{"id":"cccd9d20-8db8-4a23-85a1-1044070d3a7b","arxiv_id":"2501.16446","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In the hard wall and soft wall AdS/QCD models, increasing plasma rotation lowers the deconfinement temperature and lowers the zero-temperature critical quark chemical potential.","lead":"This paper calculates how rotation and quark density together shift the temperature at which strongly interacting matter becomes deconfined, using two holographic AdS/QCD models. Faster rotation and higher density both lower this critical temperature, extending earlier holographic results to the combined case.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The soft-wall result that μ0 decreases with rotation may be an artifact: at the tabulated critical horizons (z_h√c up to 1.43) the small-z RN relation μ=q z_h^2 is off by a factor of ~3, and using the exact soft-wall gauge solution can change—possibly reverse—the μ0(ω) trend.","rationale":"The reader's weakest assumption is correct and more serious than a quantitative shift. The small-z relation μ=q z_h^2 is embedded in the definition of μ0, so the qualitative claim that μ0 decreases with rotation is exactly where the approximation is used. At the tabulated horizons the correction factor is large and has the right sign to reverse the trend: the approximate zero-temperature relation μ=√2/z_h decreases with z_h, while the exact relation increases over the relevant interval. This is not a consensus disagreement; it is an internal validity check of the model's own probe solution. If the exact gauge field changes μ0(ω), the soft-wall phase diagram and the combined-effect conclusion (Section 4) need revision. I agree with the reader's conditional verdict: the paper is worth publishing only after this check is done. I did not make the hard-wall equation typos the main concern because they are likely typographical and do not directly threaten the qualitative rotation trend, though they should be fixed.","tokens_in":16273,"tokens_out":37531,"duration_ms":326817,"concrete_test":"Replace Eq. (2.5) by the exact soft-wall gauge field A_t(z)=μ[1-(e^{cz^2}-1)/(e^{cz_h^2}-1)] in the action (3.6)–(3.9), keep the RN metric and η=1, and recompute the soft-wall Hawking-Page curves. Compare μ0(ωl=0.5) and μ0(ωl=0) with Eq. (4.7). If μ0 no longer decreases with ωl, the central soft-wall claim fails; if it still decreases, the approximation is safe.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The soft-wall branch of the central claim—especially μ0(ω) decreasing with rotation—rests on Eq. (2.9), μ=η q z_h^2, obtained from the small-z RN gauge field (2.5). In the soft-wall dilaton background the exact Maxwell solution is A_t(z)=μ[1-(e^{c z^2}-1)/(e^{c z_h^2}-1)], so the charge–potential relation is η q=μ c/(e^{c z_h^2}-1), not μ/z_h^2. The critical horizons in Tables 1 and 3 reach z_h√c≈1.43, where e^{z_h^2}-1≈3.1 z_h^2; the approximation is not 'small z'. With the exact relation, the T→0 condition q^2 z_h^6/2=1 becomes μ=√2(e^{z_h^2}-1)/z_h^3, which is increasing in z_h over the tabulated range, whereas the approximate μ=√2/z_h is decreasing. Since rotation moves the zero-temperature critical horizon from z_h≈0.99 (ωl=0) to ≈1.43 (ωl=0.5), the exact solution can plausibly reverse the claimed decrease of μ0 with ω. The statement in Section 4 that the tabulated horizons legitimize Eq. (2.5) is therefore not supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":16600,"tokens_out":15557,"duration_ms":144556,"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":[{"comment":"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.","section":"§2 and §3.2, Eqs. (2.5)-(2.9), (3.23); Tables 1 and 3"},{"comment":"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.","section":"§4, Eqs. (4.6)-(4.7) and Abstract"}],"minor_comments":[{"comment":"There are several typographical errors: 'hidrodynamic' in the Introduction, and 'ploted', 'criterea', and 'happpens' in Section 4.","section":"Introduction and Section 4"},{"comment":"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.","section":"Eq. (3.18)"},{"comment":"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.","section":"Table 2, row \\bar\\mu=0.650"},{"comment":"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.","section":"Eq. (3.15)"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe clean half of this paper is the hard wall calculation. It extends the authors' earlier Hawking-Page results to the combined (μ,ω) plane, reduces to the right limits, and produces a phase diagram surface that people doing rotating heavy-ion phenomenology will want. The claim that μ0 decreases with rotation is a genuine new output of the hard wall model.\n\nThe soft wall half does not hold up. The gauge field is taken as A0(z)≈i(μ−ηqz^2), which is the RN solution without the dilaton. In the soft wall background the exact Maxwell solution is A_t(z)=μ[1−(e^{cz^2}−1)/(e^{cz_h^2}−1)], so the charge–potential relation is ηq=μc/(e^{cz_h^2}−1) rather than μ/z_h^2. At the critical horizons listed in Tables 1 and 3, z_h√c reaches ~1.4; e^{z^2}−1 is three times z^2 there, so the approximation is not small-z. Using the exact relation, the T→0 condition qz_h^3=√2 gives μ0 ∝ (e^{z_h^2}−1)/z_h^3, which increases with z_h in the tabulated range, while the approximate μ0∝1/z_h decreases. Since rotation shifts the extremal horizon from about 0.99 to 1.43, the soft wall result for μ0(ω) likely reverses sign once the exact gauge field is used. The Section 4 claim that the tabulated horizons legitimize the approximation is therefore not supported.\n\nTwo smaller points. The last paragraph says the results agree with experimental data; there is no direct experimental determination of the phase boundary's dependence on vorticity, so that is an overstatement. And the lattice gluodynamics results [17,18] showing Tc increasing with rotation deserve more than a one-line mention in the introduction, given that both models here predict the opposite sign.\n\nThe hard wall result is worth having, and the soft wall problem is a fixable approximation issue rather than a fatal conceptual error. A referee should ask for the soft wall to be redone with the exact gauge field solution and the claims restated. I'd send it out.","headline":"Hard wall result is solid, but the soft wall's μ0(ω) conclusion is probably an artifact of the small-z gauge field approximation.","tokens_in":17129,"tokens_out":6411,"would_cite":true,"duration_ms":50839,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["holographic QCD","Hawking-Page transition","rotating quark-gluon plasma","confinement/deconfinement","quark chemical potential","AdS/QCD","Reissner-Nordström black hole"],"falsifier":"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.","tokens_in":16039,"feed_emoji":"🌀","tokens_out":7610,"duration_ms":65689,"temperature":0.7,"pith_summary":"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.","feed_headline":"Spinning plasma lowers QCD deconfinement temperature","feed_subtitle":"Rotation and quark density push the quark-gluon plasma boundary to lower temperatures and densities.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the rotating charged AdS black-hole metric and the approximate gauge-field solution used to identify the chemical potential.","marker":"[32]"},{"why":"Gives the zero-density, zero-rotation hard- and soft-wall Hawking–Page calculation, fixing the infrared scales and the reference critical temperatures.","marker":"[42]"},{"why":"Establishes the finite-density, zero-rotation Hawking–Page transition that this paper extends by adding angular velocity.","marker":"[44]"},{"why":"Computes the deconfinement temperature for a rotating plasma at zero chemical potential in the same approach, the case generalized here.","marker":"[21]"},{"why":"Provides the EMD-model rotating phase diagram used for comparison and the $\\mu/\\gamma$ rescaling of the chemical potential.","marker":"[25]"},{"why":"Gives the exact soft-wall vector-field solution that the paper cites as the check on its small-$z$ approximation.","marker":"[46]"},{"why":"Relates the gauge parameter $\\eta$ to $N_c$ and $N_f$ and connects quark to baryon chemical potentials, used for the physical $\\mu_0$ values.","marker":"[34]"}],"fun_headline_variants":["Spinning plasma drops QCD deconfinement threshold","Rotation lowers deconfinement temperature in dense QCD","Hawking-Page maps rotation effect on QCD phase diagram","Rotating quark plasma weakens confinement transition","Angular momentum eases deconfinement in holographic QCD"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Spinning plasma drops QCD deconfinement threshold","Rotation lowers deconfinement temperature in dense QCD","Hawking-Page maps rotation effect on QCD phase diagram","Rotating quark plasma weakens confinement transition","Angular momentum eases deconfinement in holographic QCD"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000249,"raw_usage":{"total_tokens":1521,"prompt_tokens":890,"completion_tokens":631,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":506,"completion_tokens_details":{"reasoning_tokens":549}},"tokens_in":506,"tokens_out":631,"duration_ms":6195,"temperature":1.0,"reasoning_tokens":549,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T13:15:20.993560+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"A Dual Geometry of the Hadron in Dense Matter","cited_arxiv_id":null,"evidence_quote":"Supplies the rotating charged AdS black-hole metric and the approximate gauge-field solution used to identify the chemical potential."},{"cited_title":"A Holographic Prediction of the Deconfinement Temperature","cited_arxiv_id":null,"evidence_quote":"Gives the zero-density, zero-rotation hard- and soft-wall Hawking–Page calculation, fixing the infrared scales and the reference critical temperatures."},{"cited_title":"Hawking-Page transition in holographic QCD at finite density","cited_arxiv_id":null,"evidence_quote":"Establishes the finite-density, zero-rotation Hawking–Page transition that this paper extends by adding angular velocity."},{"cited_title":"Confinement-deconfinement temperature for a rotating quark-gluon plasma","cited_arxiv_id":null,"evidence_quote":"Computes the deconfinement temperature for a rotating plasma at zero chemical potential in the same approach, the case generalized here."},{"cited_title":"Phase diagram of holographic thermal dense QCD matter with rotation","cited_arxiv_id":null,"evidence_quote":"Provides the EMD-model rotating phase diagram used for comparison and the $\\mu/\\gamma$ rescaling of the chemical potential."},{"cited_title":"Cold Quark Matter, Quadratic Corrections and Gauge/String Duality","cited_arxiv_id":null,"evidence_quote":"Gives the exact soft-wall vector-field solution that the paper cites as the check on its small-$z$ approximation."},{"cited_title":"Holography, Heavy-Quark Free Energy, and the QCD Phase Diagram","cited_arxiv_id":null,"evidence_quote":"Relates the gauge parameter $\\eta$ to $N_c$ and $N_f$ and connects quark to baryon chemical potentials, used for the physical $\\mu_0$ values."}],"review_version":1}