{"id":"95075510-8fd9-4039-837b-bd4bccddfe03","arxiv_id":"2412.15827","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"AC conductivities of the D3/D7 holographic Weyl semimetal show peaks and troughs near the WSM-insulator transition, traced to quasinormal-mode poles with small imaginary parts.","lead":"Physicists computed how a holographic model of a strongly interacting Weyl semimetal responds to oscillating electric fields, and found sharp resonances that appear as the material is tuned toward an insulating transition. The result gives a concrete top-down prediction for frequency-dependent conductivities and long-lived excitations in a strongly coupled Weyl semimetal, where perturbative methods are unreliable.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim rests on identifying quasinormal poles by pseudospectral grid-size agreement alone; an independent pole-location check is needed before the AC peaks can be attributed to near-real poles.","rationale":"The paper is a careful numerical extension of an established top-down model, with two independent methods for the conductivities and a plausible physical mechanism tying near-critical embeddings to long-lived modes. However, the central claim has two load-bearing numerical and interpretive links. First, the quasinormal poles are identified solely by K=90 vs K=100 stability in a pseudospectral generalized eigenvalue problem. Stability under grid refinement is standard evidence but not conclusive: spurious eigenvalues can persist, especially when an extra boundary condition is imposed at the singular point. The paper provides no convergence order, no residual check, and no independent ODE-based calculation of A₀(ω)=0. The reader's weakest assumption is exactly this, and it is the right one. Second, the paper connects the small imaginary parts to approach of the critical embedding, which occurs at the maximal black-hole mass m≈0.0819 b√λ, not at the first-order transition m≈0.0733 b√λ. The plotted modes at the transition value are less dramatically close to the real axis; Fig. 12's extrapolation to Im ω→0 is in the metastable/spinodal regime. This does not invalidate the resonance claim, but it means the abstract's 'close to the phase transition' needs qualification. The proposed contour-integration and independent zero-finding test would settle whether the near-axis poles are genuine and whether they actually drive the observed σxx peak. Since the reader already issued a conditional verdict, my read does not change the verdict.","tokens_in":29887,"tokens_out":5834,"duration_ms":55503,"concrete_test":"Choose the A+ mode nearest the real axis at m=0.073 b√λ, T=0 (ω₀/b ≈ 0.25−0.2i from Fig. 10). Independently integrate Eq. (3.5) from r=0 with the ingoing condition (3.6), and compute A₀(ω)/A₂(ω) on a small contour around ω₀ using adaptive ODE integration; verify a simple zero with winding number 1. Also re-locate the zero by complex secant using A₀(ω)=0 and repeat at K=120/140 to quantify convergence. If no zero is found, the near-axis poles are numerical artifacts; if the zero is found but its residue does not reproduce the height of the σxx peak, the 'pole causes peak' narrative needs revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The strongest claim—that the sharp AC peaks near m≈0.0733 b√λ come from poles with small imaginary part—depends on Section 4's identification of genuine quasinormal modes. The only filter is that modes agree for K=90 and K=100 while branch-cut discretizations move with K (Fig. 11). This is a necessary but not sufficient test: spurious eigenvalues of a generalized eigenvalue problem (B.13) can be K-stable, and the extra boundary condition imposed at r=-1 via Eq. (B.12) can seed artifacts. No convergence rate, error bars, or independent zero-finding of A₀(ω)=0 is reported. If the near-axis modes were artifacts, the resonance interpretation collapses. A secondary issue is that Fig. 12 shows Im ω→0 only as η→∞, i.e., near the critical/maximum-mass embedding m≈0.0819 b√λ, while the thermodynamic transition is at m≈0.0733 b√λ; the abstract's 'close to the phase transition' glosses this gap, and the peak position should be checked against the actual pole at the transition value.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper extends the top-down D3/D7 holographic Weyl-semimetal model of ref. [23] to nonzero frequency, computing the AC conductivities σxx, σxy, and σzz via the Kubo formula from gauge-field fluctuations on black-hole embeddings. At zero temperature and for masses close to the WSM/insulator transition, the authors find a peak in Re σxx and troughs in Re σzz and Re σxy. They also derive a membrane-paradigm formula for the DC σzz, and they compute the complex-frequency poles (quasinormal modes) of the conductivities at T=0 using a pseudospectral method, finding modes whose imaginary parts decrease as the near-critical embedding is approached. The central claim is that these near-real-axis poles are responsible for the optical features.","tokens_in":30047,"tokens_out":7516,"duration_ms":69247,"significance":"If the central claim holds, the paper provides a concrete top-down holographic example of sharp, long-lived AC conductivity resonances near a WSM-insulator transition, a result that would be of interest to the holographic transport community. The paper has clear strengths: it uses a fully top-down model with no fitted parameters; the m=0 limit is analytic; the low-frequency analytic matching reproduces the numerical Re σxx and Re σzz; the two numerical methods (shooting and pseudospectral) agree where checked; and the DC σzz formula in Eq. (3.29) is a useful new addition. The main weakness is that the pole identification rests on a single numerical stability criterion, and the relationship between the near-critical poles and the thermodynamic phase transition is stated more loosely in the abstract than the computations warrant.","major_comments":[{"comment":"The central claim that the AC conductivity peaks and troughs arise from poles with small imaginary part rests entirely on the pseudospectral quasinormal-mode computation. The only stability filter reported is that candidate modes agree for grid sizes K=90 and K=100, while other eigenvalues drift with K (Figs. 10 and 11). Agreement of a generalized eigenvalue problem (B.13) at two grid sizes is necessary but not sufficient: spurious eigenvalues can be grid-stable, especially because the additional boundary condition (B.12) is imposed at r=-1 and does not independently constrain spurious modes. The authors should corroborate the near-real-axis modes by an independent method, for example by direct shooting/zero-finding of A0_n(ω)=0 from Eqs. (3.4)-(3.5), by checking the residues of the candidate poles against the conductivity peak in Figs. 5-6, or by a convergence-rate study. Without such a check, the 'sharp resonance' interpretation is not established.","section":"Section 4, Appendix B.2"},{"comment":"The abstract states that the paper finds poles with small imaginary part 'at low temperatures and close to the phase transition', but Section 4 explicitly computes quasinormal modes only at T=0 and leaves their determination at nonzero temperature to future work. The finite-temperature AC plots in Figs. 8-9 show the peaks and troughs being washed out by T=0.1 b, so the 'low temperatures' part of the abstract is not supported by any pole computation. The abstract and Section 1 should be reworded to distinguish the T=0 pole result from the T>0 conductivity features, or the finite-temperature quasinormal-mode calculation should be performed.","section":"Abstract; Section 4"},{"comment":"Fig. 12 shows that Im ω approaches zero only as η→∞, i.e. as the black-hole embeddings approach the critical embedding at the maximum mass m≈0.0819 b√λ, while the first-order phase transition occurs at m≈0.0733 b√λ (η≈0.989). At the transition mass the modes in Fig. 11 have finite imaginary parts, for example ω/b ≈ ±0.12−0.19 i for Az. The parameter distance between the transition and the near-critical regime is about 10%, and the latter lies on the metastable extension of the WSM branch. The authors should explicitly quantify the pole positions at the actual transition value and clarify whether the resonance claim refers to the stable phase at the transition or to the metastable near-critical branch; the current wording in the abstract and Section 4 conflates the two.","section":"Section 4, Fig. 12"}],"minor_comments":[{"comment":"The caption describes the left panel as 'zero temperature T=0.1 b'; this is contradictory and should read T=0 (the right panel presumably shows T=0.1 b).","section":"Figure 3 caption"},{"comment":"The text says the fluctuation equations are 'evaluated on an N-point grid' while the matrix equation (B.13) is K×K; the symbol N should be K for consistency.","section":"Section 4, numerical description"},{"comment":"The phrase 'black hole emebddings' contains a typo and should read 'embeddings'.","section":"Section 3.3.1, after Eq. (3.20)"},{"comment":"The sentence 'There are also many other channels in which one could study the holographic Green’s functions and quasinormal modes of the flavour brane WSM model, for example, for example one can study...' contains a duplicated 'for example'.","section":"Section 5"},{"comment":"The data release is cited as 'to appear', so the reproducibility statement in Section 1 ('may be downloaded from the accompanying data release') is currently not verifiable; the reference should be updated or the statement qualified.","section":"Reference [43]"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a serious numerical paper that adds the missing AC conductivities, the DC σzz, and the current-current quasinormal modes to the flavour brane WSM model. The results look internally consistent, and the central physical picture—sharp optical features near the WSM-insulator transition—is plausible. The one claim I would press on is the identification of the near-real poles from grid-size stability alone.\n\nWhat is actually new: frequency-dependent σxx, σxy, σzz at T=0 and small T; the DC σzz, which the Karch–O'Bannon method in the original model paper could not reach; and the first current-current QNM spectrum for this top-down setup. The paper is careful: two independent numerics (shooting and pseudospectral) agree where checked, and the analytic low-frequency matching reproduces Re σ ∝ ω. The exact m=0 results are a useful check. The promised data release will help others verify the plots.\n\nSoft spots, in proportion. The quasinormal mode identification is the load-bearing point, and it rests on a single filter: poles that do not move between K=90 and K=100, while branch-cut discretizations do. That is necessary but not sufficient. Spurious generalized eigenvalues can be K-stable, and the boundary condition (B.12) can seed artifacts. No convergence rates or independent root-finding of A0(ω)=0 are reported. If those near-axis modes are artifacts, the resonance interpretation collapses. I would want an independent check—a contour integral of the Green's function, or direct zero-finding—before accepting the central claim.\n\nSecondary issues: the abstract claims poles with small imaginary part at low temperatures, but the QNM computation is only at T=0; Section 4 says this explicitly, so the abstract overstates. Also, Im ω goes to zero only in the η→∞ limit, corresponding to m≈0.0819, while the first-order transition sits at m≈0.0733. The paper plots both lines, but the 'close to the phase transition' wording glosses an ~11% gap. If the poles explain the AC peaks, the relevant comparison is at the transition value, not the maximum mass.\n\nWho for: holographic transport people and anyone working on top-down Weyl semimetals. It deserves a serious referee; the main claims are testable and the numerical work is careful. I would send it to review, with a request for the data, convergence diagnostics, and either a verification of the T=0 poles or a softened abstract.","headline":"Careful numerical extension of the D3/D7 WSM model with genuinely new transport data; the near-real pole claim needs an independent check before it carries the paper.","tokens_in":30630,"tokens_out":3091,"would_cite":true,"duration_ms":26091,"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":"Near its transition to the insulating phase, the holographic flavour brane Weyl semimetal develops sharp peaks and troughs in its AC conductivities, originating from quasinormal-mode poles close to the real frequency axis.","keywords":["Weyl semimetal","holography","AdS/CFT","AC conductivity","quasinormal modes","D7-brane","flavour brane","first-order phase transition"],"falsifier":"Compute the retarded Green's function of $J_x$ on the same background and integrate it along a small contour around $\\omega\\approx 0.26 - i\\delta\\,b$ at $m=0.073\\,b\\sqrt{\\lambda}$: a non-zero residue would confirm a pole, while a residue consistent with zero would show the resonance peak has a different origin. A second, independent check is to solve the fluctuation equation with a shooting method and locate zeros of $A^{(0)}(\\omega)$, avoiding the pseudospectral discretisation entirely.","tokens_in":29650,"feed_emoji":"⚡","tokens_out":5782,"duration_ms":49321,"temperature":0.7,"pith_summary":"The paper computes, for the first time, the frequency-dependent electrical conductivities of a top-down holographic Weyl semimetal built from D3/D7 branes. At zero temperature and for a hypermultiplet mass close to the first-order transition into the insulating phase, the longitudinal conductivity $\\sigma_{xx}$ develops a peak near frequency $\\omega \\approx 0.26\\,b$ while $\\sigma_{zz}$ and $\\sigma_{xy}$ develop troughs. The paper attributes these features to poles of the current-current correlators, dual to quasinormal modes, whose imaginary parts shrink as the critical embedding is approached. If the claim holds, strongly coupled Weyl semimetals should show sharp, long-lived resonances in their optical response right before they turn insulating.","feed_headline":"Optical response of holographic Weyl semimetal sharpens at transition","feed_subtitle":"Near the phase boundary its AC conductivity develops peaks and troughs from long-lived quasinormal modes.","key_machinery":"The central objects are the quasinormal modes of the D7-brane world-volume gauge field fluctuations $A_\\pm = A_x \\pm i A_y$ and $A_z$, evaluated at zero momentum on black hole embeddings at $T=0$; their complex frequencies are poles of the retarded Green's functions and hence of the conductivities via the Kubo formula. The machinery is a pseudospectral Chebyshev method (grid sizes $K=90$ and $K=100$) that solves the embedding equation for $R(r)$ and the fluctuation equations with ingoing boundary conditions, keeping only modes stable under grid refinement. A flux conservation identity for $F_+(\\omega)$ and $F_z(\\omega)$ relates the real parts of $\\sigma_{xx}$ and $\\sigma_{zz}$ to boundary data and yields $\\operatorname{Re}\\sigma_{xx} = \\operatorname{Re}\\sigma_{zz} = (N_f N_c/8\\pi)\\,\\omega$ for $\\omega \\ll b$.","core_discovery":"The central claim is that the AC response of the flavour brane Weyl semimetal is governed, near the phase transition, by quasinormal modes close to the real frequency axis. At $T=0$, for $m/b\\sqrt{\\lambda}$ just below 0.0733, the pole closest to the real axis in the $A_\\pm$ channels has a small negative imaginary part, producing the peak in $\\operatorname{Re}\\sigma_{xx}$; the $A_z$ channel shows an analogous pole producing the trough in $\\sigma_{zz}$, and $\\sigma_{xy}$ dips through the same mechanism. The imaginary parts of these poles decrease toward zero as the black hole embedding approaches the critical embedding, matching the expectation that the spectra of black hole and Minkowski embeddings coincide there. The paper presents these poles as the origin of the peaks and troughs and connects their near-reality to the first-order nature of the transition.","pith_inferences":["If the poles are genuine, the peak/trough structure should obey a spectral-weight sum rule: the extra weight in $\\sigma_{xx}$ near $\\omega\\approx 0.26\\,b$ must be borrowed from other frequencies, and checking this numerically would test the interpretation without contour integration.","Near the critical embedding the model exhibits discrete scale invariance with complex critical exponents; one might expect families of poles accumulating toward the real axis in a log-periodic pattern, a signature that could be searched for in the existing spectrum.","The mechanism proposed here, that poles approach the real axis because black hole and Minkowski embeddings have matching spectra at criticality, may be generic for first-order holographic transitions with a gapped insulating side, beyond the D3/D7 construction."],"forward_implications":["At $T=0$, $\\sigma_{xx}$ has a peak near $\\omega\\approx 0.26\\,b$ for $m=0.073\\,b\\sqrt{\\lambda}$, while $\\sigma_{xy}$ has a trough near $\\omega\\approx 0.50\\,b$; both sharpen as $m/b\\sqrt{\\lambda}$ approaches the phase transition.","The peaks and troughs are washed out as temperature rises, essentially disappearing by $T\\approx 0.1\\,b$.","The imaginary parts of the relevant quasinormal-mode frequencies fall as the embedding approaches criticality, so the resonances become longer lived exactly at the Weyl-semimetal/insulator boundary.","The DC longitudinal conductivity $\\sigma_{zz}$ is computed for the first time; at low temperature it is approximately a step function of $m/b\\sqrt{\\lambda}$, dropping discontinuously at the transition.","At large frequency the conductivities become mass independent, controlled by the UV AdS asymptotics of the D7-brane embedding."],"supporting_citations":[{"why":"Defines the flavour brane Weyl semimetal model, its phase diagram, and the DC $\\sigma_{xx}$ and $\\sigma_{xy}$ that this paper extends to AC.","marker":"[23]"},{"why":"Provides the holographic recipe for retarded Green's functions with ingoing boundary conditions used for all conductivities.","marker":"[41]"},{"why":"Supplies the analytic $m=0$ solutions and conductivity formula used as a check and for massless limits.","marker":"[59]"},{"why":"Gives the membrane paradigm method used to derive the DC $\\sigma_{zz}$ formula.","marker":"[64]"},{"why":"Provides the spectral method foundation for the pseudospectral scheme used for embeddings, conductivities, and quasinormal modes.","marker":"[67]"},{"why":"Computes hydrodynamic modes and poles in a bottom-up holographic Weyl semimetal, the comparison where small imaginary parts also appear but through a second-order transition.","marker":"[31]"},{"why":"Studies quasinormal modes of the pseudoscalar in the same flavour brane model, providing the precedent for the quasinormal-mode analysis here.","marker":"[65]"},{"why":"Computes AC conductivities in the bottom-up holographic Weyl semimetal model, giving the comparison point for frequency scaling of the conductivities.","marker":"[30]"}],"fun_headline_variants":["Holographic Weyl semimetal's sharp AC peaks from near-real poles","Near critical point, Weyl semimetal AC response sharpens","Quasinormal modes drive sharp AC features in holographic Weyl semimetal","Holographic Weyl semimetal: long-lived modes create AC peaks and troughs","AC conductivities of Weyl semimetal sharpen as transition nears"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The near-real-axis poles are judged genuine because their frequencies match between grid sizes $K=90$ and $K=100$, and this grid-stability test is the only evidence that they are true poles rather than artifacts of discretising a branch cut.","fun_headline_variants_meta":{"raw":{"variants":["Holographic Weyl semimetal's sharp AC peaks from near-real poles","Near critical point, Weyl semimetal AC response sharpens","Quasinormal modes drive sharp AC features in holographic Weyl semimetal","Holographic Weyl semimetal: long-lived modes create AC peaks and troughs","AC conductivities of Weyl semimetal sharpen as transition nears"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000311,"raw_usage":{"total_tokens":1736,"prompt_tokens":873,"completion_tokens":863,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":489,"completion_tokens_details":{"reasoning_tokens":760}},"tokens_in":489,"tokens_out":863,"duration_ms":6780,"temperature":1.0,"reasoning_tokens":760,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T11:03:55.904631+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the retarded Green's function of $J_x$ on the same background and integrate it along a small contour around $\\omega\\approx 0.26 - i\\delta\\,b$ at $m=0.073\\,b\\sqrt{\\lambda}$: a non-zero residue would confirm a pole, while a residue consistent with zero would show the resonance peak has a different origin. A second, independent check is to solve the fluctuation equation with a shooting method and locate zeros of $A^{(0)}(\\omega)$, avoiding the pseudospectral discretisation entirely.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the spectral method foundation for the pseudospectral scheme used for embeddings, conductivities, and quasinormal modes."},{"cited_title":"Atashi and K","cited_arxiv_id":null,"evidence_quote":"Studies quasinormal modes of the pseudoscalar in the same flavour brane model, providing the precedent for the quasinormal-mode analysis here."}],"review_version":1}