{"id":"0ca3a4dd-041f-4b25-8578-4a5e00e552f5","arxiv_id":"2411.09737","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"New wrapped-brane supergravity solutions on disk×disk and spindle⋉disk are constructed, uplifted to 11D and massive IIA, and their central charges and entropies are computed.","lead":"Minwoo Suh constructs new supergravity solutions describing M5-branes and D4-branes wrapped on a disk times a disk, and on a spindle combined with a disk, then computes the holographic central charge and black hole entropy. The results extend a systematic program of brane-wrapping geometries dual to lower-dimensional quantum field theories.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The AdS2 × disk × disk solution in (4.7)/(4.10) is presented without derivation or verification; substituting it into the six-dimensional equations of motion (A.4)–(A.6) is the load-bearing check.","rationale":"The paper has two constructions. The AdS3 × disk × disk piece rests on the known consistent truncation of [17]; even there, two correction footnotes are stated without derivation, but the underlying mechanism is established in the cited literature. The genuinely new result is the AdS2 × disk × disk solution, and it is labelled 'by trial and error' with no verification. The reader's verdict is CONDITIONAL precisely because this verification is missing. I agree with that assessment: the correct verdict is CONDITIONAL, not ACCEPT or REJECT. An outright rejection would be inappropriate because the ansatz has the right qualitative structure (it reduces correctly to the AdS4 × disk solution when X = 1 and s1 = 0, as stated below (4.23), and the flux quantization and Euler-characteristic checks are internally consistent). A symbolic substitution into (A.4)–(A.6) is a decisive, cheap test: if the equations hold for general parameters, the core new claim is sound; if not, the entropy formula falls. I do not find a separate stronger objection: the numerical-factor corrections to [17] are a secondary worry but they only affect the AdS3 results, which are less central and can be checked by recomputation; the possible sign typo in (2.30) is trivial and does not affect the logic; and the 'smeared D4-D8-branes' interpretation is a qualitative remark, not a load-bearing step. Hence the strongest concern is exactly the one the reader identified: verification of the equations of motion for the trial-and-error ansatz.","tokens_in":25278,"tokens_out":2678,"duration_ms":22501,"concrete_test":"Substitute the local ansatz (4.7) (equivalently the h-form (4.10)) into the six-dimensional equations of motion (A.4)–(A.6), with the definitions (4.8)–(4.9) and the relation 2g = 3m. Verify that the Einstein equations, both scalar equations, and all four field equations are satisfied identically for general parameters q1, s1, g, m, or identify the first equation that fails. If a symbolic computation (e.g., Mathematica) confirms the identities, the central concern is resolved; if any component fails, the entropy formula (4.46) and its N^{5/2} scaling are not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of section 4 is that (4.7)/(4.10) is a genuine solution of the U(1)^2-gauged supergravity theory defined by (4.4). The paper states the solution was found 'by trial and error' and does not verify the equations of motion. Unlike the AdS3 × disk × disk construction, which inherits validity from the consistent truncation of [17], the AdS2 ansatz has no derivation chain: the four-form flux in (4.23), the Bekenstein-Hawking entropy (4.46), and the N^{5/2} scaling all depend on this ansatz satisfying (A.4)–(A.6). The explicit functions F(y), f(x), p(x), X(x) in (4.8)–(4.9) are highly non-generic; small errors in exponents or signs in A1, A2, B, or the scalar parametrization would break the Bianchi identities and field equations. The reader flagged this correctly, and the paper's own self-assessment ('by trial and error') signals that no independent check is supplied. Since a false ansatz would invalidate the main new construction, this is the most load-bearing point.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs new holographic solutions in seven- and six-dimensional gauged supergravity: AdS3 × disk × disk and AdS3 × spindle ⋉ disk from a consistent truncation of 7D maximal supergravity, and AdS2 × disk × disk and AdS2 × spindle ⋉ disk in 6D F(4) gauged supergravity. The 7D solutions are uplifted to eleven-dimensional supergravity, with flux quantization and a central charge (2.34); the 6D solutions are uplifted to massive type IIA supergravity, with flux quantization and a Bekenstein-Hawking entropy (4.46). The paper also computes Euler characteristics of the disk factors, obtaining 1/ℓ and 1/k, and checks that the 6D four-form flux reduces to the known AdS4 × disk result when X=1 and s1=0. The main new claim is the AdS2 × disk × disk solution (4.7)/(4.10), stated to have been found 'by trial and error' and not verified against the equations of motion.","tokens_in":25535,"tokens_out":15467,"duration_ms":139821,"significance":"If correct, the paper provides explicit new examples of wrapped-brane geometries: AdS3 × disk × disk with N^3 central charge and AdS2 × disk × disk with N^{5/2} entropy, the latter being a candidate dual to a class of 5d SCFTs compactified on disk × disk. The explicit uplifted metrics, the flux quantizations, and the disk Euler-characteristic checks are useful, and the reduction of the 6D flux to the known AdS4 × disk solution is a good consistency check. The main limitation is that the new 6D solution is not supported by a verification of the field equations, and the 7D flux-quantization section contains an algebraic inconsistency that affects the central-charge formula.","major_comments":[{"comment":"The central new result of the paper, the AdS2 × disk × disk solution (4.7)–(4.10), is presented with no check that it satisfies the equations of motion (A.4)–(A.6). The text states that it was obtained 'by trial and error' and that 'we only present the obtained solution.' Since the massive-IIA uplift (4.20)–(4.23), the flux quantization (4.35)–(4.43), and the entropy (4.46) are all derived from this ansatz, a direct substitution into (A.4)–(A.6) with the residual shown is load-bearing and should be included, or the solution should be derived from a consistent truncation as was done for the 7D case. Without this verification, the central claim is not supported.","section":"§4.2 and Appendix A.2"},{"comment":"The flux integral and its inversion are algebraically inconsistent. With t ≡ sqrt(1+4s1), the ratio in (2.30) simplifies to (t−1)/(2t), so the quantization condition M = (N/k)(t−1)/t gives t = N/(N−M k), not t = N/(N+M k) as stated in (2.31). The same sign affects the expression D = (N+M k)/(N k) and consequently the central charge (2.34) and the spindle generalization (3.8). Please correct the sign in (2.30), in the definition of M, or in (2.31), and recompute the affected formulas.","section":"§2.5, Eqs. (2.30)–(2.31)"},{"comment":"The corrections to the uplift ansatz of [17] — ds^2_5 → 4 ds^2_5 and the rescalings of A34, A45, A53 — are stated without derivation. These normalizations enter the 11D metric and gauge fields and therefore affect the flux integrals (2.27)–(2.30) and the central charge (2.34). The authors should either derive these factors from the conventions of [17] and the present paper or provide an independent check, such as verifying that the uplifted metric and fluxes solve the 11D equations of motion.","section":"Footnote 2 and §2.3"}],"minor_comments":[{"comment":"The text says the AdS2 × spindle ⋉ disk solution is obtained from '(5.1)', but equation (5.1) is first introduced there; the reference should be to (4.7) or (4.10).","section":"§5, first sentence"},{"comment":"The x-disk data are not introduced in this section; x1, E(s1), D, and k are taken from Appendix C only later in §4.5. Please state the global range 0 < x < x1 and the definitions when the ansatz is first presented.","section":"§4.2"},{"comment":"The phrase 'It is amazing that the dependence on X disappears all along' is informal; a sentence explaining that the X dependence cancels because h(y1)=0 would be helpful.","section":"§4.5, after Eq. (4.39)"},{"comment":"The footnote changes the gauge-field notation relative to the main text, making Table 1 hard to compare with §2 and §4; a small table with both notations would improve readability.","section":"Introduction, footnote 1 and Table 1"},{"comment":"The entry 'AdS2 × disk × Riemann' has no reference and is not discussed in the text; please either add a reference or remove the entry.","section":"Table 2"}],"recommendation":"major_revision","confidential_remarks":"The main gap is verifiability: the §4.2 ansatz is presented without an equations-of-motion check, and the 'by trial and error' wording signals that the authors did not supply one. If the check can be added, the paper is likely within the scope of the journal and the construction is of interest. The sign inconsistency in §2.5 also needs to be fixed before the central-charge results can be trusted. I do not see grounds for rejection if these points are addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a useful, careful paper in the disk/spindle compactification program. It does not pretend the AdS3 × disk × disk solution is new—it credits [17] and adds the flux quantization, corrected uplift factors, and holographic central charge. The AdS2 × disk × disk solution in section 4 is the genuinely new piece, with an uplift to massive IIA and a Bekenstein-Hawking entropy that scales as N^{5/2}. That scaling is physically sensible, and the paper's overall classification table is a nice summary.\n\nThe soft spots, in order. First, the AdS2 ansatz is presented 'by trial and error' with no verification against the equations of motion in A.4–A.6. Everything downstream—the four-form flux, the entropy, the N^{5/2} scaling—depends on that ansatz being an actual solution. This is the load-bearing check, and the paper does not supply it. A referee should ask for a direct substitution, a Mathematica notebook, or a derivation through a consistent truncation. Second, there is a sign typo in the flux quantization (2.30): as written, combining it with the solution in (2.31) forces the flux integer M to be negative for positive s1. That's a minor fix, but it needs to be done. Third, the corrections to [17]'s uplift factors in footnote 2 are stated without derivation; they may be right, but since the AdS3 central charge depends on them, the derivation or at least a consistency check should appear.\n\nThe calculations that are present look standard and careful. The Euler-characteristic computations are consistency checks, not fitted results, and the flux quantization is explicit. The paper is squarely aimed at people working on wrapped-brane holography and AdS/CFT for disk and spindle compactifications; those readers will want this as a reference. It deserves a serious referee, but the referee's main job is to verify the AdS2 solution. I would accept it for peer review with revision expected.","headline":"Useful classification addendum: the AdS3 disk×disk results are sound, but the new AdS2 ansatz is missing the one check that would make me trust it—the equations of motion.","tokens_in":26095,"tokens_out":5168,"would_cite":false,"duration_ms":44196,"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 constructs new AdS3 × disk × disk and AdS2 × disk × disk supergravity solutions describing M5- and D4-branes wrapped on orbifolds, and derives the dual central charge and black hole entropy.","keywords":["gauged supergravity","disk × disk","spindle ⋉ disk","M5-branes","D4-branes","flux quantization","holographic central charge","Bekenstein-Hawking entropy"],"falsifier":"Substitute the local ansatz (4.7)/(4.10) into the six-dimensional equations of motion (A.4)-(A.6) with $2g=3m$ and check whether the Ricci, scalar, and gauge equations vanish identically; any nonzero component would falsify the existence claim. The same check applies to the seven-dimensional ansatz (2.4)/(2.7) against (A.1)-(A.3), although there the consistent truncation of [17] already guarantees it if the truncation is correct.","tokens_in":25027,"feed_emoji":"🌌","tokens_out":7789,"duration_ms":64312,"temperature":0.7,"pith_summary":"The paper aims to construct supersymmetric AdS solutions that describe M5-branes and D4-branes wrapped on two orbifolds at once: a disk times a disk, and the related spindle semi-direct disk. Using a previously built consistent truncation of seven-dimensional gauged supergravity on a disk, it produces an AdS3 × disk × disk solution, uplifts it to eleven-dimensional supergravity, and computes its holographic central charge. By analogy, it then writes down an AdS2 × disk × disk solution of six-dimensional U(1)^2-gauged supergravity, uplifts it to massive type IIA, and computes the Bekenstein-Hawking entropy of the presumed black hole. The central results are the scalings $c \\sim N^3$ and $S_{\\mathrm{BH}} \\sim N^{5/2}$, matching the expectations for compactifications of 6d (2,0) theories and 5d Seiberg theories respectively.","feed_headline":"Branes wrapped on disk pairs give N^3 and N^{5/2} scaling","feed_subtitle":"New AdS3 and AdS2 backgrounds with two disk factors give central charge and entropy with expected large-N scaling.","key_machinery":"The central machinery is the consistent truncation of seven-dimensional maximal gauged supergravity on the maximal AdS5 × disk solution, which turns a disk factor in five dimensions into a second disk in seven dimensions, together with the six-dimensional U(1)^2-gauged-supergravity action (4.4) and the uplift formulas to eleven-dimensional and massive type IIA supergravity. The disk geometry is encoded by functions $f(x)$ and $h(y)$ whose zeroes define orbifold singularities with period conditions $E(q_1)=1/(C\\ell)$ and $E(s_1)=1/(Dk)$, imposing the Euler characteristic $\\chi=1/\\ell$ for each disk. Flux quantization of the four-form through the four-cycles converts the continuous parameters $q_1, s_1$ into the integers $N, K, M, k, \\ell$, and the resulting expressions (2.34) and (4.46) factor as products of contributions from the two disks.","core_discovery":"The paper's central claim is that the local ansatze in (2.4)/(2.7) and (4.7)/(4.10) are genuine solutions of U(1)^2-gauged supergravity in seven and six dimensions, respectively. The seven-dimensional AdS3 × disk × disk solution is obtained by uplifting the known AdS3 × disk solution using the consistent truncation of [17]; the six-dimensional AdS2 × disk × disk solution is presented directly, found by trial and error with two distinct non-trivial U(1) gauge fields. In each case the internal space is an S1 fibration over a rectangle whose corner structure gives a monopole source, and the y-z surface is a disk with Euler characteristic $1/\\ell$. The paper claims that flux quantization fixes the parameters in terms of integers $N, K, M, \\ell, k$, yielding holographic central charge (2.34) and Bekenstein-Hawking entropy (4.46), which scale as $N^3$ and $N^{5/2}$ when the charges are comparable. The same local solutions are completed as spindle ⋉ disk solutions, with the spindle central charge (3.8) also computed.","pith_inferences":["If the six-dimensional ansatz is verified against (A.4)-(A.6), the same trial-and-error strategy could produce AdS2,3 × disk × disk solutions embedded in the minimal, rather than maximal, AdS4,5 × disk backgrounds, which the paper leaves open.","The explicit entropy formula suggests that the black hole with AdS2 × disk × disk horizon should admit a microscopic counting via the topologically twisted index of the dual 5d gauge theory, in direct analogy to the Riemann-surface cases; this is a testable prediction if the index computation can be performed.","The piecewise-constant monopole function $L(y,\\xi)$ with a jump at the corner of the base rectangle is the same structure seen in other disk and spindle uplifts, so a closer look at that corner could reveal whether the smeared D4-D8 sources are the only singularities or whether a localized source is required for consistency."],"forward_implications":["If the solutions are genuine, the AdS3 × disk × disk background is the holographic dual of a 2d SCFT obtained from compactifying a 4d Argyres-Douglas theory on a disk, with central charge $c = \\frac{N^2 K^2 \\ell}{12(N+K\\ell)}\\frac{8M^2 k}{N(N+Mk)}$.","The AdS2 × disk × disk background describes a presumed black hole in massive IIA whose entropy $S_{\\mathrm{BH}} = \\frac{2\\sqrt{6}\\pi}{5}\\sqrt{8-N_f}\\sqrt{\\frac{N^3 K^3 \\ell}{N+K\\ell}}\\sqrt{\\frac{M^3 k}{g^2 N^2(2gN+3Mk)}}$ scales as $N^{5/2}$ for comparable charges, matching 5d Seiberg-theory compactifications.","The spindle ⋉ disk solutions provide the same local physics with a spindle replacing one disk, and the central charge (3.8) again factorizes into a disk contribution times a spindle contribution.","The fact that both disk factors carry Euler characteristic $1/\\ell$ and the flux quantizations reduce to quantizations of the seven- and six-dimensional field strengths means that the observables are determined purely by the integers $N, K, M$ and orbifold data, with no remaining continuous parameters."],"supporting_citations":[{"why":"Supplies the consistent truncation of seven-dimensional gauged supergravity on the disk that is used to obtain the AdS3 × disk × disk solution.","marker":"[17]"},{"why":"Provide the AdS3 × disk solutions in five dimensions that are uplifted via [17] to produce the AdS3 × disk × disk background.","marker":"[7, 8]"},{"why":"Give the maximal AdS5 × disk solutions and their Argyres-Douglas duals, which the disk factor embeds and whose central charge a4d enters (2.35).","marker":"[3, 4]"},{"why":"Supply the uplift formula from six-dimensional U(1)^2-gauged supergravity to massive type IIA used for the AdS2 × disk × disk solution.","marker":"[11, 29]"},{"why":"The flux quantization analysis for D4-branes on a disk is followed in section 4.5.","marker":"[10]"},{"why":"Provides the Bekenstein-Hawking entropy formula and the D4-brane-on-spindle conventions used in (4.45)-(4.46).","marker":"[27]"},{"why":"Supplies the holographic central-charge formula and the spindle period expression used in (2.34) and (3.8).","marker":"[24]"},{"why":"Gives the eleven-dimensional uplift formula, as presented in [28], used for the M5-brane solution.","marker":"[33]"}],"fun_headline_variants":["Disk×disk brane wraps give N^3 and N^{5/2} scaling","AdS3 and AdS2 from disk pairs: N^3 and N^{5/2} scaling","M5 and D4 branes on disk pairs yield N^3, N^{5/2}","Spindle⋉disk solutions give central charge and entropy","AdS3×disk×disk and AdS2×disk×disk from branes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument stands on the unverified assertion that the six-dimensional ansatz (4.7)/(4.10) actually solves the equations of motion (A.4)-(A.6); the paper says it was found by trial and error and presents no check, and if the ansatz fails, the massive-IIA uplift and entropy (4.46) are not valid.","fun_headline_variants_meta":{"raw":{"variants":["Disk×disk brane wraps give N^3 and N^{5/2} scaling","AdS3 and AdS2 from disk pairs: N^3 and N^{5/2} scaling","M5 and D4 branes on disk pairs yield N^3, N^{5/2}","Spindle⋉disk solutions give central charge and entropy","AdS3×disk×disk and AdS2×disk×disk from branes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000708,"raw_usage":{"total_tokens":3206,"prompt_tokens":978,"completion_tokens":2228,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":594,"completion_tokens_details":{"reasoning_tokens":2123}},"tokens_in":594,"tokens_out":2228,"duration_ms":13731,"temperature":1.0,"reasoning_tokens":2123,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T20:22:13.014120+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Substitute the local ansatz (4.7)/(4.10) into the six-dimensional equations of motion (A.4)-(A.6) with $2g=3m$ and check whether the Ricci, scalar, and gauge equations vanish identically; any nonzero component would falsify the existence claim. The same check applies to the seven-dimensional ansatz (2.4)/(2.7) against (A.1)-(A.3), although there the consistent truncation of [17] already guarantees it if the truncation is correct.","supporting_citations":[],"review_version":1}