{"id":"ca701950-fe5f-4f1e-812e-e15115a3f6cb","arxiv_id":"2412.01146","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The authors derive second-order transport coefficients and the explicit driving force for non-conformal relativistic fluids dual to Chamblin-Reall gravity with a probe scalar field.","lead":"This paper calculates how an external scalar field pushes a relativistic fluid, using a holographic model built from Chamblin-Reall gravity. It produces explicit formulas for new transport coefficients and for the driving force on the fluid, extending earlier conformal results to non-conformal fluids.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The scalar transport coefficients in (2.36), (2.45), and (3.20)-(3.23) depend on second-order metric perturbations that the paper explicitly does not display; until that omitted algebra is checked the central claim is unverified.","rationale":"The reader's conditional verdict identifies the boundary coupling form in Eq. (1.1) as the weakest assumption. I agree that this coupling is chosen rather than derived, but it is the model definition: the paper computes the holographic dual of a specific bulk action, so different couplings define a different model. The more load-bearing issue is the explicit limitation stated in the manuscript: the second-order metric perturbations are solved but omitted. Since the scalar probe contributes to the Einstein equations at second order, those omitted perturbations are necessary to determine the scalar-induced terms in the stress tensor and the driving force; without them the displayed coefficients cannot be checked from the text. The paper's own discussion in Section 2.2 confirms that scalar effects on the metric begin at second order, making the omission central rather than cosmetic. This does not prove the result is wrong; it makes the result conditional on unpublished algebra. The proposed check would settle whether the omitted computation is consistent. If the test reproduces the displayed coefficients, the central claim is supported; if not, the coefficients would require revision. Because the reader already assigned a conditional verdict and flagged the omitted algebra in the rationale, my concern does not move the verdict; it sharpens the reason for conditionality.","tokens_in":20065,"tokens_out":25972,"duration_ms":245638,"concrete_test":"Pick the reduced AdS black hole with p=3, q=1. Using the displayed first-order solutions (2.17)-(2.18) and the scalar solution (2.27), solve the second-order equations (2.12)-(2.15) for k^(2), alpha^(2), h^(2), w^(2), and j^(2) including the scalar source term. Substitute into (2.32) and (2.42) and verify independently that the coefficients reproduce (2.36) and (2.45), and that \\(\\nabla_\\mu T^{\\mu\\nu}=e^{-\\phi}L\\nabla^\\nu\\phi\\) holds identically. A mismatch in any order-one coefficient would show the omitted algebra is unreliable.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central results are extracted at second order in boundary derivatives. Section 2.2 states: \"The second-order metric perturbations are solved ... the results will be omitted in this paper\"; Section 3.2 similarly says only the scalar solution is offered. Yet the scalar probe enters the Einstein equations at second order through the probe stress tensor in (2.6), so the second-order metric perturbations contain scalar-sourced parts. These perturbations enter the surface tensor (2.32)/(3.18) through K_mu_nu and h_mu_nu, enter the \\(\\bar\\nabla^2\\Phi\\) term in the Lagrangian-density definitions (2.42)/(3.21), and feed the second-order Navier-Stokes constraints (2.29)-(2.31) through \\(\\delta r_H^{(1)}\\). Any error or omission in those unshown solutions would change \\(\\lambda_\\phi\\), \\(\\xi_\\phi\\), and all five \\(\\xi_{\\phi i}\\) without leaving a trace in the displayed equations. No independent derivation or machine-checked algebra is supplied, so the central claim currently rests on the correctness of algebra that the text withholds.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends the fluid/gravity correspondence with a bulk scalar probe to the non-conformal Chamblin-Reall backgrounds. Starting from the reduced compactified AdS black hole, the reduced/compactified Dp-branes, and the smeared Dp-brane, it computes the boundary stress tensor and the Lagrangian density e^{-\\phi}L that produces a driving force \\nabla_\\mu T^{\\mu\\nu}=e^{-\\phi}L\\nabla^\\nu\\phi. The claimed results are two stress-tensor coefficients (\\lambda_\\phi, \\xi_\\phi) and five force coefficients (\\zeta_\\phi, \\xi_{\\phi 1..4}), together with seven identities relating them to the known transport coefficients. The first-order metric perturbations are shown and agree with earlier work; the second-order metric perturbations are, however, explicitly omitted, even though the final coefficients depend on them.","tokens_in":20318,"tokens_out":12415,"duration_ms":110624,"significance":"If the omitted algebra is correct, the paper provides a useful unified generalization of the conformal forced-fluid results of [9,10] to a class of non-conformal holographic models, with explicit q-dependence and T-duality relations. The paper is honest about what it does and does not show: it displays the first-order perturbations, the scalar solutions, and the final coefficient tables, and it claims the q=0 limit reduces to [10]. The claimed identities (\\xi_\\phi=\\tfrac12\\gamma^2\\lambda_\\phi, \\zeta_\\phi=\\eta, etc.) are falsifiable and can be compared with independent computations. The main weakness is that the second-order metric perturbations—which carry scalar-sourced contributions and feed the surface tensor—are withheld, so the central coefficients are not independently verifiable from the manuscript. No machine-checked algebra or ancillary files are provided.","major_comments":[{"comment":"The central results (2.36) and (2.45) are extracted from the surface tensor (2.32) and the Lagrangian-density definition (2.42), but the second-order metric perturbations that enter these expressions are explicitly not shown: §2.2 states “the results will be omitted in this paper.” The scalar probe enters the Einstein equations at second order through (2.6), so α^(2), h^(2), k^(2), w^(2), and j^(2) contain scalar-sourced parts; these feed into K_{μν}, the induced metric in ∇̄²Φ, and the Navier-Stokes constraints (2.29)–(2.31). Since no ancillary computation or independent verification is supplied, the coefficients in (2.36) and (2.45) cannot be checked from the material in the paper. This omission is load-bearing and must be repaired before the central claim can be assessed.","section":"§2.2–2.3"},{"comment":"The same problem occurs for the reduced compactified Dp-brane. The text states that the second-order metric perturbations are solved but only Φ^(2) is given (Eq. (3.12)), and the stress tensor (3.19), the coefficients (3.20), and the Lagrangian coefficients (3.23) are then quoted. The reader has no way to verify that the unshown metric perturbations do not alter these coefficients, particularly because the scalar-induced parts are new relative to [5,6]. The section therefore does not establish its headline results.","section":"§3.2–3.3"},{"comment":"The holographic identification (2.42) relies on the near-boundary relation lim_{r→∞} ∇̄^νΦ = C(r) ∇̄^νϕ with C(r) = (r/L)^{2p/(p-q)} (Table 2 and Eq. (2.40)). With ∇̄^ν defined using the induced metric h^{νρ}, whose inverse scales as (r/L)^{-2p/(p-q)}, one expects ∇̄^νΦ to scale as C(r)^{-1} rather than C(r); the displayed relation therefore appears to have the conformal factor inverted. If this is only a notational convention in which ∇̄^ν is rescaled, it should be stated explicitly; as written, the power-counting in (2.40) is not transparent and obscures the comparison with the q=0 conformal limit.","section":"§2.3, Eq. (2.42)"}],"minor_comments":[{"comment":"The statement that “the final results of the transport coefficients related to both the external scalar field and the driving force … are q-independent” is too strong: ξ_φ in (2.36) depends on q through q/[p(p−1)(p−q)], while the driving-force coefficients in (2.45) are indeed q-independent. Please revise the sentence to specify which coefficients are q-independent.","section":"§2.2, after Eq. (2.27)"},{"comment":"The claimed match with the conformal results [9,10] is asserted (“one can check”) but not demonstrated. A short appendix that sets q=0 in (2.43)–(2.45) and explicitly matches the conventions of [9,10], including the normalization of κ² and of the hypergeometric function H, would strengthen the paper and partially compensate for the omitted second-order metric perturbations.","section":"§2.3 and §5"},{"comment":"The smeared Dp-brane results (4.6) are obtained by the p→p+q substitution rather than by a direct computation of the perturbations. Since the T-duality argument in [2] covers the background transport coefficients, please state explicitly whether the scalar probe sector is also assumed to map under the same T-duality; otherwise the coefficients (4.6) are an extrapolation rather than a derivation.","section":"§4"},{"comment":"The symbol ϕ is used both for the external scalar field in the boundary action (1.1) and for the boundary value of the bulk probe in (2.10), while the bulk dilaton is φ. A short notation table or an explicit sentence distinguishing these objects would avoid confusion.","section":"throughout"}],"recommendation":"major_revision","confidential_remarks":"The omission of the second-order metric perturbation solutions is the single blocking issue. If the authors can include those solutions (even as an ancillary computation) or provide a clear argument that the scalar-induced parts cancel before the boundary limit, the paper would become publishable. I would not reject on the basis of the omitted algebra alone, since the first-order structure and the q=0 limit are consistent with prior work; but as it stands the manuscript's central coefficients cannot be independently verified. The paper is within the scope of the journal and the topic is a natural extension of [9,10]."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a competent, conventional fluid/gravity calculation that does something genuinely new—it puts a probe scalar into the Chamblin-Reall class and extracts the forced-fluid transport coefficients for the reduced AdS black hole, Dp-brane, compactified Dp-brane, and smeared Dp-brane. The Dp-brane scalar coefficients and the seven identities among the seven coefficients are new; the q=0 limit reduces to the known conformal results of Ashok. Credit where due: no coefficients are fitted, the dictionary is standard, and the self-citations to [1–6] are legitimate background input, not the result. The first-order perturbations are displayed and are unchanged by the probe, which is consistent with the scalar entering at second order.\n\nThe soft spots are real. The second-order metric perturbations are explicitly not shown. The scalar probe sources those perturbations through the Einstein equations, and they enter the boundary stress tensor through the surface tensor, the Lagrangian density through the \\bar\\nabla^2 Φ term, and the Navier-Stokes constraints through δr_H^(1). The authors state the results are omitted and give only the Φ^(2) solution. That means the central numbers in (2.36), (2.45), (3.20)–(3.23), and (4.6) cannot be checked from the text. I don't think this is fatal—the pattern of the calculation is standard and the first-order check is encouraging—but it is a genuine verification gap, and a referee should ask for the omitted algebra or a code supplement. The second soft spot is smaller: for the reduced AdS black hole, the driving-force coefficients coincide numerically with the conformal results, so the incremental novelty is mostly in the Dp-brane sections. Finally, the assumed coupling e^{-φ} L is taken from the conformal literature; if the boundary scalar couples through a different operator, the coefficients would change. That is a limitation of the model, not an error.\n\nWho it's for: researchers in holographic hydrodynamics who want explicit non-conformal scalar-force coefficients or who plan electromagnetic/chemical-potential extensions. It deserves a serious referee, but with a request for the omitted algebra. I would not desk-reject.","headline":"New scalar-force transport coefficients for Chamblin-Reall backgrounds, with a verification gap: the second-order metric perturbations are omitted.","tokens_in":20814,"tokens_out":2955,"would_cite":true,"duration_ms":26462,"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":"A probe scalar in the bulk of Chamblin-Reall gravity drives the dual fluid away from conservation.","keywords":["holography and hydrodynamics","fluid/gravity correspondence","Chamblin-Reall gravity","non-conformal relativistic fluid","probe scalar","driving force","transport coefficients","D-branes"],"falsifier":"Compute the holographic stress tensor and its divergence directly from the boundary limit of the bulk surface tensor using an independent near-boundary expansion or a different holographic renormalization scheme for a single Chamblin-Reall background with a time- and space-dependent boundary scalar, and check whether $T^{\\phi}_{\\mu\\nu}$ matches (2.36) and whether the divergence equals the forcing term with coefficients (2.45); a mismatch in any coefficient would disprove the universal seven-identity structure.","tokens_in":19863,"feed_emoji":"🌊","tokens_out":7414,"duration_ms":60548,"temperature":0.7,"pith_summary":"This paper extends the fluid/gravity correspondence to non-conformal Chamblin-Reall backgrounds that carry a probe scalar field in the bulk. It aims to show that the boundary value of the probe, an external scalar field, acts as a driving force on the dual relativistic fluid, so the stress tensor is no longer conserved. By solving the bulk perturbations through second order, the authors extract the transport coefficients tied to the external scalar and the explicit Lagrangian density of the forcing term. The result covers the reduced compactified AdS black hole, the reduced compactified Dp-brane, and the reduced smeared Dp-brane, and it produces seven identities relating the new coefficients to each other and to the known fluid transport coefficients. If correct, the calculation gives a systematic holographic description of forced non-conformal fluids with a scalar external field.","feed_headline":"Probe scalar in gravity forces its dual fluid off conservation","feed_subtitle":"Seven scalar-induced transport coefficients and their identities are extracted from the holographic fluid.","key_machinery":"The load-bearing object is the holographic Lagrangian-density formula $e^{-\\phi}\\mathcal{L} = \\frac{1}{2\\kappa^2}\\lim_{r\\to\\infty}\\left(\\frac{r}{L}\\right)^{\\frac{p(p-q+1)}{p-q}}\\left[-\\nabla_n\\Phi - \\frac{L}{p-1}\\left(\\frac{r}{L}\\right)^{\\frac{q}{p-q}} \\bar{\\nabla}^2\\Phi\\right]$, obtained by comparing the boundary limit of the surface-tensor divergence with the forced Navier-Stokes equation $\\nabla_\\mu T^{\\mu\\nu} = e^{-\\phi}\\mathcal{L}\\nabla^\\nu\\phi$. This formula converts the bulk probe solution into boundary transport coefficients, and it is the step that carries the argument. The perturbation scheme is the standard fluid/gravity expansion: boost the background, promote $r_H$, $u^\\mu$ and the scalar boundary value to functions of $x$, then solve the Einstein-scalar system order by order; the first-order scalar perturbation is $\\Phi^{(1)} = \\tfrac{1}{2} F(r)\\,D\\phi$, and the second-order solution fixes the scalar terms in the stress tensor and the forcing Lagrangian.","core_discovery":"On the gravity side one adds a scalar probe $\\Phi$ that does not backreact on the metric; its boundary limit $\\phi(x)$ is an external scalar field coupled to the dual fluid. The paper claims that the dual fluid's stress tensor acquires the scalar-induced viscous terms $T^{\\phi}_{\\mu\\nu} = \\lambda_\\phi \\partial_{\\langle\\mu}\\phi\\,\\partial_{\\nu\\rangle}\\phi + \\xi_\\phi P_{\\mu\\nu}(\\partial_\\perp\\phi)^2$, with $\\lambda_\\phi$ and $\\xi_\\phi$ given explicitly for each Chamblin-Reall background, and that the forcing Lagrangian density takes the form $e^{-\\phi}\\mathcal{L} = -\\zeta_\\phi D\\phi + \\xi_{\\phi 1} u^\\mu u^\\nu \\partial_\\mu\\partial_\\nu\\phi + \\xi_{\\phi 2}\\partial_\\perp^2\\phi + \\xi_{\\phi 3}\\partial u\\,D\\phi + \\xi_{\\phi 4}D u^\\mu \\partial_\\mu\\phi$, with coefficients listed in (2.45), (3.23) and (4.6). It further claims that these coefficients obey seven identities, including $\\xi_\\phi = \\tfrac{1}{2}\\gamma^2\\lambda_\\phi$, $\\xi_{\\phi 3} = c_s^2\\xi_{\\phi 1} + \\xi_{\\phi 2}$, $\\xi_{\\phi 4} = \\xi_{\\phi 1} - c\\,\\xi_{\\phi 2}$, and the four relations $\\zeta_\\phi = \\eta$, $\\xi_{\\phi 2} = \\lambda_\\phi$, $\\xi_{\\phi 3} = -\\frac{2 c_s^2}{(p-q)\\gamma^2}\\eta\\tau_\\pi^*$, $\\xi_{\\phi 4} = \\eta\\tau_\\pi$. A structurally important point is that in the reduced AdS black hole case all forcing coefficients are independent of the number $q$ of compactified directions, and the smeared Dp-brane coefficients follow from the compactified Dp-brane ones by $p\\to p+q$.","pith_inferences":["The paper does not pursue non-minimal or derivative interactions for the bulk probe, but the same extraction formula would then produce additional forcing terms beyond the five-coefficient Lagrangian, making the seven identities a diagnostic of the minimal coupling.","The same machinery could be applied to an external electromagnetic field by replacing the scalar probe with a bulk gauge field; the forcing terms would then be built from $F_{\\mu\\nu}$ and its derivatives, and the analog of the identity $\\xi_\\phi = \\tfrac{1}{2}\\gamma^2\\lambda_\\phi$ would presumably become a relation between charge and magnetic transport coefficients.","Because the forcing coefficients are independent of $q$ for the reduced AdS black hole, one could look for a similar $q$-independence in higher-order or non-linear response data, where the compactified dimensions might enter only through subleading orders."],"forward_implications":["If the central claim is right, any Chamblin-Reall gravity with a probe scalar has a dual forced fluid whose stress tensor is determined by the two scalar transport coefficients $\\lambda_\\phi$ and $\\xi_\\phi$.","The driving force in the forced Navier-Stokes equation is fixed by the five coefficients $\\zeta_\\phi, \\xi_{\\phi 1}, \\ldots, \\xi_{\\phi 4}$, so no additional unknown functions are needed at second order.","The seven identities reduce the independent scalar-sector data: only two of the four second-order forcing coefficients are independent, and the forcing coefficients are locked to the shear viscosity $\\eta$ and relaxation times $\\tau_\\pi, \\tau_\\pi^*$.","Since the reduced smeared Dp-brane results are obtained from the compactified Dp-brane by $p \\to p+q$, the scalar-sector transport is T-duality covariant in the same way as the background transport.","For $q=0$, the results reproduce the conformal forced-fluid coefficients of the AdS black hole in general dimensions, providing a consistency check."],"supporting_citations":[{"why":"Supplies the Chamblin-Reall backgrounds and the known non-conformal fluid transport coefficients that this paper extends.","marker":"[1]"},{"why":"Introduces the probe-scalar method and the forced-fluid framework that this paper generalizes to non-conformal backgrounds.","marker":"[9]"},{"why":"Provides the conformal arbitrary-dimension forced-fluid result that gives the q=0 limit of the holographic Lagrangian definition.","marker":"[10]"},{"why":"Gives the smeared Dp-brane transport coefficients and the T-duality relation used to obtain Section 4.","marker":"[2]"},{"why":"The original fluid/gravity correspondence framework whose derivative expansion the paper uses.","marker":"[7]"},{"why":"Provides the reduced Dp-brane first-order perturbation solutions and transport coefficients used for comparison.","marker":"[5]"},{"why":"Gives the compactified Dp-brane second-order transport coefficients and perturbation background.","marker":"[6]"}],"fun_headline_variants":["Probe scalar forces dual fluid off conservation","Scalar gradients push holographic fluid out of equilibrium","Chamblin-Reall gravity: scalar probe drives dual fluid","External scalar field induces non-conservation in dual fluid","Seven transport coefficients emerge from scalar-gravity duality"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes the external scalar couples to the dual fluid through the specific matter action $S_M = \\int d^d x \\sqrt{-g}\\,e^{-\\phi} L[g,T,u,\\phi]$, so that the driving force is exactly $e^{-\\phi} L\\nabla^\\nu\\phi$; a different coupling would change the extracted coefficients and identities.","fun_headline_variants_meta":{"raw":{"variants":["Probe scalar forces dual fluid off conservation","Scalar gradients push holographic fluid out of equilibrium","Chamblin-Reall gravity: scalar probe drives dual fluid","External scalar field induces non-conservation in dual fluid","Seven transport coefficients emerge from scalar-gravity duality"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001458,"raw_usage":{"total_tokens":5932,"prompt_tokens":1075,"completion_tokens":4857,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":691,"completion_tokens_details":{"reasoning_tokens":4781}},"tokens_in":691,"tokens_out":4857,"duration_ms":30889,"temperature":1.0,"reasoning_tokens":4781,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:40:13.264083+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the holographic stress tensor and its divergence directly from the boundary limit of the bulk surface tensor using an independent near-boundary expansion or a different holographic renormalization scheme for a single Chamblin-Reall background with a time- and space-dependent boundary scalar, and check whether $T^{\\phi}_{\\mu\\nu}$ matches (2.36) and whether the divergence equals the forcing term with coefficients (2.45); a mismatch in any coefficient would disprove the universal seven-identity structure.","supporting_citations":[{"cited_title":"Compactified AdS black holes, Chamblin-Reall background, and their dual non-conformal relativistic fluids","cited_arxiv_id":"2111.04091","evidence_quote":"Supplies the Chamblin-Reall backgrounds and the known non-conformal fluid transport coefficients that this paper extends."},{"cited_title":"Forced Fluid Dynamics from Gravity in Arbitrary Dimensions","cited_arxiv_id":"1309.6325","evidence_quote":"Provides the conformal arbitrary-dimension forced-fluid result that gives the q=0 limit of the holographic Lagrangian definition."},{"cited_title":"Second order transport coefficients of nonconformal relativistic fluids in various dimensions from Dp-brane","cited_arxiv_id":"1807.08268","evidence_quote":"Provides the reduced Dp-brane first-order perturbation solutions and transport coefficients used for comparison."},{"cited_title":"Second order transport coefficients of nonconformal fluids from compactified Dp-branes","cited_arxiv_id":"2012.14699","evidence_quote":"Gives the compactified Dp-brane second-order transport coefficients and perturbation background."}],"review_version":1}