{"id":"9b36917e-5df0-46bc-864d-f960f2933dd6","arxiv_id":"2509.09536","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Gauge and gravitational late-time correlators in de Sitter are mapped to EAdS Witten diagrams, with new Mellin-space propagators and a treatment of even boundary dimensions.","lead":"Late-time correlations of photons and gravitons in de Sitter space can be re-expressed as boundary correlators in Euclidean anti-de Sitter space, where standard conformal methods apply. This paper supplies explicit Feynman rules and propagators for scalar QED, Yang-Mills, and Einstein gravity, easing future computations of primordial cosmological correlators.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Even-d massless propagator identities in §3.4 are asserted, not proved: Ω^{AdS}_ν=0 for ν∈-iN and Γ(-iν)Ω^{AdS}_ν finite are the bridge from divergent c^{dS-AdS} coefficients to the advertised Feynman rules. A wrong pole or sign here breaks all even-d gauge/gravity diagrams.","rationale":"The reader's weakest-assumption pick is right. Section 3.4 is the only place the paper addresses the even-d massless cases, and those cases are the reason the paper exists: gauge and graviton propagators have ν=-i(d/2-1) and ν=-id/2, which for even d are in -iN. The rest of the construction is algebraic once the propagator identities are exact, and the paper supplies good supporting material: Mellin-space derivations in Section 3, the Raju comparison in A.3, and explicit bulk-to-boundary expressions. But the crucial limit is asserted. Footnote 9 points to (A.3), from which Ω=0 is visible, but the finiteness of Γ(-iν)Ω requires also knowing the residue of Γ(-iν) at its pole and the coefficient in (3.61); the paper does not display this one-line check. Because no verification is given for any even-d diagram, the central claim is conditional. I would not raise this to reject: the gap is plausibly fillable and references [1,2] give strong prior evidence for the general map. But it is not a stylistic issue. A single explicit limit calculation, or one finite even-d three-point test, would settle it. The loop-level statement in Section 2 is also asserted rather than demonstrated for the new rules, but it is secondary; if the Section 3.4 limit is correct, the loop extension is the same branch-sum mechanism.","tokens_in":53471,"tokens_out":15104,"duration_ms":178006,"concrete_test":"Set d=4, where gauge ν=-i and graviton ν=-2i. First, analytically expand both sides of (3.61) and the finite formulas for G^{±±}, G^{±∓} in ε around ν=-in using the explicit Bessel representations (3.7) and (A.3), keeping the first subleading term in Ω^{AdS}_ν; check that the ε^0 remainder equals the exact dS Schwinger-Keldysh propagator (3.19) at the same ν. End-to-end: for d=4, compute the pure-Yang-Mills three-point contact diagram (5.7) with falloffs Δ+Δ+Δ- directly in the Schwinger-Keldysh formalism. The EAdS sine table gives sin(dπ/2)=0 and this channel is IR-finite, so the direct SK result must vanish up to local counterterms; any nonzero non-local remainder disproves the central claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's new content is the EAdS Feynman rules for gauge bosons and gravitons, and the most subtle cases—massless fields in even boundary dimension d—are handled in Section 3.4 by a limiting procedure that is never carried out. The text states that for ν=-in the two shadow projectors coincide (3.60), that the EAdS harmonic function Ω^{AdS}_ν vanishes at these points, and that Γ(-iν)Ω^{AdS}_ν supplies the finite nonzero remainder after the divergence in c^{dS-AdS}_{d/2-iν} cancels (3.61)–(3.63), footnote 9. Footnote 9 refers to representation (A.3), from which Ω=0 is indeed visible, but the finiteness and value of Γ(-iν)Ω require also controlling the residue of Γ at its pole and the relative coefficient in (3.61); neither is shown. Since the dS propagators themselves are finite, any error in this limit is invisible elsewhere in the paper. Yet equations (4.3)–(4.7), (5.4)–(5.6), (6.4)–(6.6) are exactly the objects that inherit the Section 3.4 result, so the central claim is conditional on this unproved identity. A secondary, related gap is the Section 2 assertion that the factorization (2.18) holds 'both at tree and loop level'; the paper's explicit examples stop at tree exchange, and no loop-level check is given for the new even-d rules. The first issue is the more immediately load-bearing.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops the perturbative map between late-time dS correlators and EAdS Witten diagrams for gauge bosons and gravitons, building on the authors' prior framework. Working in Mellin space, it derives dS and EAdS bulk-to-bulk and bulk-to-boundary propagators for spin-1 and spin-2 fields in axial/temporal gauge, including longitudinal components, and verifies them against Raju's representation. It then gives explicit EAdS Feynman rules for scalar QED, pure Yang-Mills, and Einstein gravity, with sinusoidal prefactors, and illustrates them on contact and tree-level exchange diagrams. A section addresses massless representations in even boundary dimensions, where the standard dS-AdS coefficient diverges.","tokens_in":53951,"tokens_out":14394,"duration_ms":155579,"significance":"If correct, the paper would reduce spinning cosmological correlator computations to standard AdS/CFT diagrammatics, and the Mellin-space representation of full propagators (including longitudinal parts) is a useful technical contribution. The derivation is parameter-free and the Mellin expressions are benchmarked against known representations; selection rules for falloffs follow from the sinusoidal prefactors. However, the even-dimensional limit is the pivot of the new rules, and the evidence for it is currently incomplete, so the result is conditional.","major_comments":[{"comment":"The even-d treatment rests on three assertions: (i) Omega^{AdS}_nu vanishes at nu=-in; (ii) Gamma(-i nu) Omega^{AdS}_nu is finite and nonzero; (iii) after inserting (3.61) into (2.13), the divergent c^{dS-AdS}_{d/2+n} cancels. The text cites representation (A.3) for (i) and states (ii)-(iii) without proof. From (A.3) and (3.12b), Omega=0 follows from the factor 1/Gamma(1-n) in K^{AdS}_{d/2-n}, but extracting the finite value of Gamma(-i nu)Omega requires a matched epsilon-expansion around nu=-in that is not given. Since equations (4.3)-(4.7), (5.4)-(5.6), (6.4)-(6.6) inherit this limit, every even-d gauge/gravity diagram is conditional on this point. Please provide the explicit nu=-in+epsilon expansion and a derivation of (3.61).","section":"Section 3.4, Eqs. (3.60)-(3.63) and footnote 9"},{"comment":"The statement that on-shell factorization gives the sinusoidal coefficients 'both at tree and loop level' is not demonstrated for the new gauge/gravity rules. All explicit checks in Sections 4-6 are tree-level contact or exchange. The loop-level factorization may follow from [1,2] for generic spins, but the even-d modifications of Section 3.4 have no loop-level check, so the 'any perturbative contribution' claim is stronger than the evidence presented. A one-loop check (or a proof that the Section 3.4 limit commutes with the Mellin sums in loops) would close the gap.","section":"Section 2, Eq. (2.18)"}],"minor_comments":[{"comment":"Both sides read omega_{-in}; presumably the second factor should be omega_{+in} (or omega_{in}), otherwise the equality is a tautology.","section":"Eq. (3.60)"},{"comment":"The right-hand side has K^{AdS d/2-i nu}; comparing with (3.58), (4.4), and (5.5), the superscript should be d/2+i nu.","section":"Eq. (6.5)"},{"comment":"'sinusodial' should be 'sinusoidal'.","section":"Section 4, after Eq. (4.11)"}],"recommendation":"major_revision","confidential_remarks":"The key issue is localized: if the authors can supply the missing even-d limiting argument (explicit nu=-in+epsilon expansion and derivation of (3.61)), I expect the paper to be acceptable. I recommend major revision rather than rejection because the rest of the derivation is careful and benchmarked."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a look before you use the dS/EAdS Feynman rules for spin-1 and spin-2 in even d. The paper takes the earlier map and makes it concrete for gauge bosons and gravitons: Mellin-space propagators in axial/temporal gauge, including longitudinal pieces, with checks against Raju's representation and [54]. That part is solid and genuinely useful. The sinusoidal selection rules for contact and tree exchange in scalar QED, Yang-Mills, and gravity are spelled out cleanly, including which falloff combinations give vanishing non-local parts.\n\nThe soft spot is exactly where the stress-test puts it. Section 3.4, which handles massless fields in even boundary dimension, needs Omega^AdS_nu=0 for nu in -iN and needs Gamma(-i nu) Omega^AdS_nu to supply the finite remainder after the c^{dS-AdS} divergence cancels. The text points to representation (A.3) and footnote 9, but neither actually demonstrates the residue control that makes the limit work. Since the dS propagators are finite, an error here wouldn't show up elsewhere, yet the advertised Feynman rules inherit this result. That is load-bearing, not a cosmetic gap. A referee should ask for a proper derivation of (3.61)-(3.63), or at least a direct check for low d.\n\nSecondary, minor: the factorization (2.18) is claimed to hold at tree and loop level, but the examples only show tree exchange. That is an assertion, not a demonstration. It doesn't undermine the tree-level machinery, but it is worth flagging in a paper whose selling point is a practical framework.\n\nOverall: clear, honest about scope, and the new propagator expressions are a real service. The even-d issue is a gap in proof, not a clear sign of a wrong result. I would send it to a serious referee and ask for the missing derivation. If that gets fixed, I would cite it and use the rules.","headline":"Useful extension of the dS/EAdS map to spin-1 and spin-2, but the even-dimension limit in Section 3.4 is asserted rather than proven and is load-bearing for the advertised Feynman rules.","tokens_in":54361,"tokens_out":2617,"would_cite":true,"duration_ms":26564,"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 shows that late-time correlators of gauge fields and gravitons in de Sitter space can be rewritten exactly as sums of Euclidean AdS Witten diagrams, with sinusoidal coefficients.","keywords":["cosmological correlators","de Sitter space","Euclidean AdS","Witten diagrams","Schwinger-Keldysh formalism","Mellin space","gauge bosons","gravitons"],"falsifier":"A direct numerical computation of a four-point exchange diagram in dS Yang-Mills in, say, d=4, evaluated both via the Schwinger-Keldysh integral and via the proposed EAdS combination, should agree exactly. A mismatch in any partial wave or a failure of the sine-factor selection rule would falsify the map.","tokens_in":53393,"feed_emoji":"📐","tokens_out":3462,"duration_ms":38131,"temperature":0.7,"pith_summary":"This paper claims that the late-time (Schwinger-Keldysh) correlators of scalar QED, pure Yang–Mills theory, and Einstein gravity in de Sitter space can be rewritten exactly as linear combinations of Euclidean AdS Witten diagrams. The map turns each dS propagator into a pair of EAdS propagators with shadow scaling dimensions, with the branch structure of the in-in contour producing sinusoidal prefactors. The authors work out the Mellin-space forms of gauge and graviton propagators, including longitudinal components, and give explicit Feynman rules for the three theories. They also address the technical case of even boundary dimensions, where the naive decomposition diverges, and show how to regulate it with an EAdS harmonic function. If correct, this gives a practical way to compute cosmological correlators of massless fields using standard AdS/CFT diagrammatics.","feed_headline":"Gauge and gravity correlators in dS become AdS Witten diagrams","feed_subtitle":"Explicit Feynman rules turn de Sitter late-time correlators into EAdS calculations, including massless gauge fields and gravitons.","key_machinery":"The central object is the Mellin-space representation of bulk-to-bulk and bulk-to-boundary propagators in (EA)dS, which diagonalizes dilatations and makes the analytic continuation between the two spaces manifest. The key identity is the decomposition of each Schwinger–Keldysh propagator into two EAdS propagators with shadow dimensions Delta± (equations 2.13, 3.45, 3.57), together with the phase factors that combine into sinusoidal prefactors at the level of amplitudes. For even boundary dimensions, the machinery is extended by the EAdS harmonic function Omega_AdS_nu, which supplies the finite correction where the coefficient c_dS-AdS diverges.","core_discovery":"Starting from the observation that de Sitter and Euclidean AdS share the same isometry group and are related by double Wick rotation, the paper establishes a perturbative equivalence: any late-time correlator in the Bunch–Davies vacuum can be expressed as a sum over EAdS Witten diagrams for the shadow pair of scaling dimensions Delta±, with coefficients given by trigonometric functions. For scalar QED, pure Yang–Mills, and Einstein gravity, the paper gives explicit propagator and vertex rules in axial/temporal gauge. In even boundary dimensions, where the coefficient c_dS-AdS diverges, the paper shows how the divergence cancels against a homogeneous EAdS harmonic function, yielding finite an","pith_inferences":["The same harmonic-function regularization for even d may apply to other massless fields (e.g., higher-spin gauge fields) that sit at the exceptional-series boundary.","The selection rules suggest that many dS correlators in these theories are purely local (IR counterterms) after renormalization, which could simplify inflationary predictions.","The equivalence implies that the analytic structure of dS late-time correlators matches that of EAdS boundary correlators, so conformal partial wave expansions and crossing may apply directly.","One could test the framework by explicitly computing a known dS correlator (e.g., the three-graviton contact diagram in even d) via direct Schwinger-Keldysh integration and comparing with the EAdS rule."],"forward_implications":["Late-time correlators of gauge fields and gravitons can be computed by standard EAdS Witten diagram techniques, including Mellin space and bootstrap methods.","The sinusoidal prefactors act as selection rules: for certain combinations of late-time falloffs, the non-local part of the correlator vanishes, simplifying the calculation.","Even in even boundary dimensions, where the naive dS-to-EAdS decomposition diverges, the rules give finite results, extending the framework to all d.","The Mellin-space forms of the gauge and graviton propagators, including longitudinal components, provide a convenient basis for checking Ward identities and studying IR divergences."],"fun_headline_variants":["dS late-time correlators become EAdS Witten diagrams","Map dS gauge and gravity to AdS Feynman rules","De Sitter correlators solved via Euclidean AdS","Cosmological correlators from AdS boundary diagrams","New Feynman rules for dS gravitons and gauge fields"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"For massless fields in even boundary dimensions, the treatment assumes that the EAdS harmonic function Omega_AdS_nu vanishes identically at nu = -i n and that the product Gamma(-i nu) Omega_AdS_nu provides the required finite correction; this property is asserted but not proven in the paper.","fun_headline_variants_meta":{"raw":{"variants":["dS late-time correlators become EAdS Witten diagrams","Map dS gauge and gravity to AdS Feynman rules","De Sitter correlators solved via Euclidean AdS","Cosmological correlators from AdS boundary diagrams","New Feynman rules for dS gravitons and gauge fields"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000216,"raw_usage":{"total_tokens":1291,"prompt_tokens":791,"completion_tokens":500,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":535,"completion_tokens_details":{"reasoning_tokens":414}},"tokens_in":535,"tokens_out":500,"duration_ms":5620,"temperature":1.0,"reasoning_tokens":414,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T18:55:33.172942+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct numerical computation of a four-point exchange diagram in dS Yang-Mills in, say, d=4, evaluated both via the Schwinger-Keldysh integral and via the proposed EAdS combination, should agree exactly. A mismatch in any partial wave or a failure of the sine-factor selection rule would falsify the map.","supporting_citations":[],"review_version":1}