{"id":"14b08ca9-c928-4338-9db2-29f50b8cc814","arxiv_id":"2508.06602","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Explicit two-, three-, and four-point Carrollian and celestial amplitudes for massless scalars in D dimensions, connected to the flat/Carrollian limit of AdS/CFT correlators.","lead":"Researchers derive explicit Carrollian and celestial amplitudes for massless scalar scattering in any spacetime dimension D, and show they can be reached by taking a Carrollian limit of AdS/CFT correlators. The paper matters because it extends flat-space holography beyond four dimensions, but it also unearths an unexplained extra term in the three-point limit that the correspondence does not predict.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 3-point boundary Carrollian limit does not reproduce the Carrollian amplitude: it yields C3 + C~3, and both the extraction of C3 and the closed form for C~3 rest on the unproven distributional ansatz (5.9)/(A.1).","rationale":"The reader's weakest_assumption identifies the same structural weakness: the 3-point boundary limit is the point where the claimed correspondence is least secure, because (5.14) yields C3 + C~3 and the extraction of C3 relies on the ansatz (5.9)/(A.1). My stress-test adds precision: the Sokhotsky split (5.13) is what isolates C3, and both pieces---the delta and the principal value---are controlled by the same assumed distributional form; the ansatz is motivated by the answer (3.10) rather than derived. The Appendix A computation is itself restricted to a generic-parameter regime (Delta_1 > D/4, Sigma_Delta > D, no overlapping singularities, A.8-A.9), and the branch point at epsi1 omega1 + epsi2 omega2 = 0 is explicitly deferred. This makes the central claim ('these amplitudes naturally arise') conditional: it is verified cleanly for 2 points, plausibly for 4 points assuming the leading-singularity / subleading-drop steps, and only partially for 3 points. I do not see an internal inconsistency or a fraudulent step; the authors even flag the gap in the Outlook. Hence CONDITIONAL is the right verdict, matching the reader, and my concrete test---an independent re-derivation for small integer cases---would settle whether the ansatz in fact holds.","tokens_in":30435,"tokens_out":2274,"duration_ms":22199,"concrete_test":"Derive the Carrollian limit of the 3-point CFT correlator (5.5) without invoking (5.9): perform the c->0 limit directly in position space, e.g. using the Mellin-Barnes representation (A.4) and evaluating the integral over x12, x13 for a small set of integer dimensions (D=4,5 and simple Delta_i, e.g. Delta_i = (D-2)/2 + m_i with small m_i) via an independent symbolic computation. If the result equals C3 + C~3 with the same C~3 as (A.15), the extra contribution is real and the ansatz is validated for those cases; if the delta-locus form differs (e.g. a different g(omega_i) or a non-delta piece), the claimed extraction of C3 and the abstract's 'naturally arise' statement are not supported.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that Carrollian amplitudes in general D arise from the Carrollian limit of AdS/CFT boundary correlators. The 2-point check (5.4) works, but the 3-point limit is the decisive case because it is the first place where the electric limit is nontrivial and where the distributional structure of the correlator must be derived rather than assumed. Equation (5.14) states that the limit equals C3 + C~3, with C~3 an extra contribution that the authors explicitly say is 'unclear how to interpret' (Sec. 6.3, Outlook). The abstract's claim that the amplitudes 'naturally arise' therefore fails for the 3-point function: only a sum containing the amplitude is obtained, and the amplitude itself is separated from C~3 by a Sokhotsky delta/prescription choice (5.13). The load-bearing assumption is the ansatz (5.9), reused as (A.1): the limit of the Schwinger-parameterized CFT correlator is asserted to be g(omega_i)|x12|^{D-4} delta^{D-2}(x12) delta^{D-2}(x13), and the function g is then fixed by integral (5.11) that reintroduces exactly the pole structure needed to produce C3. The authors state this is 'an ansatz motivated by the Carrollian amplitude (3.10)', so the extraction of C3 partly builds in the answer. The explicit C~3 computation in Appendix A is also restricted to the parameter regime Delta_1 > D/4, Sigma_Delta > D, with generic (non-overlapping) conformal dimensions (A.9), and a branch-point contribution (epsi1 omega1 + epsi2 omega2 = 0) is deferred in Sec. 5.2. Thus the central correspondence is not demonstrated for 3 points unless the ansatz is derived from the CFT (or its validity established for the needed regime), and the 4-point check inherits the same 'leading singular locus only' philosophy with the additional unproved dropping of the sigma_2 |x4,n|^4 term in (5.32) and an implicit assumption about reproducing the support S of (3.22). A reader should not reject the paper on this basis---the 2-point check is clean, the 4-point matches in D=4 [25],","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops Carrollian holography for massless scalar fields in D≥4. It defines Carrollian amplitudes as correlators of boundary operators at null infinity, gives a position-space Feynman-rule formulation, and derives explicit 2-, 3-, and 4-point amplitudes. It then tests the AdS/CFT origin of these objects in two ways: the flat-space (ℓ→∞) limit of AdS Witten diagrams and the Carrollian (c→0) limit of CFT_{D−1} boundary correlators. The 2-point check works, the 3-point boundary limit produces the amplitude plus an extra term C~3, and the 4-point limit is obtained through a leading-singularity ansatz. Finally, celestial amplitudes are extracted via the ui→0 limit and compared with [47].","tokens_in":30851,"tokens_out":5889,"duration_ms":69079,"significance":"If the derivations were rigorous, this would be a useful extension of the holographic dictionary to general D, with explicit closed forms for Carrollian and celestial correlators and a clear path to top-down applications (e.g., D=5 SYM). The paper is self-contained: it sets up Bondi coordinates and propagators carefully, provides explicit integral formulas, and correctly identifies the matching conditions with [47] up to normalization. The main caveat is that the 3-point and 4-point derivations rely on distributional ansätze and omit contributions that are not shown to be negligible; the central claim is therefore plausible but not fully established.","major_comments":[{"comment":"The abstract claims that Carrollian amplitudes 'naturally arise' from AdS/CFT. For the 3-point function this is not what Eqs. (5.13)–(5.14) show: the Carrollian limit equals C3 + C~3, and C~3 is explicitly left uninterpreted (Sec. 6.3, Outlook). The 3-point function is the first case where the electric limit is nontrivial, so the central claim needs to be either restricted (e.g., 'the amplitude is one of two branches selected by the iε prescription') or supplemented by a physical interpretation/elimination of C~3. As written, the limit does not reproduce the Carrollian amplitude.","section":"§5.2, Eqs. (5.13)–(5.14); abstract"},{"comment":"The singular-locus ansatz L = g(ω_i)|x12|^{D−4} δ^{D−2}(x12) δ^{D−2}(x13) is motivated by the Carrollian amplitude (3.10), and g is then fixed by integral (5.11) using a pole that generates exactly the delta-function part of C3. Thus the extraction of C3 from the limit partly builds in the answer; only C~3 is genuinely new. The appendix computation is also restricted to Δ1 > D/4, ΣΔ > D and generic Δij (A.9), with the branch point ϵ1ω1 + ϵ2ω2 = 0 deferred. A derivation of the distributional limit from the Schwinger parametrization is needed for the claim to be load-bearing.","section":"§5.2 and App. A, Eqs. (5.9), (5.11)–(5.12), (A.1)"},{"comment":"The 4-point derivation relies on the leading-singularity approximation (5.17) without showing that subleading terms vanish in the Carrollian limit. After rescaling, σ2|x4,n|^4 in (5.32) is dropped as 'subleading', but no estimate is given, and this step can fail if F (or U) vanishes. More importantly, the step-function support S of the Carrollian amplitude (3.22) is never derived from the c→0 integral; the ansatz (5.23) only produces delta-function constraints. Without these steps, (5.36) is a consistency check modulo an ansatz rather than a derivation of the 4-point Carrollian amplitude.","section":"§5.3, Eqs. (5.29)–(5.36) and (3.22)"}],"minor_comments":[{"comment":"Typos: 'Thee-point' in §3.3, 'F our-point' in §3.4, 'ofcourse', 'most easilt', 'Pocchammer' in App. A. Please proofread.","section":"§3.3, §3.4, §5.3, App. A"},{"comment":"The function RD(ci, qi) is introduced only schematically and never defined. Since Eq. (5.23) is an ansatz, please state its precise form or remove it.","section":"§5.3, Eq. (5.23)"},{"comment":"The δ-function decomposition assumes D≥4 and a particular choice of the vectors n_i. It would help to state explicitly that this is WLOG and that setting det(¯n)=1 is a normalization choice.","section":"§3.4, Eqs. (3.15)–(3.20)"},{"comment":"In the electric branch, the result is a distribution in u12; please spell out the iε convention for timelike separation and specify the distributional sense of the limit.","section":"§5.1, Eq. (5.2)"},{"comment":"The comparison with [47] is stated only 'up to normalization'. Please list the exact normalization mismatch for the 3- and 4-point celestial amplitudes so readers can verify the match.","section":"§6.3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is competent but overclaims the AdS/CFT derivation. The 3-point mismatch is the main issue: the limit yields C3 + C~3, and C~3 is uninterpreted. The 4-point derivation also rests on unproven subleading suppressions and does not reproduce the support S. If the authors can derive the distributional ansatz or restrict the claim appropriately, the paper would be acceptable; major revision is warranted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper gives the first explicit general-D Carrollian 2-, 3-, and 4-point amplitudes for massless scalars plus a new four-point celestial amplitude, and it makes a serious attempt to derive them from the flat/Carrollian limit of AdS/CFT. The two-point dictionary is clean. The 3-point and 4-point derivations are not fully closed, and the abstract's claim that the amplitudes 'naturally arise' is stronger than what is shown.\n\nWhat's good: Section 3 has explicit closed forms for the Carrollian amplitudes, including the 4-point expression (3.21) with the step-function support S, and the boundary-operator definition is careful. The relation to celestial amplitudes in Section 6 gives a concrete four-point celestial amplitude (6.13) that appears to be new. The flat-space limit of the AdS Witten diagrams in Section 4 is handled with explicit normalizations (alpha_D, beta_3, beta_4), which is useful for follow-up work.\n\nWhere it's soft: the 3-point Carrollian limit (5.14) gives C_3 + C~_3, not C_3. The authors are upfront about this—they say C~_3 is 'unclear how to interpret'—but it means the central correspondence is not established for the 3-point function. More importantly, the extraction of C_3 relies on the distributional ansatz (5.9)/(A.1), which fixes the singular locus by hand. The derivation of g(omega_i) in (5.11)-(5.12) reintroduces the pole structure needed for C_3, so there is a real circularity risk. The 4-point derivation has a similar structure: the leading singular-locus ansatz (5.23), the unproved dropping of the sigma_2 |x4,n|^4 term in (5.32), and the support function S is not shown to emerge from the c->0 limit. None of this makes the paper wrong; it makes the derivation incomplete. The 2-point check and the D=4 limit of the 4-point match give some confidence that the final answers are correct.\n\nThe paper is worth a serious referee. It ships explicit, checkable results and is honest about its gaps. The referee should ask the authors to either prove or weaken (5.9), to characterize the support S in the 4-point limit, and to explain whether C~_3 is a genuine new contribution or an artifact of the ansatz. I'd cite this if I worked on Carrollian holography; I'd bring it to a reading group.","headline":"Useful explicit results in general-D Carrollian holography, but the 'natural emergence' from AdS/CFT is only partly demonstrated: the 3-point Carrollian limit yields the amplitude plus an uninterpreted extra term.","tokens_in":31544,"tokens_out":2309,"would_cite":true,"duration_ms":24932,"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 claims that massless flat-space scattering amplitudes in $D \\ge 4$ are the Carrollian ($c \\to 0$) limits of AdS/CFT correlators, and that celestial amplitudes follow from the same boundary operators by a Mellin transform.","keywords":["Carrollian holography","flat space holography","celestial holography","AdS/CFT correspondence","Carrollian amplitudes","massless scalar scattering","conformal Carrollian primaries","general dimensions"],"falsifier":"Compute the electric $c \\to 0$ limit directly from the exact Schwinger-parameterized three-point CFT integral without imposing the ansatz (5.9); if the resulting distribution is not $g(\\omega_i)|x_{12}|^{D-4}\\delta^{D-2}(x_{12})\\delta^{D-2}(x_{13})$ on the fully-collinear locus, then $C_3$ is not the full Carrollian limit of the three-point function and $\\tilde{C}_3$ is not the complete extra contribution. Equivalently, retain the $\\sigma_2 |x_{4,n}|^4$ term in the four-point integral and check whether the support and normalization reproduce the Heaviside factor $S$ of eq. (3.22).","tokens_in":30228,"feed_emoji":"🌀","tokens_out":10966,"duration_ms":102671,"temperature":0.7,"pith_summary":"The paper establishes a general-dimensional version of the flat-space/Carrollian holography dictionary for massless scalar fields. It defines Carrollian amplitudes — correlators of conformal Carrollian primaries at null infinity, obtained by taking the speed of light to zero — and evaluates them explicitly at two, three, and four points. It then shows that these amplitudes are the flat limit of holographic AdS/CFT correlators: taking the AdS radius to infinity in the bulk is the same operation, at the level of correlators, as taking the speed of light to zero at the boundary. The same dictionary converts Carrollian amplitudes into celestial amplitudes by a limiting Mellin-type procedure, yielding explicit celestial correlators in $D$ dimensions. A genuinely new feature is an extra, uninterpreted contribution to the three-point electric limit, which the paper exhibits in closed form.","feed_headline":"AdS/CFT correlators become flat-space amplitudes as the boundary c → 0","feed_subtitle":"The flat bulk limit equals a boundary Carrollian limit; explicit 2-, 3-, 4-point and celestial amplitudes follow.","key_machinery":"The dictionary runs through Bondi coordinates, which cover flat null infinity and the AdS boundary with the same coordinate system. The AdS boundary metric reads $ds^2 = -\\ell^{-2}du^2 + |dx|^2$, so the bulk flat limit $\\ell \\to \\infty$ is literally the boundary Carrollian limit $c \\to 0$ with $c = 1/\\ell$. Boundary operators $\\Phi_\\epsilon(u,x)$ built from on-shell bulk modes are conformal Carrollian primaries of weight $(D-2)/2$, and their correlators define Carrollian amplitudes. The AdS bulk-to-boundary propagator limits to the flat-space version up to known $\\Delta$-dependent factors, which is why contact Witten diagrams map onto Carrollian Feynman integrals. The four-point limit uses v","core_discovery":"For massless scalars in $D \\ge 4$, the paper's central claim is that Carrollian amplitudes at null infinity and holographic CFT$_{D-1}$ correlators are the same object seen through two limits. The bulk flat limit $\\ell \\to \\infty$ of AdS Witten diagrams reproduces the Feynman-diagram definition of these amplitudes for two, three and four points (eqs. (4.28), (4.34), (5.4)). The boundary electric Carrollian limit $c \\to 0$ reproduces the same two- and four-point amplitudes exactly, and the three-point function up to an extra term $\\tilde{C}_3$ (eqs. (5.14), (5.36)). Celestial amplitudes follow by taking $u_i \\to 0$, converting Carrollian correlators into Mellin transforms of the same amplitud","pith_inferences":["A testable extension the paper leaves implicit: applying the boundary Carrollian limit to $\\mathcal{N}=4$ super-Yang-Mills correlators in $D=5$ should produce four-point flat-space amplitudes; a mismatch with direct Feynman-diagram computations would locate precisely where the singular-locus approximation fails.","If $\\tilde{C}_3$ is physical, its dependence on two independent ratios (rather than the single ratio of the ordinary Carrollian amplitude) suggests it encodes soft or subleading data that the momentum-space three-point amplitude does not contain.","The structural similarity to non-conformal Dp-brane correlators noted in the Outlook could be made precise: the electric two-point function's form matches correlators with generalized conformal structure, which would predict how higher-point Carrollian limits organize themselves.","Retaining the dropped $\\sigma_2 |x_{4,n}|^4$ term in the four-point derivation would give the first subleading-in-$c$ corrections to the Carrollian amplitude, quantifying how quickly the flat-space/Carrollian approximation sets in."],"forward_implications":["If the paper is right, flat-space massless scattering in any dimension $D \\ge 4$ is encoded in ordinary CFT correlators on the $D-1$ dimensional boundary, with $c = 1/\\ell$, giving a practical route from known AdS/CFT data to flat-space amplitudes.","The explicit two-, three- and four-point Carrollian amplitudes provide concrete building blocks for constructing Carrollian CFT duals in higher dimensions.","The celestial amplitudes derived via the $u_i \\to 0$ limit complete the Carrollian/celestial correspondence in general dimensions, so flat-space S-matrix elements can be repackaged as correlators of a CFT on the celestial sphere $S^{D-2}$.","The extra three-point contribution $\\tilde{C}_3$ shows that the electric Carrollian limit does not uniquely fix the three-point function from the momentum-space amplitude alone; any complete flat-holography dictionary must account for such additional singular contributions.","Because the dictionary is stated at the level of correlators, it can be applied to any known holographic CFT$_{D-1}$, not just free scalar examples, to generate flat-space amplitudes in the corresponding bulk dimension."],"supporting_citations":[{"why":"Defines the boundary operators and the Carrollian/celestial correspondence in D=4 that this paper extends to general dimensions.","marker":"[5]"},{"why":"Supplies the original definition of Carrollian amplitudes as transforms of momentum-space amplitudes.","marker":"[13]"},{"why":"Provides the D=4 template for the flat-limit/Carrollian-limit correspondence between AdS Witten diagrams and Carrollian amplitudes.","marker":"[25]"},{"why":"Supplies the bulk-point kinematics technique and the D-dimensional celestial amplitude results that this paper's celestial formulas are compared against.","marker":"[47]"},{"why":"Gives the earlier definition of Carrollian amplitudes in general dimensions that the present work elaborates on.","marker":"[53]"},{"why":"Establishes the Carrollian conformal Ward identities used to check that the extra three-point contribution is admissible.","marker":"[17]"},{"why":"Motivates the top-down holographic application by showing how the D=4 correspondence can extract flat-space data from AdS4/CFT3.","marker":"[40]"}],"fun_headline_variants":["Flat-space amplitudes from AdS/CFT in the Carrollian limit","Carrollian and celestial correlators: explicit amplitudes in D dimensions","Two limits, one amplitude: Carrollian meets celestial holography","Bulk flat limit equals boundary c→0: explicit correlators","Massless scalars: Carrollian amplitudes from AdS/CFT"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The load-bearing premise is that, in the electric $c \\to 0$ limit, the three-point CFT correlator collapses to the singular-locus form $L = g(\\omega_i)|x_{12}|^{D-4}\\delta^{D-2}(x_{12})\\delta^{D-2}(x_{13})$ — a form the authors take from the Carrollian amplitude they are trying to derive, so the three-point correspondence partly builds in the answer it extracts.","fun_headline_variants_meta":{"raw":{"variants":["Flat-space amplitudes from AdS/CFT in the Carrollian limit","Carrollian and celestial correlators: explicit amplitudes in D dimensions","Two limits, one amplitude: Carrollian meets celestial holography","Bulk flat limit equals boundary c→0: explicit correlators","Massless scalars: Carrollian amplitudes from AdS/CFT"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000748,"raw_usage":{"total_tokens":3161,"prompt_tokens":729,"completion_tokens":2432,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":473,"completion_tokens_details":{"reasoning_tokens":2339}},"tokens_in":473,"tokens_out":2432,"duration_ms":20075,"temperature":1.0,"reasoning_tokens":2339,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T22:41:11.174361+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the electric $c \\to 0$ limit directly from the exact Schwinger-parameterized three-point CFT integral without imposing the ansatz (5.9); if the resulting distribution is not $g(\\omega_i)|x_{12}|^{D-4}\\delta^{D-2}(x_{12})\\delta^{D-2}(x_{13})$ on the fully-collinear locus, then $C_3$ is not the full Carrollian limit of the three-point function and $\\tilde{C}_3$ is not the complete extra contribution. Equivalently, retain the $\\sigma_2 |x_{4,n}|^4$ term in the four-point integral and check whether the support and normalization reproduce the Heaviside factor $S$ of eq. (3.22).","supporting_citations":[],"review_version":1}