{"id":"6e992711-501e-4aa4-b7ac-1207b76b77bb","arxiv_id":"2608.13301","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For a rotating plasma dual to a general Myers-Perry black hole, the confinement temperature measured by a co-rotating observer can decrease, increase, or be non-monotonic with angular velocity, depending on the angle and the ratio of the two rotation parameters.","lead":"This paper extends a holographic model of the rotating quark-gluon plasma to a black hole with two different rotation speeds, breaking spherical symmetry. It finds that the apparent confinement temperature depends on the observer's position and rotation frame, and can decrease, increase, or be non-monotonic as rotation speeds up.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Angular dependence of the co-rotating critical temperature rests on identifying the global HP temperature with a local Tolman-Ehrenfest temperature; a local order-parameter check is needed to confirm it is a confinement temperature.","rationale":"The reader's weakest assumption matches the concern I find most load-bearing: attaching a local, observer-dependent confinement temperature to a global Hawking-Page transition is an interpretive step carried over from Ref. [31] and is not derived from first principles. The free-energy calculation and the resulting formula (3.19)/(4.5) are internally consistent, reduce correctly to the equal-angular-momentum and single-spin limits, and the critical-horizon condition r_c = l reproduces the standard Kerr-AdS result, so I do not see a technical error in the central derivation. The remaining issue is physical interpretation: the system is globally either confined or deconfined, and the local temperature profile is a kinematic Tolman-Ehrenfest effect. The paper explicitly acknowledges this limitation, and the mixed-phase construction it cites as future work is precisely the calculation that would validate or falsify the interpretation. Because the mathematical core is sound and the limitation is transparent, the appropriate verdict remains ACCEPT; the concern would only become decisive if a future mixed-state computation showed that the local transition boundary disagrees with Eq. (4.5).","tokens_in":17870,"tokens_out":31456,"duration_ms":357853,"concrete_test":"Construct the inhomogeneous mixed-state candidate for the MP-AdS dual along the lines of Ref. [64]: glue the thermal-AdS and MP-black-hole saddles along a boundary hypersurface at fixed theta, and minimize the total free energy as a function of global T and (a,b) to find the phase-separating angle theta_*(T,a,b). Then compare the local Tolman temperature at that boundary, gamma(theta_*) T, with Eq. (4.5). If the locus where gamma(theta) T equals T_rot_c(theta) coincides with theta_*(T), the local-temperature identification is supported; if not, Eq. (4.5) is only a kinematic redshift and the angular dependence is not a genuine feature of the confinement transition.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is Eq. (4.5): T_rot_c = gamma * T_c. The derivation in Sec. 4.2 only multiplies the global Hawking-Page critical temperature by the Tolman-Ehrenfest factor gamma. This is a kinematic statement: it tells what local temperature a co-rotating observer reads when the global system sits at the HP transition. Whether that local reading determines the local phase is not derived. The authors explicitly acknowledge (Secs. 1 and 5) that the system is either in a plasma or in a hadronic state independent of the observer, and that the model cannot describe the inhomogeneous mixed phases seen in lattice QCD. The novel angular profile — decrease near a rotation axis and monotonic increase near theta = pi/2 — is entirely controlled by gamma(theta). If the Tolman-Ehrenfest identification carried over from Ref. [31] fails, the central qualitative claim about angular dependence loses its physical meaning. This does not invalidate the free-energy calculation or the kinematic formula, but it is the weakest link between the holographic computation and the title's 'confinement temperature.'","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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).","tokens_in":18037,"tokens_out":22557,"duration_ms":209759,"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":[{"comment":"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.","section":"Sec. 4.2, Eq. (4.5)"}],"minor_comments":[{"comment":"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.","section":"Eq. (3.16)"},{"comment":"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).","section":"Eq. (4.10)"},{"comment":"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).","section":"Throughout"},{"comment":"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.","section":"Sec. 5"},{"comment":"The caption says 'v_psi = 0.8' while the text and panel labels specify v_phi = 0.8; please correct.","section":"Fig. 6(b)"},{"comment":"References [14] and [15] are the same paper and should be merged or one removed.","section":"References"}],"recommendation":"minor_revision","confidential_remarks":"This is a competent and clearly written extension of the authors' previous work [31]. The new ingredient is the general a != b case, which yields an angular-dependent co-rotating temperature. The main risk is that the paper's central claim is phrased more strongly than the Tolman-Ehrenfest identification warrants; however, the authors' own caveats in Secs. 1 and 5 largely mitigate this. I would be comfortable with publication after a minor revision that addresses the interpretation and the small technical errors listed above."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is Eq. (4.5): for unequal rotation parameters the co-rotating confinement temperature depends on the polar angle and on the ratio w = v_psi/v_phi, and it can decrease, increase, or turn over as the velocity grows. That is a real step beyond the authors' own equal-rotation paper, and it is not a trivial add-on. The free-energy calculation is done for the full Myers-Perry metric, the critical horizon radius still comes out at r_+ = l, and the reduction to known limits (a=b, a=b=0, small velocity) checks out. The new integration trick in Sec. 3.1 is a nice piece of technique that should be useful elsewhere. I re-derived Eq. (4.5) from their expressions and found no algebraic issues. The small-velocity expansion, the threshold angle Eq. (4.9), and the near-luminal behavior all follow consistently.\n\nThe soft spot is exactly where the stress-test note points: identifying T_rot = gamma T_BH in Eq. (4.5) as a local confinement temperature is an interpretive jump. The Tolman-Ehrenfest factor says what a co-rotating observer measures when the global system sits at the Hawking-Page transition; it does not by itself show that the local phase boundary is controlled by that local reading. The authors say this themselves in Secs. 1 and 5, and they acknowledge the model cannot describe the inhomogeneous mixed phases seen in lattice QCD. So this is not a hidden flaw, but it is the load-bearing assumption for the paper's title claim. I would not call it fatal: the kinematic statement is correct, the comparison with lattice is framed qualitatively, and the limitation is openly stated. The quantitative mismatch with lattice B2 coefficients is about a factor of a few, and the qualitative behavior for w > 1/sqrt(2) is honestly presented. Two minor issues: Ref. [14] and [15] look like the same paper listed twice, and in Fig. 6(b) the caption says v_psi = 0.8 where the text indicates v_phi = 0.8. Neither affects the results.\n\nThis paper is for people working on holographic descriptions of rotating QGP and on reconciling frame choices with lattice results. It deserves a serious referee: the math is reproducible, the new angular dependence is derived cleanly, and the limitations are not hidden. I would accept it for review and expect it to be publishable after minor revision, mainly tightening the interpretive language around 'local confinement temperature.' I would cite it, and I would bring it to a reading group as a useful example of how to extend a known holographic setup without overclaiming.","headline":"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.","tokens_in":18631,"tokens_out":1216,"would_cite":true,"duration_ms":15125,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["quark-gluon plasma","confinement/deconfinement","Myers-Perry black hole","holographic QCD","Tolman-Ehrenfest law","rotating plasma","Hawking-Page transition","frame dependence"],"falsifier":"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.","tokens_in":17609,"feed_emoji":"🌀","tokens_out":9578,"duration_ms":95404,"temperature":0.7,"pith_summary":"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.","feed_headline":"Angle and frame decide how rotation shifts plasma temperature","feed_subtitle":"Holographic model with two unequal rotation axes predicts deconfinement temperature can rise, fall, or peak with rotation.","key_machinery":"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.","core_discovery":"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\n$$$T^{{\\mathrm{rot}}$}_c(v_\\phi,v_\\psi,\\$\\theta$)=\\frac{\\gamma}{3}\\left(1+\\frac{1}{\\gamma_\\phi}+\\frac{1}{\\gamma_\\psi}\\right)T_c(0,0),\\qquad \\gamma=\\left(1-v_\\$phi^{2}$\\$sin^{2}$\\$\\theta$-v_\\$psi^{2}$\\$cos^{2}$\\$\\theta$\\right)^{-1/2}.$$\nIn 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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Establishes the equal-angular-momentum result this paper generalizes: co-rotating observers see the confinement temperature increase while static observers see it decrease.","marker":"[31]"},{"why":"Witten's Hawking-Page identification of black-hole and thermal-AdS phases with deconfined and confined gauge-theory states is what grounds the temperature extraction.","marker":"[38]"},{"why":"Hawking-Page's original computation of the AdS black-hole to thermal-AdS phase transition is the thermodynamic setup being adapted to the Myers-Perry geometry.","marker":"[50]"},{"why":"The Tolman-Ehrenfest law relating local temperature to the reference temperature is the mechanism that converts the critical temperature into static and co-rotating frames.","marker":"[33, 34]"},{"why":"Provides the Myers-Perry black-hole solution with two independent rotation parameters that serves as the dual spacetime.","marker":"[55, 56]"},{"why":"The Gibbons-Perry-Pope first law fixes the thermodynamically relevant angular velocities and justifies the horizon/boundary subtraction used in the thermodynamics.","marker":"[59]"},{"why":"Lattice gluodynamics results in the co-rotating frame supply the small-velocity coefficient the frame-corrected holographic prediction is meant to match.","marker":"[21, 22]"}],"fun_headline_variants":["Rotation's effect on plasma temperature depends on observer and angle","Holographic plasma: frame and angle decide how rotation shifts critical temperature","Unequal rotations make deconfinement temperature angle-dependent","Co-rotating observer sees plasma temperature rise, fall, or peak with rotation","Myers-Perry: angle and frame decide rotation's effect on critical temperature"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Rotation's effect on plasma temperature depends on observer and angle","Holographic plasma: frame and angle decide how rotation shifts critical temperature","Unequal rotations make deconfinement temperature angle-dependent","Co-rotating observer sees plasma temperature rise, fall, or peak with rotation","Myers-Perry: angle and frame decide rotation's effect on critical temperature"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001795,"raw_usage":{"total_tokens":7086,"prompt_tokens":974,"completion_tokens":6112,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":590,"completion_tokens_details":{"reasoning_tokens":6019}},"tokens_in":590,"tokens_out":6112,"duration_ms":45442,"temperature":1.0,"reasoning_tokens":6019,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:16:05.435011+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Unraveling the effect of rotation on the confinement/deconfinement transition of the quark-gluon plasma","cited_arxiv_id":"2511.22464","evidence_quote":"Establishes the equal-angular-momentum result this paper generalizes: co-rotating observers see the confinement temperature increase while static observers see it decrease."},{"cited_title":"Witten,Anti-de sitter space, thermal phase transition, and confinement in gauge theories, Adv.Theor.Math.Phys.2(1998) 505","cited_arxiv_id":null,"evidence_quote":"Witten's Hawking-Page identification of black-hole and thermal-AdS phases with deconfined and confined gauge-theory states is what grounds the temperature extraction."},{"cited_title":"Gibbons, M.J","cited_arxiv_id":null,"evidence_quote":"The Gibbons-Perry-Pope first law fixes the thermodynamically relevant angular velocities and justifies the horizon/boundary subtraction used in the thermodynamics."}],"review_version":1}