{"id":"cdd0d15c-0134-4270-9f31-d3b0b75bebc5","arxiv_id":"1908.03411","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Lattice simulations with exact supersymmetry give central charges and a scaling dimension matching ADE minimal model predictions, supporting the Landau-Ginzburg to superconformal field theory correspondence.","lead":"This paper reports numerical simulations of two-dimensional supersymmetric quantum field theories and compares measured central charges and a scaling dimension with exact predictions for ADE minimal models. The values agree, supporting a long-standing conjecture and the lattice formulation used.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The unresolved locality of the massless momentum-cutoff formulation, admitted in Sec. 2, is load-bearing: without a local continuum limit, eqs. (3.1) and (4.1) need not describe the minimal-model SCFT, and Table 2 has no a-to-0 extrapolation.","rationale":"The reader's weakest-assumption pick is exactly where the argument's security is lowest, and the manuscript itself flags it. I agree that the central claim requires the massless momentum-cutoff formulation to have a local continuum limit; without that, the SCFT fitting forms in eqs. (3.1) and (4.1) do not have their standard interpretation. My stress-test adds two concrete observations that reinforce the same concern: the central-charge results in Table 2 are not extrapolated to a = 0, so their agreement with minimal-model values could be a finite-cutoff coincidence, and the linear continuum extrapolation behind eq. (4.4) is applied to only one observable in one model, so it cannot certify the locality of the EMT correlators used for c. A mass-to-zero test is a concrete way to check whether the massless theory is the local m-to-0 limit of the massive formulation, for which locality restoration is argued perturbatively. Since the paper is a proceedings summary and its claims are tentative, the conditional verdict already captures this situation; no stronger or weaker verdict is needed.","tokens_in":6709,"tokens_out":8375,"duration_ms":100265,"concrete_test":"Add a small supersymmetric mass term to the A2 (or A3) theory in the same momentum-cutoff formulation and simulate it for m = 0.2, 0.1, 0.05, and 0.02 in lattice units, at L/a = 24, 32, 40, and 48. For each m, extract 1-h-hbar from the scalar susceptibility and c from the EMT correlator, extrapolate m to 0 at fixed a/L, and compare with the massless runs. If the massless results are not the m-to-0 limit of the massive theory, the admitted nonlocality of the massless formulation in Sec. 2 is a real obstruction and the central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's own Sec. 2 states that the momentum-cutoff regularization 'breaks the locality of the theory' and that 'for the massless case, it is not clear whether the locality is automatically restored so far.' This admission is not a peripheral caveat. Equation (3.1) is the exact two-point function of the energy-momentum tensor in a local 2D SCFT, and eq. (4.1) is the power-law scalar correlator of a local conformal field; if the continuum limit of the regularized massless WZ model is nonlocal, the constants fitted from these forms need not coincide with the central charges and dimensions of the ADE minimal models. Table 2 strengthens this worry: the central charges are quoted at one lattice spacing only (the maximal box), with no a-to-0 extrapolation, and the quoted systematic error is described as a finite-volume effect, not a cutoff effect. Thus the agreement in Table 2 could in principle be a cutoff artifact of a nonlocal theory. The A2 dimension in eq. (4.4) does have a continuum extrapolation, but it is a single observable in one model and does not by itself certify locality of the EMT correlators used for c. The conclusion therefore rests on an unverified assumption rather than on a demonstrated property of the formulation; the paper's 'we believe' is not evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports numerical tests of the conjectured Landau–Ginzburg/SCFT correspondence for ADE-type N=2 Wess–Zumino models using the momentum-cutoff/Nicolai-map formulation of Kadoh and Suzuki. It measures the central charge from the two-point function of the energy-momentum tensor for several ADE superpotentials (Table 2 lists A2, A3, D3, D4, and E7; the text also claims E6), and reports values consistent with the minimal-model predictions. It also develops a finite-size-scaling method with a continuum extrapolation and applies it to the A2 model, obtaining 1-h-hbar = 0.6699(77)(87), consistent with the exact value 2/3 (Eq. (4.4)). The paper presents this as evidence that the massless WZ model with the momentum-cutoff formulation realizes the conjectured ADE minimal-model SCFTs.","tokens_in":6989,"tokens_out":7347,"duration_ms":75859,"significance":"If correct, these results would provide valuable non-perturbative numerical evidence for the LG/SCFT correspondence and would support the SUSY-preserving momentum-cutoff formulation as a practical tool for 2D N=2 models, including possible applications to Calabi–Yau compactifications. The strengths are the manifestly supersymmetric construction, the direct use of Noether-current correlators to extract the central charge, and a concrete finite-size-scaling method with a continuum limit for the scaling dimension. The significance is tempered, however, by the paper's own admission that locality restoration is not established in the massless case, and by the absence of a continuum extrapolation for the central-charge results; the reported agreement at one lattice spacing is suggestive but not conclusive.","major_comments":[{"comment":"The paper explicitly states in Sec. 2 that the momentum-cutoff regularization breaks locality and that 'for the massless case, it is not clear whether the locality is automatically restored so far.' This is load-bearing because Eq. (3.1) is the two-point function of a local 2D SCFT, and the central charges in Table 2 are extracted by fitting this form at one finite cutoff. If the continuum limit of the massless formulation is nonlocal, the fitted constants need not be the central charges of the ADE minimal models. Please provide evidence for locality restoration in the continuum limit (for example, tests of local Ward identities or a study of the cutoff dependence of the EMT correlator), or explicitly frame the conclusion as conditional on this assumption.","section":"Sec. 2 and Eq. (3.1); Table 2"},{"comment":"The central charges are quoted only at the maximal box size for each setup, with no a/L -> 0 extrapolation, and the systematic error is described as a finite-volume effect rather than a cutoff effect. Since a is the UV cutoff and the formulation is nonlocal for finite a, the agreement with the minimal-model values could in principle be a cutoff artifact. Please show the a-dependence of the fitted central charge for at least one model, or justify quantitatively that cutoff effects are negligible at the simulated lattice spacings.","section":"Sec. 3, Table 2"},{"comment":"The D3 fit has chi^2/d.o.f. = 3.598, whereas the other rows are close to 1. This indicates that the fit form (3.1) over the stated momentum range does not describe the D3 data within the quoted uncertainties. Please show the fit residuals and examine the stability of c under variations of the fitted momentum interval; if the poor chi^2 persists, the reported D3 central charge should carry a correspondingly larger systematic uncertainty.","section":"Sec. 3, Table 2 (D3 row)"},{"comment":"The main precision result for the A2 scaling dimension is not self-contained: the underlying fit table (table 4 of Ref. [13]) and the details of the 'slightly different fitted region' used for the systematic error are not given. Since Eq. (4.4) is one of the two main results, please reproduce the essential information (number of volumes, values of ln chi, fitted ranges, and the linear-fit parameters) so that the extrapolation can be assessed directly.","section":"Sec. 4, Eq. (4.4)"},{"comment":"The text and the conclusion state that the E6 (approximately A2 times A3) model was simulated and is consistent with the expected central charge, but Table 2 contains no E6 row. Either include the E6 numerical result with its statistical and systematic errors and chi^2/d.o.f., or remove the claim from the summary and conclusion.","section":"Sec. 3 and Sec. 5, E6 claim"}],"minor_comments":[{"comment":"The definition of Sigma(u,a/L) = ln chi(sL)|a uses the symbol s without stating its value; please state explicitly that s=2 (or the actual rescaling factor used in the analysis).","section":"Sec. 4, Eq. (4.3)"},{"comment":"'a coherence picture' should be 'a coherent picture'; similarly, 'we simply applies' in Sec. 4 should be 'we simply apply'.","section":"Abstract and Sec. 5"},{"comment":"The affiliation contains 'Nis hi-ku'; this should read 'Nishi-ku'.","section":"Author affiliation, first page"},{"comment":"The phrase 'The fitting curve (3.1) is depicted at once' is unclear; consider 'The fitting curve from Eq. (3.1) is shown together with the data'.","section":"Fig. 1 caption"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings-style contribution whose central claims rely on the unverified locality of a nonlocal regularization in the massless case, and the paper itself flags this in Sec. 2. The numerical consistency is encouraging, but the missing continuum extrapolation for c, the poor D3 chi^2, and the absent E6 row are all fixable and should be addressed before the claims are accepted. I would not reject on the basis of disagreement with the community consensus; the issue is an internal evidence gap."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a proceedings write-up, not a new research paper. The numerical results in Tables 2 and 3 and the extrapolated scaling dimension in eq. (4.4) are taken from the author's own earlier papers [11-13], with citations in the text. What is new here is the compact summary and a clear description of the finite-volume-scaling method used for the continuum limit. The method is sensible: tune the lattice coupling to keep ln chi fixed, compute at L and 2L, and read off 1-h-hbar from the ratio. The A2 result, 1-h-hbar = 0.6699(77)(87), agrees with 2/3 and is the cleanest piece of evidence.\n\nThe paper deserves credit for being transparent. Section 2 states without burying it that the momentum-cutoff regularization breaks locality and that for the massless case restoration in the continuum limit is not yet clear. The conclusion repeats the caveat. Six measured central charges matching minimal-model values is a nontrivial consistency check, even though each individual measurement has limited precision.\n\nSoft spots, in proportion. The stress-test has one fair point: Table 2 gives central charges at a single lattice spacing, with no a-to-0 extrapolation, so the agreement with the minimal-model values could in principle be an artifact of the nonlocal cutoff. The author should have shown at least a few lattice spacings for one model to demonstrate the trend. Second, the D3 fit has chi^2/d.o.f. = 3.6, which weakens that data point. Third, the raw data and full fit details are not in the paper; for a proceedings that's tolerable, but a standalone claim would need a repository.\n\nThe locality issue is real but not fatal to the paper's actual conclusion, because that conclusion is explicitly one of consistency, not proof. I largely agree with the reader's conditional verdict: accept as a proceedings summary if we keep in mind that the data are already published elsewhere.\n\nWho benefits: lattice supersymmetry specialists and people tracking the LG/SCFT conjecture numerically. If this were submitted as a regular research article, I would send it to a referee because the underlying results are significant and the locality question deserves expert scrutiny. As a proceedings record, it is a solid summary.\n\nRecommendation: engage if you work in this area; cite the original papers rather than this summary.","headline":"An honest proceedings summary of previously published lattice SUSY results; clear about its open locality question, but adds no new measurements itself.","tokens_in":7535,"tokens_out":3766,"would_cite":false,"duration_ms":39948,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81T60","81T25","81T40"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper reports numerical evidence that the massless two-dimensional N=2 Wess-Zumino model, regularized with a supersymmetry-preserving momentum cutoff, flows in the infrared to the expected ADE-classified minimal-model superconformal…","keywords":["N=2 Wess-Zumino model","Landau-Ginzburg correspondence","ADE minimal models","Nicolai map","supersymmetric momentum-cutoff regularization","central charge","scaling dimension","finite-size scaling continuum extrapolation"],"falsifier":"Repeat the finite-size-scaling continuum extrapolation for the A2 model at $a\\lambda$ values below 0.3; if the extrapolated $1-h-\\bar h$ moves outside $0.6699 \\pm 0.016$ or the infrared central charge drifts from $c=1$, the claimed consistency with the LG/SCFT correspondence fails.","tokens_in":6479,"feed_emoji":"⚛️","tokens_out":14627,"duration_ms":138346,"temperature":0.7,"pith_summary":"This paper tests the Landau-Ginzburg (LG) description of two-dimensional $\\mathcal{N}=2$ superconformal field theory: the conjecture that the massless $\\mathcal{N}=2$ Wess-Zumino (WZ) model with a quasi-homogeneous superpotential flows in the infrared to one of the ADE-classified minimal-model SCFTs. Using a momentum-cutoff regularization that keeps the full supersymmetry and translation invariance through the Nicolai map, the author extracts central charges from the two-point function of the energy-momentum tensor for the A2, A3, D3, D4, E6 (via its A2$\\otimes$A3 factorization), and E7 cases and finds values consistent with the minimal-model predictions. A new finite-size-scaling continuum extrapolation is then applied to the A2 model, yielding $1-h-\\bar h = 0.6699(77)(87)$, consistent with the exact $2/3$. The significance is that the LG correspondence is a non-perturbative strong-coupling statement that resists analytic proof, so a numerical demonstration that the infrared data match the SCFT data supports both the conjecture and the validity of this SUSY-preserving formulation.","feed_headline":"Wess-Zumino simulations match ADE minimal-model central charges","feed_subtitle":"A SUSY-preserving cutoff simulation finds central charges 1, 1.5, 2, 8/3 and dimension 0.6699(77)(87), matching LG/SCFT.","key_machinery":"The argument rests on two pieces. The first is the Nicolai map $N_I(p) = 2 i p_z A_I(p) + \\partial W^*/\\partial A_I^*(p)$, a change of variables from the scalar fields to Gaussian-distributed variables; because the fermion determinant equals the Jacobian of this map (up to sign), the partition function becomes a Gaussian integral over $\\{N\\}$ plus a sum over solutions of the algebraic equation, and configurations are generated by drawing $\\{N\\}$ from a Gaussian and solving for $\\{A\\}$. This regularization preserves all supersymmetries and translation invariance at finite cutoff, so the Noether energy-momentum tensor is available and the central charge can be read from the SCFT two-point function $\\langle T(p)T(-p)\\rangle = (L_0L_1/\\pi)(c/12)\\,p_z^3/\\bar p_z$ in the infrared. The second piece is the finite-size-scaling continuum extrapolation: fix $u = \\ln \\chi(L)$, compute $\\Sigma(u, a/L) = \\ln \\chi(sL)|_a$ for $s=2$, and extrapolate $a/L \\to 0$; the scaling dimension follows from $1-h-\\bar h = (1/\\ln s^2)[\\lim_{a/L\\to 0}\\Sigma(u,a/L) - u]$, which simultaneously removes the cutoff and the finite volume.","core_discovery":"The paper claims that the massless 2D $\\mathcal{N}=2$ WZ model, when regularized with the SUSY-preserving momentum cutoff, shows infrared behavior matching the ADE minimal models. The measured central charges are $c = 1.061(36)(34)$ for A2, $1.415(36)(36)$ for A3, $1.595(31)(41)$ for D3, $2.172(48)(39)$ for D4, and $2.638(47)(59)$ for E7, against the expected $1$, $3/2$, $3/2$, $2$, and $8/3$; E6 is covered through its equivalence to A2$\\otimes$A3 in the two-superfield computation. The effective central charge, plotted as a function of momentum, interpolates between the free-field value $c = 3N_\\Phi$ in the ultraviolet and the minimal-model value in the infrared, matching the expected renormalization-group flow picture. After a newly developed continuum and thermodynamic extrapolation, the A2 scaling dimension is $1-h-\\bar h = 0.6699(77)(87)$, consistent with $2/3$. The author concludes that the results form a coherent picture consistent with the conjectured LG/SCFT correspondence and support the validity of the formulation.","pith_inferences":["If locality is indeed restored in the massless continuum limit, a direct check would be to verify the momentum-space Ward identities for the energy-momentum tensor at small $a/L$; the paper flags this restoration as not yet established.","The same continuum extrapolation applied to the central charges of D3, D4, and E7, rather than only to A2, would test whether the small deviations seen at finite volume approach the exact values as $a/L \\to 0$.","Extending the framework to the A4 model or to a non-minimal LG model corresponding to the quintic Calabi-Yau compactification could turn this numerical strategy into a probe of string-theory world-sheet data; the author names this as a future direction rather than a result."],"forward_implications":["The measured central charges for A2, A3, D3, D4, E6, and E7 agree with the minimal-model values, giving non-perturbative numerical evidence that each superpotential lands on the predicted SCFT in the infrared.","The A2 scaling dimension $1-h-\\bar h = 0.6699(77)(87)$ agrees with $2/3$ after a simultaneous continuum and thermodynamic extrapolation, establishing a precision benchmark for this regularization.","The effective central charge interpolates between $c=3N_\\Phi$ in the ultraviolet and the minimal-model central charge in the infrared, matching the expected renormalization-group flow picture.","The finite-size-scaling extrapolation method is formulated for general lattice or cutoff actions with a single dimensionful coupling, so earlier Nicolai-map computations of scaling dimensions can be upgraded to continuum-limit results."],"supporting_citations":[{"why":"States the LG/SCFT conjecture that the WZ model realizes the N=2 minimal models, the claim being tested.","marker":"[1]"},{"why":"Classifies the ADE superpotentials and gives the expected central charges in table 1.","marker":"[2]"},{"why":"Earlier Nicolai-map lattice measurement of the A2 scaling dimension, providing the susceptibility finite-size-scaling benchmark.","marker":"[8]"},{"why":"Previous numerical simulation of the A2 model using the momentum-cutoff formulation; its central-charge and scaling-dimension procedures are generalized here.","marker":"[9]"},{"why":"Constructs the SUSY-preserving momentum-cutoff regularization with the Nicolai map used for all simulations.","marker":"[10]"},{"why":"Supplies the EMT two-point function and susceptibility data for the single-superfield (A-type) models.","marker":"[11]"},{"why":"Supplies the two-superfield central-charge computation that covers D-type and E6-type models.","marker":"[12]"},{"why":"Develops the continuum extrapolation method and the A2 precision scaling-dimension result used as the paper's second main result.","marker":"[13]"}],"fun_headline_variants":["WZ simulations validate ADE central-charge predictions","Numerical study supports N=2 LG/SCFT correspondence","SUSY-cutoff sims match ADE minimal-model predictions","Precision sims confirm ADE scaling dimension and c values","Lattice WZ test agrees with LG/SCFT for ADE models"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the massless momentum-cutoff WZ model regains locality in the continuum limit, so that measured correlators are those of a local quantum field theory; without this, the agreement of the central charge and scaling dimension with minimal-model values would not establish the LG/SCFT correspondence.","fun_headline_variants_meta":{"raw":{"variants":["WZ simulations validate ADE central-charge predictions","Numerical study supports N=2 LG/SCFT correspondence","SUSY-cutoff sims match ADE minimal-model predictions","Precision sims confirm ADE scaling dimension and c values","Lattice WZ test agrees with LG/SCFT for ADE models"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000886,"raw_usage":{"total_tokens":3841,"prompt_tokens":975,"completion_tokens":2866,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":591,"completion_tokens_details":{"reasoning_tokens":2778}},"tokens_in":591,"tokens_out":2866,"duration_ms":22786,"temperature":1.0,"reasoning_tokens":2778,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:13:56.887835+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the finite-size-scaling continuum extrapolation for the A2 model at $a\\lambda$ values below 0.3; if the extrapolated $1-h-\\bar h$ moves outside $0.6699 \\pm 0.016$ or the infrared central charge drifts from $c=1$, the claimed consistency with the LG/SCFT correspondence fails.","supporting_citations":[{"cited_title":"V afa and N","cited_arxiv_id":null,"evidence_quote":"Classifies the ADE superpotentials and gives the expected central charges in table 1."},{"cited_title":"A lattice study of N=2 Landau-Ginzburg model using a Nicolai map","cited_arxiv_id":"1005.4671","evidence_quote":"Earlier Nicolai-map lattice measurement of the A2 scaling dimension, providing the susceptibility finite-size-scaling benchmark."},{"cited_title":"Numerical simulation of the $\\mathcal{N}=(2,2)$ Landau-Ginzburg model","cited_arxiv_id":"1107.1367","evidence_quote":"Previous numerical simulation of the A2 model using the momentum-cutoff formulation; its central-charge and scaling-dimension procedures are generalized here."},{"cited_title":"Supersymmetric nonperturbative formulation of the WZ model in lower dimensions","cited_arxiv_id":"0909.3686","evidence_quote":"Constructs the SUSY-preserving momentum-cutoff regularization with the Nicolai map used for all simulations."},{"cited_title":"Numerical study of the $\\mathcal{N}=2$ Landau--Ginzburg model","cited_arxiv_id":"1805.10735","evidence_quote":"Supplies the EMT two-point function and susceptibility data for the single-superfield (A-type) models."},{"cited_title":"Numerical study of the $\\mathcal{N}=2$ Landau--Ginzburg model with two superfields","cited_arxiv_id":"1810.02519","evidence_quote":"Supplies the two-superfield central-charge computation that covers D-type and E6-type models."},{"cited_title":"Continuum limit in numerical simulations of the $\\mathcal{N}=2$ Landau--Ginzburg model","cited_arxiv_id":"1906.00653","evidence_quote":"Develops the continuum extrapolation method and the A2 precision scaling-dimension result used as the paper's second main result."}],"review_version":1}