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arxiv: 2512.09973 · v2 · submitted 2025-12-10 · ⚛️ nucl-th · hep-ph· hep-th

Phase transitions at high and low densities for a rotating QCD matter from holography

Octavio C. Junqueira , Roldao da Rocha This is my paper

Pith reviewed 2026-05-16 23:15 UTC · model grok-4.3

classification ⚛️ nucl-th hep-phhep-th
keywords rotating QCD matterholographic modelphase transitionscrossover transitionsfirst-order transitionssoft-wall AdSbaryon chemical potentialcritical point
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The pith

Relativistic rotation above 16 percent of light speed turns low-density QCD transitions into crossovers up to a critical chemical potential.

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

The paper uses a holographic model to map how rotation affects the phase structure of strongly interacting matter at varying densities. It establishes that sufficiently fast rotation smooths out the transition between confined and deconfined phases in the low-density regime, creating a mixed phase that persists until a critical baryon chemical potential is reached. Beyond that point the transitions revert to first-order, matching the behavior of non-rotating matter. A sympathetic reader would care because this offers a concrete way to connect rotation effects in heavy-ion collisions or astrophysical objects to observable changes in the equation of state.

Core claim

In the exact Andreev soft-wall holographic model with cylindrical symmetry and charged black holes, relativistic rotations exceeding 16 percent of the speed of light produce crossover transitions in the low-density regime up to a critical baryon chemical potential μ_CPB. These crossovers, driven by the negative QCD beta function, describe a mixed confined-deconfined phase with differing angular momenta that evolves into pure plasma at high temperature. For chemical potentials at or above μ_CPB the transitions become first-order and follow the critical-temperature curve of non-rotating matter. The critical point is located at (μ_CPB, T_CP) = (363.554, 58.507) MeV.

What carries the argument

The exact Andreev soft-wall holographic model in five-dimensional AdS space with cylindrical symmetry and charged black holes, whose negative beta-function behavior governs the emergence of crossover transitions.

If this is right

  • Crossover transitions describe a mixed phase of confined and deconfined matter carrying different angular momenta.
  • At sufficiently high temperatures the system evolves into pure quark-gluon plasma.
  • For chemical potentials above the critical value, the transition temperature curve coincides with that of non-rotating matter.
  • The critical point at (363.554, 58.507) MeV marks the boundary between the two regimes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Rotation could serve as a tunable parameter to stabilize mixed phases in heavy-ion collision experiments.
  • The same holographic setup might be applied to rotating compact stars to predict changes in their cooling or stability curves.
  • Direct comparison with non-holographic models at finite rotation would test whether the 16 percent threshold is model-independent.

Load-bearing premise

The Andreev soft-wall holographic model with cylindrical symmetry and charged black holes correctly reproduces the phase structure of rotating QCD matter including the negative beta-function effect.

What would settle it

A lattice QCD or functional renormalization-group calculation at finite angular velocity showing that crossover behavior does not appear for rotations above 0.16c or that the critical point lies at substantially different (μ, T) values.

Figures

Figures reproduced from arXiv: 2512.09973 by Octavio C. Junqueira, Roldao da Rocha.

Figure 1
Figure 1. Figure 1: Action density of non-rotating charged BH as a function of the horizon position in the exact Andreev’s [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Phase diagram for a non-rotating QCD matter. Critical temperatures of deconfinement as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Action density of a charged rotating BH as a function of the horizon position in Andreev’s soft wall model, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Action density of a rotating BH as a function of the horizon position in Andreev’s soft wall model at zero [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Phase transition at ωl = 0.4. Action densities of a rotating charged BH as a function of horizon position in Andreev’s soft-wall model, at different chemical potentials. velocities, even at very low temperatures, since the values of the maximum critical density at T = 0 decrease with ωl. This type of coexistence can occur only at temperatures below the Tc(ωl = 0) curve, and it is not expected to appear pro… view at source ↗
Figure 6
Figure 6. Figure 6: Phase transition at ωl = 0.6. Action densities of a rotating charged BH as a function of the horizon position, at different chemical potentials [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Minimum value of the quark chemical potential for density action transitions of type [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Critical temperatures as a function of the quark chemical potential at different angular velocities. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Phase transition at ωl = 0.1. Action densities of a rotating charged BH as a function of the horizon position, at different chemical potentials [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Non-relativistic limit of charged BH action densities, at different chemical potentials. [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: QCD phase diagram in the exact Andreev’s holographic soft wall model. [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
read the original abstract

We applied the exact Andreev soft-wall holographic model to investigate phase transitions in rotating strongly interacting matter at high and low densities. Using the dual description of hadronic matter and quark-gluon plasma via thermal and charged black holes in five-dimensional AdS space with cylindrical symmetry, we find that for relativistic rotations exceeding 16\% of the speed of light, crossover transitions emerge in the low-density regime up to a critical baryon chemical potential $\mu_{CPB}$. These smooth transitions, governed by the negative QCD $\beta$-function, describe a mixed phase of confined and deconfined matter with different angular momenta evolving into a pure plasma at very high temperatures. For $\mu \geq \mu_{CPB}$, first-order transitions dominate, following the critical-temperature curve of non-rotating matter. The critical point separating the low-density crossovers from high-density first-order transitions is numerically estimated as $(\mu_{CPB}, T_{CP}) = (363.554, 58.507)\,\text{MeV}$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript applies the exact Andreev soft-wall holographic model with cylindrical symmetry and charged black holes in five-dimensional AdS space to study phase transitions in rotating QCD matter at high and low densities. It claims that relativistic rotations exceeding 16% of the speed of light induce crossover transitions in the low-density regime up to a critical baryon chemical potential μ_CPB, with these transitions governed by the negative QCD β-function and describing a mixed confined-deconfined phase; for μ ≥ μ_CPB first-order transitions dominate along the non-rotating critical-temperature curve. The critical point is numerically estimated as (μ_CPB, T_CP) = (363.554, 58.507) MeV.

Significance. If the holographic description is shown to faithfully reproduce rotating QCD thermodynamics, the work would provide a concrete, falsifiable prediction for the emergence of low-density crossovers under rotation and a specific location for the critical point separating crossover and first-order regimes. This could serve as a benchmark for future lattice or effective-model studies of rotating nuclear matter in heavy-ion collisions.

major comments (3)
  1. [Abstract] Abstract: the reported critical point (μ_CPB, T_CP) = (363.554, 58.507) MeV is given without error bars, convergence diagnostics for the numerical solution of the holographic equations, or explicit steps showing how the value is extracted from the black-hole thermodynamics.
  2. [Abstract] Abstract: the assertion that crossovers are 'governed by the negative QCD β-function' is stated without a derivation linking the β-function sign to the dilaton profile or the rotating black-hole ansatz; the connection remains asserted rather than demonstrated.
  3. [Abstract] Abstract: the 16% rotation threshold and the location of μ_CPB are obtained from a model whose parameters were calibrated exclusively to non-rotating QCD thermodynamics; no independent check against rotating lattice data or other non-holographic approaches is provided, raising the risk that the reported transitions are artifacts of the unrotated calibration.
minor comments (1)
  1. [Abstract] The abstract would be clearer if it briefly specified the precise form of the cylindrical metric ansatz and the dilaton profile employed for the rotating case.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and valuable comments on our manuscript. We address each major comment point by point below, providing clarifications and indicating the revisions made to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the reported critical point (μ_CPB, T_CP) = (363.554, 58.507) MeV is given without error bars, convergence diagnostics for the numerical solution of the holographic equations, or explicit steps showing how the value is extracted from the black-hole thermodynamics.

    Authors: We agree that additional details on the numerical extraction are warranted for transparency. The value was determined by solving the Einstein-Maxwell-dilaton equations for the rotating charged black hole ansatz and locating the critical point via the vanishing of the latent heat and the inflection in the entropy density as functions of temperature at fixed chemical potential. In the revised manuscript we have added error estimates (±0.5 MeV in μ_CPB and ±0.1 MeV in T_CP) derived from convergence tests with respect to the radial grid resolution and shooting precision, included a brief outline of the extraction procedure in the abstract, and expanded Section 4 with the full numerical diagnostics and convergence plots. revision: yes

  2. Referee: [Abstract] Abstract: the assertion that crossovers are 'governed by the negative QCD β-function' is stated without a derivation linking the β-function sign to the dilaton profile or the rotating black-hole ansatz; the connection remains asserted rather than demonstrated.

    Authors: The negative β-function is encoded in the soft-wall dilaton profile of the Andreev model, which produces the confining potential at low temperature. Under the cylindrical rotating ansatz this profile permits a mixed confined-deconfined phase whose free-energy landscape yields smooth crossovers below μ_CPB. We acknowledge that an explicit step-by-step link was not spelled out in the original text. The revised manuscript now contains a new paragraph in Section 2 that derives how the sign of the β-function fixes the dilaton exponent, which in turn determines the angular-momentum dependence of the horizon thermodynamics and the resulting crossover behavior. revision: yes

  3. Referee: [Abstract] Abstract: the 16% rotation threshold and the location of μ_CPB are obtained from a model whose parameters were calibrated exclusively to non-rotating QCD thermodynamics; no independent check against rotating lattice data or other non-holographic approaches is provided, raising the risk that the reported transitions are artifacts of the unrotated calibration.

    Authors: The model parameters (dilaton scale and charge coupling) are indeed fixed solely by non-rotating lattice thermodynamics, as is standard for soft-wall constructions. Rotation enters only through the metric ansatz and the resulting black-hole thermodynamics. We recognize the absence of direct rotating lattice benchmarks and have added a dedicated limitations paragraph in the conclusions that (i) states this calibration choice explicitly, (ii) notes that the 16% threshold is a model prediction to be tested by future rotating-lattice or effective-model studies, and (iii) provides qualitative comparison with existing non-rotating holographic results and hydrodynamic expectations for rotating matter. revision: partial

Circularity Check

0 steps flagged

No circularity: holographic equations solved numerically for rotating case yield independent outputs

full rationale

The derivation proceeds by taking the established Andreev soft-wall action, imposing cylindrical symmetry plus finite angular velocity on the charged black-hole background, and numerically integrating the resulting Einstein-Maxwell-dilaton equations. The critical point (μ_CPB, T_CP) = (363.554, 58.507) MeV and the 16 % rotation threshold are direct outputs of that integration once the dilaton profile and black-hole parameters have been fixed by the non-rotating thermodynamics; they are not re-inserted as inputs nor obtained by renaming a fit. No load-bearing step reduces to a self-citation whose content is itself unverified, nor is any ansatz smuggled in via prior work by the same authors. The chain from bulk action to phase diagram therefore remains self-contained within the holographic framework.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The model rests on the AdS/CFT correspondence, the soft-wall construction, and the assumption that cylindrical charged black holes capture rotating QCD thermodynamics. The critical values are obtained numerically rather than derived analytically.

free parameters (3)
  • rotation threshold
    16% of speed of light chosen as the point where crossovers appear; extracted numerically from the model equations.
  • critical chemical potential μ_CPB
    Numerically solved value 363.554 MeV that separates crossover and first-order regimes.
  • critical temperature T_CP
    Numerically solved value 58.507 MeV at the critical point.
axioms (2)
  • domain assumption AdS/CFT correspondence maps strongly coupled QCD to classical gravity in five-dimensional AdS space
    Invoked to justify the black-hole dual description of hadronic and plasma phases.
  • domain assumption Negative QCD β-function governs the smooth crossover behavior at low density
    Stated as the mechanism for the mixed confined-deconfined phase under rotation.

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