{"id":"07b3f2a7-99e2-4dd5-9112-a487422a83ab","arxiv_id":"2507.20233","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"In a holographic model of chiral matter, thermodynamically unstable states show growing long-wavelength perturbations, and the scalar spectrum displays a diffusion-to-propagating transition with a low-frequency transport peak.","lead":"Using a holographic model of strongly interacting matter, the authors show that unstable states near a first-order chiral phase transition develop growing perturbations and that the dominant excitation changes from a diffusive mode to a propagating, sound-like mode. The result gives a concrete picture of how quark matter may respond near the QCD transition and what spectral signals could be looked for.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Probe-limit backreaction is the load-bearing assumption: kc, the spinodal region, and the QNM spectrum are computed on a fixed AdS-Schwarzschild metric, and no test of backreaction or finite-k nonlinear evolution is provided.","rationale":"The reader's weakest assumption and the main risk coincide. The paper uses a standard bottom-up model and the linearized equations look internally consistent, so I found no obvious mathematical error. But the quantitative claims, especially kc(T) and the transport peak, depend on the frozen geometry; the probe limit is not tested. The missing nonlinear PDE and the k=0-only run further weaken the 'both linear and nonlinear' statement in the abstract. I also flag the summary sentence in Sec. VI that states instability appears for backgrounds which 'lack thermodynamical instability'; this contradicts the abstract and Sec. IV and should be fixed, though it appears to be a wording slip. Because the underlying linear QNM analysis is plausible and the missing checks are precisely what the CONDITIONAL verdict already requires, I recommend keeping that verdict rather than accepting or rejecting.","tokens_in":15286,"tokens_out":14482,"duration_ms":162878,"concrete_test":"Solve the coupled Einstein-scalar system (including the scalar stress tensor from the action in Eq. (1)) at leading order in the backreaction, and recompute the spinodal boundaries and the lowest scalar QNM at T=173.3 MeV. Specifically, check whether the unstable branch still has Im[omega] > 0 for 0 < k < kc, and whether kc shifts by more than 10%. If backreaction is negligible, the probe-limit results stand; if not, Figs. 3-5 are not predictions of the full model.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claims of this paper are computed entirely in the probe limit: the metric is the fixed AdS-Schwarzschild black hole (Eq. (7)), and the chiral condensate/gauge fields do not backreact (Sec. II.B). This is more than a standard technical approximation because the paper's own logic invokes the Gubser-Mitra conjecture; that conjecture is about the classical stability of black-brane solutions in which the matter fields are part of the geometry. In the probe limit the black hole has no unstable metric mode; the positive-Im[omega] mode found in Fig. 3 is a scalar negative mode in an external potential associated with the thermodynamically unstable matter branch. The location of the spinodal region (green lines in Fig. 1), the value of kc(T) (Fig. 4), and the spectral transport peak (Figs. 8-11) could all shift if the scalar stress tensor changes the metric, horizon position, and temperature mapping. No control parameter or estimate of backreaction size (e.g., N_f/N_c or the 5D gravitational coupling) is given. The nonlinear evidence in Sec. IV.B is also restricted to k=0, with no explicit evolution equation, numerical scheme, or convergence check, so it does not directly test the finite-momentum instability that defines kc. Consequently the quantitative content of the central claim is insecure until the probe-limit assumption is tested.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies dynamical properties of chiral matter using a soft-wall AdS/QCD model with a nonlinear scalar potential and a modified dilaton profile. In the probe limit, with the metric fixed to AdS-Schwarzschild, the authors compute the chiral condensate and identify a first-order chiral phase transition with a spinodal region. They then analyze linearized scalar perturbations, Eq. (14), and extract quasi-normal modes via the condition s1(k)=0. For thermodynamically unstable background solutions they find quasi-normal modes with positive imaginary frequency for 0<=k<=k_c, which they interpret as dynamical instability; k_c(T) is computed and peaks near the transition temperature. A nonlinear evolution in Eddington-Finkelstein coordinates is also reported for k=0. Separately, the paper describes a diffusion-to-sound transition of the lowest quasi-normal mode as momentum increases, and shows that the spectral function develops a low-frequency transport peak when the diffusive mode dominates. The authors propose a heuristic interpretation relating this transition and the transport peak to chiral symmetry restoration.","tokens_in":15565,"tokens_out":7248,"duration_ms":81569,"significance":"If the results hold, the paper provides a concrete holographic example where thermodynamic instability in the spinodal region is accompanied by dynamical instability with a finite critical momentum, and it identifies an interesting diffusion-to-sound transition in the scalar quasi-normal spectrum with a corresponding transport peak. The linearized calculation and the quasi-normal mode extraction are standard and internally consistent, and the paper makes falsifiable predictions for k_c(T) and for the temperature dependence of the spectral function. The strength of the paper is the relatively complete QNM analysis connecting the unstable background branch to a growing mode and the explicit demonstration that the unstable region is momentum-bounded. The main weaknesses are the reliance on the probe limit without a backreaction estimate and the very limited nonlinear-evolution evidence, as detailed below.","major_comments":[{"comment":"The nonlinear evolution evidence is presented with insufficient detail to support the paper's central two-level claim. No nonlinear equation of motion is written (only the Eddington-Finkelstein metric (19) is given), no numerical scheme, boundary conditions, or convergence checks are described, and the calculation is restricted to spatially homogeneous perturbations. Since the critical momentum k_c in Sec. IV.A is defined by a finite-momentum dispersion relation, a k=0 evolution does not directly test the finite-momentum instability that defines k_c; moreover, a spatially homogeneous perturbation cannot be described as generating 'phase separation' in any spatial sense. Please either provide the explicit nonlinear evolution equations and numerics, or restrict the nonlinear claim to the k=0 sector.","section":"IV.B, Eq. (19)"},{"comment":"All dynamical results are computed in the probe limit, where the matter fields do not backreact on the AdS-Schwarzschild metric. The Gubser-Mitra conjecture, however, concerns the classical stability of black-brane solutions whose matter content is part of the geometric background; in the probe limit the spacetime itself has no unstable mode, and the positive-Im(omega) mode found in Fig. 3 is a scalar-field instability on a fixed background. The manuscript offers no control parameter, such as N_f/N_c or the 5D gravitational coupling, and no estimate of the size of the matter stress tensor. Consequently the quantitative values of k_c(T), the spinodal boundaries, and the transport peak are uncontrolled if backreaction is not negligible. A concrete estimate of the backreaction, or an explicit statement that all conclusions refer to the probe limit of this particular model, should be added.","section":"II.B, Eq. (7)"},{"comment":"The identification of the low-frequency peak as a transport peak and its connection to the diffusive quasi-normal mode is not made quantitative. The paper does not show that the residue of the quasi-normal pole controls the peak height, and Eq. (20) explicitly acknowledges that no transport coefficient, such as a diffusion constant, is extracted from rho(omega,k)/omega. The claims that the peak width is governed by the imaginary part of the lowest QNM and that the peak amplitude is maximal at T~190 MeV should be supported by a fit to a pole-residue form rather than by visual comparison of Figs. 8-11. As written, the interpretation in Sec. V remains heuristic, and a quantitative pole analysis would substantially strengthen the central transport-peak claim.","section":"V.B, Figs. 8-11"}],"minor_comments":[{"comment":"The first paragraph contains a typo: 'the existing of possible dynamical instability' should be 'the existence of possible dynamical instability'.","section":"VI"},{"comment":"The sentence 'the dynamical instability only appears with respect to the background which lacks thermodynamical instability' appears to contradict the results of Sec. IV.A, where instability is found precisely on the thermodynamically unstable background; this should be corrected to 'possesses thermodynamical instability'.","section":"VI"},{"comment":"The numerical method used to solve Eq. (14) and locate the quasi-normal modes is not described. Please mention the discretization or shooting method, the treatment of the incoming-wave boundary condition at the horizon, and the precision checks used for the reported frequencies.","section":"III"},{"comment":"The symbol sigma is used both for the perturbation field in Eq. (12) and for the chiral condensate on the vertical axis of Fig. 5, which may confuse the reader; please use distinct notation in the figure or in the text.","section":"Eq. (12) and Fig. 5"},{"comment":"The caption of Fig. 3 states 'with respect to three different background solutions'; it would be clearer to say 'for the three background solutions at the same temperature T=173.3 MeV'.","section":"IV.A, Fig. 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is a model study in the established soft-wall AdS/QCD framework, and its main novelty is the finite-momentum QNM analysis of the spinodal instability and the diffusion-to-sound transition. I believe the central linearized calculation is sound, but the probe-limit assumption and the under-documented nonlinear section need to be addressed before publication. This is fixable in revision; I do not see a fatal internal error."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a clean model-level exercise. It takes the established soft-wall AdS/QCD chiral model, places scalar perturbations on the spinodal-region backgrounds, and shows that the thermodynamically unstable branch has a positive-imaginary quasi-normal mode for 0 ≤ k ≤ kc, with kc ≈ 348 MeV at T = 173.3 MeV. It also documents a diffusion-to-sound transition in the lowest scalar mode and ties the diffusive regime to a transport peak in the spectral function. Those are genuinely new results in this model, and the QNM/retarded-correlator formalism in Secs. III and V is standard and internally consistent. I believe the central qualitative message: unstable thermodynamic branch leads to dynamical instability, with a finite critical momentum.\n\nThe soft spots are real and mostly concentrated in what is not shown. The whole calculation is in the probe limit: the chiral scalar and gauge fields live on a fixed AdS-Schwarzschild metric, and there is no estimate of backreaction from the 5D gravitational coupling or N_f/N_c. The paper leans on the Gubser-Mitra conjecture, which in its standard form concerns black-brane geometries where matter is part of the geometry, so it does not automatically transfer to a negative scalar mode in an external potential. That does not sink the observation—the scalar mode is still a legitimate instability of the matter sector—but it means kc and the spinodal boundaries are only as good as the probe approximation. I would have liked one paragraph with a control parameter or a backreacted check.\n\nSecond, the numerics. There is no code, no data release, and no convergence checks for the QNM solver or the time evolution. The nonlinear section is restricted to k = 0, so it does not directly probe the finite-momentum instability that defines kc. The claim about full nonlinear evolution rests on a figure with no explicit equation of motion or numerical scheme. That is a checkable omission, not a fatal flaw.\n\nThird, a small but irritating internal contradiction: the summary says dynamical instability appears for backgrounds that lack thermodynamical instability, while the body and the physics say it appears on the thermodynamically unstable branch. The abstract and Sec. IV agree with the body, so I read the summary phrase as a typo, but it needs fixing. The physical interpretation of the transport peak is also heuristic; the connection to chiral restoration is plausible but not derived.\n\nWho is this for? People working on holographic QCD phase transitions and transport in chiral matter. It is not a lattice-QCD paper and does not claim quantitative QCD prediction; it is a model-level demonstration. It deserves a serious referee: the formalism is standard, the new results are plausible, and the missing backreaction and numerics checks are the kind of thing a referee can reasonably request. I would accept it for review and ask for a backreaction estimate and numerical details before publication.","headline":"A plausible and clearly-written model-level demonstration that unstable chiral backgrounds in soft-wall AdS/QCD have a finite-momentum dynamical instability and a diffusion-to-sound transition, but the probe limit and missing numerical details keep the quantitative claims provisional.","tokens_in":16106,"tokens_out":2648,"would_cite":false,"duration_ms":27424,"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":"This paper shows, in a holographic soft-wall model of QCD, that chiral matter inside the spinodal region of a first-order chiral transition is dynamically unstable at long wavelengths, and that its lowest scalar mode crosses over from…","keywords":["holographic QCD","chiral phase transition","spinodal instability","quasi-normal modes","transport peak","diffusion-to-sound transition","soft-wall AdS/QCD model","chiral symmetry restoration"],"falsifier":"Relax the probe limit and solve the coupled scalar-plus-metric perturbation equations at $T = 173.3\\,\\mathrm{MeV}$: if no positive-imaginary scalar mode survives for any $k$, the claimed dynamical instability is an artifact of the fixed geometry. Alternatively, in the same probe model, evolve a perturbation with momentum just above $k_c$; if it nevertheless phase-separates, then $k_c$ is not the sharp stability boundary the paper claims.","tokens_in":15064,"feed_emoji":"⚛️","tokens_out":9478,"duration_ms":88670,"temperature":0.7,"pith_summary":"This paper asks whether chiral matter sitting in the thermodynamically unstable branch of a first-order chiral phase transition is dynamically unstable, not merely thermodynamically unstable. Using a holographic soft-wall AdS/QCD model, it finds that scalar perturbations of the chiral condensate grow exponentially on the unstable background for spatial momenta below a critical value ($k_c \\simeq 348\\,\\mathrm{MeV}$ at $T = 173.3\\,\\mathrm{MeV}$), while perturbations on the stable branches decay. The same instability appears in full nonlinear time evolution, where even tiny initial perturbations drive phase separation. The paper also finds that the lowest quasi-normal mode is a purely imaginary diffusive mode at small momentum and becomes a propagating, sound-like mode above a critical momentum; whenever the diffusive mode dominates, the spectral function of $\\bar{q}q$ develops a low-frequency transport peak. The authors connect this diffusion-to-sound transition to chiral symmetry breaking and restoration, independent of the order of the transition.","feed_headline":"Unstable chiral matter grows at long wavelengths","feed_subtitle":"Inside the first-order transition's unstable band, scalar perturbations grow; above a critical momentum they turn sound-like.","key_machinery":"The central object is the lowest quasi-normal mode of the scalar fluctuation field $\\sigma(z,t,\\mathbf{x})$ around the chiral background $\\chi(z)$. These modes solve the linearized bulk equation of motion with ingoing-wave boundary conditions at the black-hole horizon; their complex frequencies $\\omega(k)$ control long-time behavior through $e^{-i\\omega t}$, so $\\mathrm{Im}\\,\\omega > 0$ means exponential growth. The same mode frequencies are poles of the retarded correlator of the scalar operator $\\bar{q}q$, and the spectral function $\\rho(\\omega,k) = -2\\,\\mathrm{Im}\\,G_R(\\omega,k)$ converts the mode structure into the observable transport peak. The instability scale is set by the critical momentum $k_c$ where $\\mathrm{Im}\\,\\omega(k_c)=0$.","core_discovery":"Within the nonlinear soft-wall model at a quark mass of $m_q = 7\\,\\mathrm{MeV}$, the chiral transition is first order with $T_c = 175.4\\,\\mathrm{MeV}$ and a spinodal band roughly from 167.4 to 179.2 MeV. On the thermodynamically unstable background inside that band, the lowest scalar quasi-normal mode has positive imaginary frequency for $0 \\le k \\le k_c$, signaling exponential growth of long-wavelength perturbations; $k_c$ itself peaks at $T = 174.8\\,\\mathrm{MeV}$, close to the transition temperature, so the most dynamically unstable configurations are those near $T_c$. Full nonlinear evolution confirms that even $O(10^{-9})$ perturbations eventually produce macroscopic phase separation. At higher temperatures the lowest mode is purely imaginary (diffusive) at small momentum and propagating with nonzero real frequency at large momentum; the diffusive mode does not vanish but simply decays faster than the propagating one. The spectral function of the scalar operator $\\bar{q}q$ then shows a narrow low-frequency transport peak precisely when the diffusive mode dominates, and the peak height tracks the imaginary part of the lowest mode between about 180 and 190 MeV before chiral restoration weakens the dissipation that produces it.","pith_inferences":["If backreaction of the chiral condensate and gauge fields on the metric were included, the spinodal boundaries, the value of $k_c$, and the mode structure could all shift, so the quantitative peak of instability near $T_c$ is not yet tested against a fully dynamical geometry.","The diffusive mode here is non-hydrodynamic ($\\omega$ does not vanish as $k\\to 0$), so unlike standard charge diffusion it cannot be fit by $\\omega \\simeq -iD k^2$; assigning a meaningful diffusion constant to light chiral scalar fluctuations remains an open question the paper leaves unresolved.","The transport peak appears at nonzero spatial momentum, whereas the standard transport peak is defined at zero momentum; if a Kubo-type formula could be established for this scalar correlator, the peak would point to a new low-frequency transport coefficient associated with chiral condensate fluctuations.","Because the paper ties the transition to the background condensate value, a natural testable extension is to vary the quark mass or add an external magnetic field and check whether the crossover momentum and peak height track $\\langle \\bar{q}q\\rangle$ as predicted."],"forward_implications":["Any perturbation with wavelength longer than $\\ell_c = 1/k_c$ grows on a thermodynamically unstable chiral background, so long-wavelength fluctuations will drive the system toward phase separation while short-wavelength fluctuations relax.","The magnitude of the instability, measured by $k_c$, is largest near the first-order transition temperature ($T=174.8\\,\\mathrm{MeV}$), so matter closest to the transition is most dynamically fragile.","The diffusive mode remains present at all momenta, but above a critical momentum its decay is faster than that of the propagating mode, so long-time evolution is controlled by sound-like modes at short scales and by diffusion at large scales.","When a diffusive mode dominates, the scalar spectral function shows a low-frequency transport peak; the peak's height and the imaginary part of the lowest quasi-normal mode grow together in the range 180 to 190 MeV and then both fall as chiral symmetry is restored.","The diffusion-to-sound transition is not tied to the first-order character of the transition, since it also appears for crossover-like backgrounds at larger quark mass."],"supporting_citations":[{"why":"It supplies the conjecture that local thermodynamic instability induces dynamical instability, the hypothesis this paper tests.","marker":"[15, 16]"},{"why":"It supplies the modified dilaton profile and model parameters that produce spontaneous chiral symmetry breaking in the soft-wall model.","marker":"[32]"},{"why":"It supplies the first-order chiral transition behavior and the spinodal backgrounds that the perturbation analysis uses.","marker":"[33]"},{"why":"It supplies the Lorentzian AdS/CFT recipe that identifies quasi-normal modes with poles of the retarded correlator and gives the spectral function.","marker":"[12]"},{"why":"It supplies the notion of a transport peak in a thermal spectral function, which the paper generalizes to nonzero spatial momentum.","marker":"[55]"}],"fun_headline_variants":["Holographic chiral matter shows dynamical instability at long wavelengths","Chiral matter's transport peak tied to diffusive-to-propagating mode shift","Instability peaks near critical temperature in holographic chiral matter","Spinodal region triggers exponential growth in chiral matter perturbations","Chiral symmetry breaking shapes transport peak in holographic model"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire calculation is done in the probe limit, meaning the chiral condensate and gauge fields are taken not to react back on the AdS black-hole metric; if that backreaction is non-negligible, the spinodal region, the unstable backgrounds, and the quasi-normal mode spectrum could all change.","fun_headline_variants_meta":{"raw":{"variants":["Holographic chiral matter shows dynamical instability at long wavelengths","Chiral matter's transport peak tied to diffusive-to-propagating mode shift","Instability peaks near critical temperature in holographic chiral matter","Spinodal region triggers exponential growth in chiral matter perturbations","Chiral symmetry breaking shapes transport peak in holographic model"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000223,"raw_usage":{"total_tokens":1450,"prompt_tokens":929,"completion_tokens":521,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":545,"completion_tokens_details":{"reasoning_tokens":436}},"tokens_in":545,"tokens_out":521,"duration_ms":5577,"temperature":1.0,"reasoning_tokens":436,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:47:23.601842+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Relax the probe limit and solve the coupled scalar-plus-metric perturbation equations at $T = 173.3\\,\\mathrm{MeV}$: if no positive-imaginary scalar mode survives for any $k$, the claimed dynamical instability is an artifact of the fixed geometry. Alternatively, in the same probe model, evolve a perturbation with momentum just above $k_c$; if it nevertheless phase-separates, then $k_c$ is not the sharp stability boundary the paper claims.","supporting_citations":[],"review_version":2}