{"id":"bd198e71-4975-4574-9ae6-c892a19c42bc","arxiv_id":"1908.09846","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The author uplifts supersymmetric AdS6 black holes from F(4) gauged supergravity into massive type IIA and type IIB supergravity, and verifies an entropy match in the IIA case.","lead":"This paper builds new black hole solutions in ten-dimensional string theory by lifting known six-dimensional black holes with established formulas. One of the new solutions passes a quantum gravity consistency check: its holographic entanglement entropy exactly equals the black hole entropy.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"IIA central claim rests on an unverified sign change in the F(4) uplift formula (footnote 3, §2.1); if the original [25] sign is correct, the IIA black hole is not the claimed uplift.","rationale":"The reader's weakest assumption is exactly the sign correction in footnote 3, and I agree that this is the most load-bearing point. The IIA construction is the paper's primary new result, and the claimed supersymmetric massive IIA black hole depends on a modified F(4) flux whose correctness is asserted but not derived. The entropy matching in eq. (2.27) does not depend on the sign of the ∗6 F~(2) term, since it uses only the metric and dilaton, so that result would survive even if the sign were wrong; but the central claim that the solution is the uplift of the F(4) seed, and is supersymmetric, would not. The IIB numerical verification gap is real but less serious because the IIB uplift formula from [29] is not modified, and the author's numerical checks provide partial support. Since the sign issue can in principle be settled by a focused calculation, and the paper already presents the result conditionally, the appropriate verdict remains CONDITIONAL; no change is needed from the reader's assessment.","tokens_in":17224,"tokens_out":10551,"duration_ms":114391,"concrete_test":"Independently re-derive the massive IIA uplift formula by reducing the type IIA four-form flux on the S^3 ansatz of [25] using the conventions of footnote 2, and compare the coefficient of ∗6 F~(2) in the resulting F(4) with eq. (2.7). Equivalently, substitute a symbolic F(4) seed with nonzero F~(2) and F~(3) into the massive IIA Bianchi identity dF(4) = F(2) ∧ H(3) (eq. B.6) for both signs; the sign that makes the identity hold identically before imposing the F(4) equations of motion is the correct one. If the derivation or the Bianchi check favors the original [25] sign, the IIA solution is not the claimed uplift and the IIA central claim fails; if it favors the author's sign, the concern is resolved and the correction should be documented as a derivation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In §2.1, footnote 3, the author states: 'We suspect a typographical error in [25]. We changed the sign of ∗6 F~(2) term in F(4) from [25].' No derivation is given. For the black hole seed, the U(1) gauge field vanishes but B_tr is nonzero, so F~(2) = (2/3)gB and the ∗6 F~(2) term in eq. (2.7) contributes to F(4); the sign is not inert. The IIA solution, its supersymmetry, and the claim that it is an uplift of the F(4) seed all depend on this altered flux. The stated check that the solution satisfies the massive IIA equations of motion (using the corrected sign) verifies the ansatz, but does not establish that the formula is the correct reduction of [25]; if the original sign was correct, e.g., because [25] uses the opposite orientation of the six-dimensional Hodge star, the solution presented is not the uplift and may fail the IIA Killing-spinor equations. The IIB section has a weaker but related verification gap: the Einstein equations are checked only at 'numerous specific numerical values' of (ρ, ξ), without an analytic proof.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uplifts the supersymmetric AdS6 black holes of F(4) gauged supergravity found in [31] to ten-dimensional massive type IIA and type IIB supergravity, using the uplift formulae of [25] and [29]. The IIA solution is claimed to be asymptotic to the Brandhuber-Oz vacuum and to preserve supersymmetry; the holographic entanglement entropy computed on the horizon, eq. (2.27), is shown to equal the Bekenstein-Hawking entropy of the seed black holes. The IIB solution is claimed to be asymptotic to the non-Abelian T-dual of Brandhuber-Oz, with a holographic entanglement entropy given in eq. (3.51). The paper also reviews the relevant uplift formulae and collects the supergravity equations of motion in appendices.","tokens_in":17526,"tokens_out":12457,"duration_ms":115524,"significance":"If the constructions are correct, the IIA result provides a concrete ten-dimensional embedding of asymptotically AdS6 black holes and gives a direct holographic entanglement entropy derivation of their Bekenstein-Hawking entropy, strengthening the AdS6/CFT5 correspondence and the microscopic counting of [37]. The IIB solutions are new examples of supersymmetric AdS6 black holes in type IIB, though their field-theory interpretation is less developed. A positive feature is that the entropy match in (2.27) is not obtained by fitting parameters; it follows from the geometry and the horizon data. However, the significance is contingent on resolving the sign ambiguity in the IIA uplift and on providing full verification of the equations of motion.","major_comments":[{"comment":"The sign change in the F(4) flux is a load-bearing modification of the uplift formula of [25] that is not derived. In the seed solution the U(1) gauge field vanishes but B_tr is nonzero, so F~(2) = (2/3)g B and the ∗6 F~(2) term in eq. (2.7) contributes; the sign is not inert. If the original sign in [25] is correct, for example because of a different orientation of the Hodge star, the IIA solution presented is not the uplift and may fail the massive IIA equations. The author should either derive the corrected formula from the dimensional reduction or verify it by comparing with the reduction of the Brandhuber-Oz solution. The assertion in §2.2 that the solution solves the massive IIA equations of motion is also not substantiated: the check is not shown, and checking the ansatz with the corrected sign does not establish the correctness of the uplift formula itself.","section":"§2.1, footnote 3, eq. (2.7)"},{"comment":"In §3.2.2, the Einstein equations of the IIB solution are checked only at 'numerous specific numerical values' of (ρ, ξ). This does not prove that the solution satisfies the IIB equations of motion identically, which is a central claim of the paper. The text states that the uplifted solution 'explicitly checked' the equations of motion, but then qualifies the Einstein equations as numerical only. The author should provide an analytic verification of the Einstein equations, or show that the uplift formula of [29] is a consistent truncation so that the F(4) seed solution automatically solves the IIB equations.","section":"§3.2.2"},{"comment":"In §3.3, eq. (3.51), the holographic entanglement entropy in IIB is computed with an integral over ρ from 0 to R, where R is also the constant in the uplift formula (3.33). The Riemann surface Σ in the non-Abelian T-dual solution is non-compact (see Appendix C), so the volume of Σ is divergent; the area of the entangling surface is therefore infinite without a cutoff. The result depends on R^7, and the physical origin of the cutoff is not explained. The quantity in (3.51) is not a well-defined entanglement entropy unless a proper regularization is specified, and the paper should clarify the range of the coordinate ρ and the meaning of the cutoff.","section":"§3.3, eq. (3.51)"}],"minor_comments":[{"comment":"The value 'e^{2g1+2g2}=2/33' is inconsistent with the normalization quoted in (2.17); using m=√2 and g=3m/2 one obtains e^{4g1}=1/(g^3 m)=2/27, which is the value that gives the final result (2.27).","section":"§2.3, after (2.27)"},{"comment":"The word 'supergrvity' should be 'supergravity'.","section":"§1, paragraph 4"},{"comment":"The expression 'λ± 1' should be 'λ = ±1'.","section":"§3.2, below (3.43)"},{"comment":"The notation 'volΣ_{g≠1}' should be 'volΣ_g'.","section":"§2.3, (2.28)"},{"comment":"The symbol R is used both as a constant in the uplift formula and as the upper limit of the ρ-integration; a different symbol for the cutoff would avoid ambiguity.","section":"§3.3, (3.51)"}],"recommendation":"major_revision","confidential_remarks":"The sign change in §2.1 is the main risk: if the original sign in [25] is correct, the IIA black hole is not the claimed uplift. I recommend that the editor ask for an explicit derivation or independent check before publication. The IIB entanglement entropy result is cutoff-dependent and should be qualified or reinterpreted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nRead the Suh paper on uplifting AdS6 black holes to IIA/IIB. The genuinely new piece is the explicit uplift of the specific F(4) black holes of [31] to both massive IIA and IIB, plus the holographic entanglement entropy computation. The IIA entropy matches the Bekenstein-Hawking entropy of the seed exactly—a real quantitative check in a corner where explicit string embeddings are rare. The IIB construction is also new, and the fixed-point limit reproduces the known non-Abelian T-dual, which builds some confidence.\n\nThe soft spot is the sign change in the IIA F(4) flux (footnote 3, §2.1). The author suspects a typo in [25] and flips the sign of the *6 F~(2) term, but gives no derivation. That term is not inert for the black hole seed: B_tr is nonzero, so F~(2) = (2/3)gB contributes. The check that the ansatz solves the IIA equations of motion verifies the solution, but not that it is the reduction of the 6D theory. If [25]'s sign was actually correct (e.g., due to Hodge-star conventions), the IIA geometry presented here is not an uplift of the seed. That's a load-bearing issue for the central claim.\n\nThe IIB section has a milder gap: Einstein equations are checked only at numerical points in (rho, xi). That's weaker than an analytic check, though the similarity to the fixed-point calculation makes me less worried there. Also, the paper says 'explicitly checked' but doesn't show the algebra; that's a presentation choice, not a flaw by itself.\n\nOn balance, the IIA entropy match is the strongest result and it is suspiciously clean—makes me think the sign change is likely correct in practice, but 'likely' is not a proof. The paper deserves refereeing: a referee should ask for a derivation, or at least a consistency argument, for the sign flip. If that gets resolved, this is a solid contribution to the AdS6/CFT5 toolkit.\n\nWould I bring it to reading group? Maybe—it's a good case study for the difference between checking equations of motion and verifying an uplift. I wouldn't cite it in my own work until the sign issue is clarified.\n\nRecommendation: accept for peer review, but with heavy scrutiny on the sign point; conditional on that being resolved, publish.","headline":"New entropy match for AdS6 black holes, but the IIA sign flip lacks a derivation.","tokens_in":17985,"tokens_out":2707,"would_cite":false,"duration_ms":27403,"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 uplifts supersymmetric AdS6 black holes from six-dimensional F(4) gauged supergravity to massive type IIA and type IIB supergravity, and reports that in the IIA case the holographic entanglement entropy exactly equals the…","keywords":["AdS6 black holes","massive type IIA supergravity","type IIB supergravity","F(4) gauged supergravity","uplift formulae","holographic entanglement entropy","Bekenstein-Hawking entropy","Brandhuber-Oz solution"],"falsifier":"Re-evaluate the massive type IIA equations of motion and Bianchi identities of appendix B.1 with the four-form flux $F_{(4)}$ kept in the original sign of [25] instead of the corrected sign; if the uncorrected sign also solves the equations of motion, the sign change is not needed, and if the corrected sign fails any of (B.3)-(B.6) or $dF_{(4)}=F_{(2)}\\wedge H_{(3)}$, the IIA black hole solutions and the entropy match collapse. Independently, the IIB Einstein equations were verified only at sampled coordinate values (Section 3.2.2), so a symbolic check at generic $(\\rho,\\xi)$ would remove that residual uncertainty.","tokens_in":17055,"feed_emoji":"🕳️","tokens_out":6493,"duration_ms":62462,"temperature":0.7,"pith_summary":"This paper takes supersymmetric black holes found in six-dimensional F(4) gauged supergravity and elevates them to genuine ten-dimensional solutions of massive type IIA and type IIB supergravity using uplift formulae. In massive type IIA, the resulting black holes asymptote to the Brandhuber-Oz vacuum; in type IIB, they asymptote to the non-Abelian T-dual of that vacuum. The author then computes the holographic entanglement entropy of the entangling surface on the horizon. In the IIA case, that entropy exactly equals the Bekenstein-Hawking entropy of the seed black holes, the same value already reproduced microscopically by the topologically twisted index of five-dimensional USp(2N) gauge theory. The IIB entanglement entropy is computed explicitly and awaits a dual field theory for comparison.","feed_headline":"AdS6 black holes uplift to string theory and match entropy","feed_subtitle":"The IIA uplift's holographic entanglement entropy matches Bekenstein-Hawking; IIB produces new black hole solutions.","key_machinery":"The load-bearing machinery is the pair of uplift formulae that map F(4) gauged supergravity solutions into ten dimensions: the [25] formula to massive type IIA and the [29] formula to type IIB. The IIB formula is steered by two holomorphic functions $A_\\pm$ that select which AdS6 vacuum the solution approaches; the author uses $A_\\pm = \\frac{1}{216z^3} \\mp \\frac{i}{4z} - \\frac{i}{108}$, the choice that gives the non-Abelian T-dual of the Brandhuber-Oz solution. The seed is the supersymmetric AdS6 black hole family of [31], with magnetic charges twisted over two Riemann surfaces, a two-form field, a running scalar, and horizon AdS2 × Σ_{g1} × Σ_{g2}. The entropy checks use the standard holographic entanglement entropy formula on the horizon, where the minimal surface degenerates to a point because of the AdS2 factor.","core_discovery":"The central claim is that the uplifted solutions are genuine supersymmetric black hole geometries of massive type IIA and type IIB supergravity, not merely formal rearrangements: they interpolate between the supersymmetric AdS6 fixed point at infinity and an AdS2 × Σ_{g1} × Σ_{g2} horizon. On the IIA side, the holographic entanglement entropy computed on the horizon, $S_{\\text{EE}} = \\frac{8\\sqrt{2}\\pi(g_1-1)(g_2-1)N^{5/2}}{5\\sqrt{8-N_f}}$, exactly equals the Bekenstein-Hawking entropy of the seed black holes of [31], which is independently accounted for by the topologically twisted index of 5d USp(2N) gauge theory. On the IIB side, the paper produces new explicit supersymmetric black hole solutions asymptotic to the non-Abelian T-dual of the Brandhuber-Oz solution, with a holographic entanglement entropy given by a formula linear in $(g_1-1)(g_2-1)$ that has no microscopic comparison yet.","pith_inferences":["Beyond the paper's own claims, the exact IIA entropy match strengthens the case that the Brandhuber-Oz vacuum is a reliable anchor for quantitative AdS6/CFT5 checks, since any mismatch in higher-genus or charge extensions would now be visible in ten dimensions.","The IIB entanglement entropy depends on the product $(g_1-1)(g_2-1)$; one could test whether it satisfies the same attractor or extremality relations as the IIA value once a candidate dual theory is proposed.","The same uplift route, applied to other six-dimensional solutions such as domain walls or flows in F(4) supergravity, could generate a broader class of ten-dimensional string backgrounds without solving the full ten-dimensional equations from scratch."],"forward_implications":["The IIA black holes are genuine ten-dimensional solutions asymptotic to the unique Brandhuber-Oz vacuum, so the AdS6/CFT5 entropy match now lives inside string theory rather than only in a six-dimensional truncation.","Because the holographic entanglement entropy on the horizon equals the Bekenstein-Hawking entropy for the IIA solution, the topologically twisted index counting, the black hole entropy, and the entanglement entropy all point to the same number.","The IIB uplift produces explicit supersymmetric black holes asymptotic to the non-Abelian T-dual vacuum, with a computable entanglement entropy that becomes testable once the dual field theory is identified.","The successful use of the [25] and [29] uplift formulae on black hole backgrounds suggests the same machinery can embed other F(4) solutions into ten dimensions whenever a consistent truncation exists."],"supporting_citations":[{"why":"Supplies the massive type IIA uplift formula that carries the IIA black hole construction.","marker":"[25]"},{"why":"Supplies the type IIB uplift formula used to build the IIB black hole solutions.","marker":"[29]"},{"why":"Provides the seed supersymmetric AdS6 black hole solutions that are uplifted.","marker":"[31]"},{"why":"Defines the Brandhuber-Oz solution, the unique supersymmetric AdS6 vacuum of massive type IIA used as the asymptotic background.","marker":"[2]"},{"why":"Defines the non-Abelian T-dual of the Brandhuber-Oz solution, the asymptotic vacuum for the IIB black holes.","marker":"[8]"},{"why":"Gives the topologically twisted index whose microscopic counting matches the Bekenstein-Hawking entropy of the seed black holes.","marker":"[37]"},{"why":"Provides the Bekenstein-Hawking entropy of the seed black holes that the IIA holographic entanglement entropy is matched against.","marker":"[39]"},{"why":"Gives the holographic entanglement entropy prescription used to compute the horizon entanglement entropy.","marker":"[44, 45]"}],"fun_headline_variants":["AdS6 black holes uplift to IIA and IIB supergravity","IIA uplift matches Bekenstein-Hawking entropy for AdS6 black holes","New supersymmetric AdS6 black holes from IIB uplift","Entanglement entropy matches Bekenstein-Hawking for AdS6 IIA black holes","Uplifted AdS6 black holes: IIA entropy match, IIB new solutions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole massive type IIA construction rests on an unsupported sign change the author suspects in the four-form flux formula of [25] (footnote 3, Section 2.1); if the original sign is the correct one, the IIA uplifted black holes and the entropy match are not established.","fun_headline_variants_meta":{"raw":{"variants":["AdS6 black holes uplift to IIA and IIB supergravity","IIA uplift matches Bekenstein-Hawking entropy for AdS6 black holes","New supersymmetric AdS6 black holes from IIB uplift","Entanglement entropy matches Bekenstein-Hawking for AdS6 IIA black holes","Uplifted AdS6 black holes: IIA entropy match, IIB new solutions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001552,"raw_usage":{"total_tokens":6182,"prompt_tokens":902,"completion_tokens":5280,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":518,"completion_tokens_details":{"reasoning_tokens":5175}},"tokens_in":518,"tokens_out":5280,"duration_ms":36003,"temperature":1.0,"reasoning_tokens":5175,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:00:22.030805+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-evaluate the massive type IIA equations of motion and Bianchi identities of appendix B.1 with the four-form flux $F_{(4)}$ kept in the original sign of [25] instead of the corrected sign; if the uncorrected sign also solves the equations of motion, the sign change is not needed, and if the corrected sign fails any of (B.3)-(B.6) or $dF_{(4)}=F_{(2)}\\wedge H_{(3)}$, the IIA black hole solutions and the entropy match collapse. Independently, the IIB Einstein equations were verified only at sampled coordinate values (Section 3.2.2), so a symbolic check at generic $(\\rho,\\xi)$ would remove that residual uncertainty.","supporting_citations":[],"review_version":1}