minor comments (6)
  1. [Eq. (3.16)] Substituting M from Delta_r(r_+)=0 into the first equality gives an extra factor of 1/(2 r_+^2) in the second equality; for a=b=0 the two displayed expressions differ by a factor of 2. The phase boundary E=0 is unaffected because the factor is positive, so the critical temperature results remain valid, but the displayed free energy should be corrected.
  2. [Eq. (4.10)] The near-luminal expansion is missing the overall factor 1/3 that follows from Eq. (4.5); the sign of partial T_rot_c / partial epsilon is unchanged, but the formula should read T_rot_c / T_c(0,0) = [1 + sqrt(1-w^2) + epsilon] / [3 sqrt(1 - w^2 cos^2 theta - sin^2 theta)] + O(epsilon^2).
  3. [Throughout] There are minor typos, including 'break troughs' (p. 1), 'Tolman-Ehrenfast' (Secs. 4 and 5), '0 <= r < -infinity' (Sec. 2.1, should be 0 <= r < infinity), and 'presetend' (Sec. 3.1).
  4. [Sec. 5] The sentence 'Our results are closer to LQCD for w=1 or theta=pi/2, as the expansion coefficient is larger, B2=1/6' is confusing because the quoted lattice coefficients (0.7, 1.3, 0.5) are all larger than 1/6; please reword to make clear that the comparison is qualitative.
  5. [Fig. 6(b)] The caption says 'v_psi = 0.8' while the text and panel labels specify v_phi = 0.8; please correct.
  6. [References] References [14] and [15] are the same paper and should be merged or one removed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (4.5) is derived from an independent MP Hawking-Page free-energy computation plus the standard Tolman-Ehrenfest factor, with no fitted parameters.

full rationale

The derivation chain is self-contained. The static-frame critical temperature (3.19) is obtained from an explicit Hawking-Page free-energy calculation for the unequal-rotation Myers-Perry black hole: the regularized free energy is computed in Eq. (3.16), the transition condition E_BH = 0 gives r_c^+ = l, and the critical temperature becomes Tc/Tc(0,0) = (1/3)(1 + 1/gamma_phi + 1/gamma_psi). No free parameter is fitted to the target outcome. The co-rotating temperature (4.5) is then formed by applying the standard Tolman-Ehrenfest law T_rot = gamma T_BH at that critical horizon, with gamma defined in Eq. (4.4) from the co-rotating boundary metric. The angular dependence of the result is a stated consequence of gamma(theta), not a hidden input. The lattice comparison in Sec. 5 uses the quoted B2 coefficients as external benchmarks, not as data used to fix the model. The use of Ref. [31] is limited to the equal-rotation limit and to the interpretive step of calling T_rot a local confinement temperature; the paper explicitly acknowledges in Sec. 1 that 'the system is either in a plasma or in a hadronic state, independent of observer' and in Sec. 5 that the model 'would not support inhomogeneities.' These are limitations of the physical interpretation, not circular reductions. No load-bearing step reduces by construction to its own input, so the honest finding is no significant circularity.

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

The model uses standard ingredients: Myers-Perry-AdS5 black holes, Hawking-Page thermodynamics, and the Tolman-Ehrenfest law. No new particles, forces, or conserved quantities are introduced. The physical parameters (l, a, b, M) are inputs from the gravity solution, not fitted to data; the ratio w is a scanned parameter.

assumptions (5)
  • domain assumption AdS/CFT duality: the 5D Myers-Perry-AdS black hole is dual to a 4D strongly coupled plasma on S^3, with the Hawking-Page transition describing deconfinement (Sec. 1, citing Witten [38]).
    This is the framework that connects black hole thermodynamics to the QGP confinement temperature; it is a modeling assumption, not derived in this paper.
  • domain assumption Tolman-Ehrenfest law T_loc sqrt(-g_tt) = const applies to the rotating boundary and determines the co-rotating local temperature (Sec. 4, Eq. 4.5).
    The law is a standard relativistic result [33,34], but applying it to assign a local 'confinement temperature' to each observer is an interpretive choice central to the claim.
  • standard math Background subtraction with thermal AdS gives the regularized free energy; the Hawking-Page transition occurs when the free energy vanishes, at r_+ = l (Sec. 3).
    This is the standard method for computing HP transitions; the paper uses it without modification.
  • domain assumption The conformal boundary is a static S^3; the conformal factor e^Phi = r/(l sqrt(Delta_theta)) is removed by a conformal transformation so that the static-frame local temperature equals T_BH (Sec. 4.1).
    The temperature transformation under conformal rescaling is standard (Ref. [63] appendix), but the cancellation is essential to the frame interpretation.
  • domain assumption Rotation parameters satisfy 0 <= a, b < l, so the boundary rotates below the speed of light and Xi_a, Xi_b > 0 (Sec. 2.1).
    This excludes regions with naked singularities and superluminal boundary rotation; it bounds the parameter space of the plots.

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Pith. "Pith review of Frame-dependency of the confinement temperature in a strongly-coupled plasma under rotation: a holographic description." pith.science (2026). https://pith.science/paper/2G74GRHQ

@misc{pith2026260813301,
  author       = {Pith},
  title        = {Pith review of: Frame-dependency of the confinement temperature in a strongly-coupled plasma under rotation: a holographic description},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2G74GRHQ}},
  note         = {Machine review of arXiv:2608.13301}
}
read the original abstract

Recently, it was demonstrated that the disagreement between lattice calculations and holographic models, regarding rotational effects in the quark-gluon plasma (QGP), occurs due to different choices of reference frames. While a static observer measures a confinement temperature that decreases with rotation, one in a co-rotating frame finds the opposite behavior. Both results are correct, and a comprehension of the frame-dependency of the critical temperature is a significant step in the description of the QGP under rotation. In this article, we generalize this previous holographic result by describing the plasma through the most general Myers-Perry black hole solution. This breaks the spherical symmetry present in the equal angular momentum case, considered before. As a consequence, the local temperature measured by a co-rotating observer has a non-trivial angular dependence: it can decrease, increase or even behave non-monotonically when rotational velocity increases.

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