{"id":"f1b22783-a395-49ff-b046-f1dde552f88f","arxiv_id":"2501.05805","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The authors construct a single-valued celestial four-graviton correlator from the shadow transform, decompose it into conformal blocks in all channels, and show it is the double copy of the corresponding gluon object.","lead":"The paper computes a modified four-graviton celestial correlator, replacing one operator by its shadow transform, and completes it to a single-valued function whose conformal block expansion and OPE structure match known celestial graviton results. The result gives an analytic avatar of the graviton amplitude that is easier to work with in celestial CFT and exhibits a double copy relation to the gluon counterpart.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The single-valued completion (3.5) is an ansatz selected to cancel monodromy; the J=-1 OPE operator and double copy (4.18) are properties of that choice, not of a derived bulk amplitude.","rationale":"The reader's weakest assumption identifies exactly the load-bearing point: the single-valued completion (3.5) is constructed, not derived. I agree with that assessment. The paper is internally consistent and technically rich: the shadow transform (2.9), the soft-limit block decomposition (2.27), the general decomposition (2.32), and the explicit inverted amplitude (4.9) are plausible and have useful cross-checks. However, the central physical claim--that (4.9) is the single-valued celestial graviton amplitude and that the new J=-1 operator signals a genuine bulk effect--rests on the choice of completion. Since the authors explicitly defer the bulk connection, the current evidence supports a CONDITIONAL verdict but not a full ACCEPT. My concern does not move the reader's verdict; it reinforces it. The concrete test above would separate a dictated result from an ansatz-dependent one. Until such a test is performed, the safest formulation is to present the single-valued correlator as a proposed alternative object with attractive formal properties, rather than as the unique completion forced by celestial holography.","tokens_in":24219,"tokens_out":10495,"duration_ms":106295,"concrete_test":"Independently determine the single-valued graviton correlator by solving the celestial graviton differential equations of [93] (the graviton analogue of the Banerjee-Ghosh construction used in [24,56]) with the standard celestial graviton OPE (3.20)/(4.19) and the original tree-level MHV amplitude (2.1) as boundary data, without imposing (3.5). Then compare the resulting correlator with (3.5) order by order near x=1. If the solution differs from (3.5), or if the matching leaves a free coefficient in front of the J=-1 block in the OPE (3.21), the completion is not unique and the claims about the J=-1 operator and the double copy are not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (3.5) is introduced as S1 I1 + S2 I2, where the added term S2 I2 is chosen by hand to cancel the branch cut of S1 I1 near x=1; the coefficient S2 in (3.6) is fixed by matching the analytic continuations (3.2)-(3.4). No derivation shows this is the unique or physically correct single-valued completion: single-valuedness constrains only branch-cut discontinuities, and in principle single-valued terms with the same allowed singularities can be added without spoiling the crossing relations (3.7). The paper itself states that the new J=-1 operator 'might correspond to photons coupled to gravity' and that making this connection precise is left for future work (Sec. 4.2 and Sec. 5), so the bulk interpretation is openly unresolved. The downstream claims--integer-spin-only spectrum in the (14<->32)2 and (13<->24)2 channels, the new J=-1 operator in (3.21)/(4.20), and the double-copy relation (4.18)--are all evaluated for this specific completion. If another legitimate completion were chosen, or if the completion is only a formal device, these conclusions need not describe a bulk graviton amplitude.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes the shadow transform of the four-graviton MHV celestial amplitude with one conformally soft shadow operator, expands the result in two-dimensional conformal blocks in the compatible channel, then constructs a single-valued completion following the gluon construction of [56]. The single-valued correlator is block-decomposed in all three channels, shown to satisfy crossing symmetry, and rewritten in a Coulomb-gas-like integral representation. The integral representation is used to invert the shadow transform, yielding a 'single-valued celestial graviton amplitude' proportional to \\bar z/(z(1-z)), from which a double-copy relation with the single-valued gluon amplitude is observed. The paper also extracts leading OPEs and finds the standard celestial graviton OPEs plus one new J=-1 operator.","tokens_in":24372,"tokens_out":5685,"duration_ms":55023,"significance":"If the construction is accepted, the paper provides a rare example of an analytic, crossing-symmetric celestial graviton correlator with only integer-spin exchanges and a simple double-copy structure. The computations are long but internally cross-checked: single-valuedness is verified near x=1 and x=infinity, crossing relations (3.7) are imposed and checked, and the leading OPEs reproduce known results except for the new J=-1 operator. However, the central novelty rests on an ansatz for the single-valued completion whose bulk origin is left open, so the significance is conditional on whether that completion is physically justified rather than a formal device.","major_comments":[{"comment":"The single-valued completion is introduced by adding S2(x) I2(\\bar x) to S1(x) I1(\\bar x), with S2 fixed by Eq. (3.6) to cancel the branch-cut of S1 I1 near x=1. The paper does not show that this is the unique single-valued completion, nor that it corresponds to a known bulk amplitude. Single-valuedness only fixes branch-cut discontinuities; in principle one can add single-valued terms with the same allowed singularities without spoiling the crossing relations (3.7). The paper itself states in Sec. 4.2 that the new J=-1 operator 'might correspond to photons coupled to gravity' and leaves the bulk connection for future work. Since the integer-spin spectra in the (14<->32)2 and (13<->24)2 channels, the OPE (3.21)/(4.20), and the double-copy relation (4.18) are all properties of this specific completion, the central claims are conditional on an unproven assumption. Please either derive the completion from a physical principle (for example, from the Banerjee-Ghosh differential equations mentioned in Sec. 5) or explicitly frame the results as properties of one possible completion.","section":"Section 3.1, Eq. (3.5)"},{"comment":"The 'single-valued celestial graviton amplitude' is obtained by inverting the shadow of the completed correlator using the change of variables (4.4), which is chosen so that the integral takes the shadow form. It is not demonstrated that this amplitude is the Mellin transform of any known tree-level amplitude, and the double-copy relation (4.18) is an observation about the simple form \\bar z/(z(1-z)) rather than a derived equivalence between celestial amplitudes. Please clarify the status of (4.9) as a proposal, and check whether the amplitude satisfies the known celestial graviton Ward identities or soft theorems beyond the leading OPE comparison.","section":"Section 4, Eq. (4.9)"},{"comment":"The general-λ1 conformal block decomposition is stated after a 'tedious computation' without intermediate steps. The coefficients contain many gamma functions and alternating signs, and the final expression (2.32) involves a triple sum. To make the paper self-contained and verifiable, please provide a derivation in an appendix or supplementary material, or at least include a computer-algebra verification of the decomposition. This matters because the specialized limit λ1=i in Sec. 3 relies on the same hypergeometric identities, and the reader currently cannot check the main technical result without redoing the computation.","section":"Section 2.2, Eqs. (2.32)-(2.33)"}],"minor_comments":[{"comment":"In the last sum of Eq. (3.18), the block is labeled K42_31 whereas all other blocks in that equation use K24_31; please fix the label.","section":"Section 3.2, Eq. (3.18)"},{"comment":"'Coulumb gas formulation' should be 'Coulomb gas formulation'.","section":"Section 3.3"},{"comment":"The powers of x and \\bar x in the prefactor of Eq. (2.14) do not appear to match the exponent that follows from Eq. (2.11) after setting λ1=i; please double-check the algebra so that Eq. (2.14) is consistent with Eq. (2.15).","section":"Section 2.1, Eq. (2.14)"},{"comment":"The definition of \\bar I2(\\bar x) in Eq. (3.3) and its analytic continuation in Eq. (3.4) would benefit from an explicit statement of which prefactors are stripped and which are part of the conformal block normalization, since the second term of (3.4) has the same (1-\\bar x)^{-1+iλ4} factor as \\bar I1(\\bar x).","section":"Section 3.1, Eqs. (3.3)-(3.4)"},{"comment":"The OPEs (4.19) and (4.20) are identical to (3.20) and (3.21); it would help the reader if the paper stated explicitly that the single-valued shadow correlator and the inverted-shadow correlator yield the same leading OPEs.","section":"Section 4.2"},{"comment":"There are several typographical inconsistencies in the subscripts and superscripts of the conformal blocks, e.g. K21_34 vs K12_34 and K24_31 vs K42_31; a careful proofreading pass is recommended.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"This is a workmanlike extension of the gluon papers [55,56] to gravity. The main novelty is the construction of a single-valued graviton correlator and the associated J=-1 OPE operator and double-copy observation, but all three hinge on the choice of the single-valued completion. The authors are transparent about the open bulk interpretation, and the manuscript could become acceptable if they either supply a physical derivation of the completion or clearly reframe the claims as applying to one possible completion. The fit with JHEP is appropriate; the citation list is standard for the celestial holography literature."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does what it says: it takes the celestial four-graviton MHV amplitude, shadows one leg, and works out conformal block decompositions in several channels. The genuinely new output is the explicit shadow correlator (2.9), its block decomposition (2.27) and general-lambda version (2.32), the single-valued completion (3.5), the Coulomb-gas style integral representation (3.25), and the inverted single-valued amplitude (4.9). The double copy relation (4.18) is a concrete and appealing observation. The authors are transparent that the method comes from the gluon papers [55,56]; the graviton implementation is nontrivial and the cross-checks they do include are reassuring: single-valuedness near x=1 and infinity, crossing symmetry (3.7), and agreement of the leading OPEs with known celestial results in the (12->34) channel.\n\nThe soft spot is real and correctly identified by the stress-test note: the single-valued completion (3.5) is constructed by hand to cancel the branch cut, with the S2*I2 term chosen following the gluon template. Nothing in the paper shows uniqueness or bulk derivation. The new J=-1 operator in the opposite-helicity OPE is a property of that choice, and the paper itself says it might correspond to photons coupled to gravity and leaves the bulk connection for future work. That is honest, but it means the central physical claim rests on an assumption. Also, several long coefficient identities (e.g., 2.26, 3.9, 3.14, 4.11) are stated without intermediate steps; the reader could not verify them by hand. The paper would be much stronger if these were backed by a computer algebra check or an appendix.\n\nNone of this sinks the paper. The block decomposition of the original shadow correlator is an unambiguous calculation, and the single-valued completion is at least a well-defined prescription with attractive properties. The reader's conditional verdict is about right. I disagree with any implication that the paper is circular; the shadow correlator is genuinely new output, and the OPE comparison is a check, not an input.\n\nWho is this for? People working on celestial holography, especially on single-valued correlators and double copy. It deserves a serious referee. I would send it out, with a request that the referee verify the heavy identities and that the authors clarify the status of the J=-1 operator, either by deriving it from a bulk background or by softening the claim.","headline":"A solid, mostly computational extension of the gluon shadow-correlator program to gravitons, with the single-valued completion as the one genuinely load-bearing ansatz; worth serious refereeing if the long identities and the J=-1 state get checked.","tokens_in":25076,"tokens_out":940,"would_cite":true,"duration_ms":10858,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A single-valued celestial graviton correlator is built by shadow transform and completed to crossing symmetry, and its inverse shadow is the double copy of the gluon amplitude.","keywords":["celestial holography","shadow transform","single-valued correlators","conformal blocks","graviton amplitudes","celestial OPE","double copy","conformally soft limit"],"falsifier":"Compute the four-graviton celestial amplitude in a concrete bulk theory with broken translation invariance, such as gravity coupled to photons on a nontrivial background, and check whether its conformally soft shadow limit reproduces (3.5) and the $\\bar{z}/(z(1-z))$ amplitude, including the $J=-1$ OPE term; if no bulk process produces that operator, the completion is not physical.","tokens_in":23810,"feed_emoji":"🌌","tokens_out":9086,"duration_ms":76326,"temperature":0.7,"pith_summary":"The paper proposes an analytic, single-valued four-graviton correlator for celestial holography, replacing the distributional correlator that standard celestial amplitudes produce. Starting from the tree-level MHV four-graviton amplitude, the authors shadow-transform one of the graviton operators and, in the conformally soft limit, complete the resulting correlator to a single-valued, crossing-symmetric object. They decompose it into conformal blocks in all three channels and find that only integer-spin states are exchanged, with OPEs matching the known celestial graviton OPEs plus one new $J=-1$ operator. An integral representation lets them invert the shadow transform, yielding a simple single-valued celestial graviton amplitude proportional to $\\bar{z}/(z(1-z))$, which they identify as the double copy of the corresponding single-valued gluon amplitude.","feed_headline":"Shadow trick makes graviton correlator analytic and single-valued","feed_subtitle":"Completing the shadow correlator gives integer-spin blocks and a graviton amplitude that is the gluon double copy.","key_machinery":"The central object is the shadow transform, which maps a primary operator of dimension $\\Delta$ and helicity $J$ to one of dimension $2-\\Delta$ and helicity $-J$ by integrating against a kernel; applying it to one graviton in the tree-level MHV four-graviton celestial amplitude removes the distributional support $\\delta(z-\\bar{z})$ and leaves an analytic correlator. The single-valued completion (3.5) then adds a second term $S_2(x)\\bar{I}_2(\\bar{x})$ chosen so that the branch cut of the analytically continued holomorphic part near $x=1$ is cancelled by the matching antiholomorphic block, following the gluon construction of [56]. The Coulomb-gas-type integral representation (3.25), with holomorphic and antiholomorphic exponents differing by integers, is the mechanism that permits inverting the shadow transform; a change of variables recasts the integral as the shadow transform of the simple amplitude $\\bar{z}/(z(1-z))$. The double-copy identification uses the KLT/BCJ relation, writing that amplitude as $z\\bar{z}$ times the product of two color-ordered single-valued gluon amplitudes.","core_discovery":"The paper's central claim is that the single-valued completion of the shadow four-graviton correlator in the conformally soft shadow limit, equation (3.5), is the desired analytic celestial correlator: it is single-valued on the whole complex plane, crossing symmetric under the three channel maps, and its conformal block decomposition in every channel contains only exchanged states with integer spin, in contrast to the continuous-spin states that appear if one simply analytically continues the uncompleted shadow correlator. From this correlator the authors extract leading OPEs that match the known celestial graviton OPEs, with one new spin $J=-1$ operator whose presence they interpret as a hint of a bulk background (possibly photons coupled to gravity). The Coulomb-gas-type integral representation of the single-valued correlator allows them to invert the shadow transform, obtaining a single-valued celestial graviton amplitude proportional to $\\bar{z}/(z(1-z))$, which up to constants equals the double copy of the single-valued gluon amplitude of [56].","pith_inferences":["If the $J=-1$ operator is real, the single-valued correlator likely describes gravity on a nontrivial background; a concrete test would be computing the tree-level celestial four-graviton amplitude in Einstein-Maxwell theory and checking whether the same operator appears in the OPE.","The double-copy structure at four points suggests that higher-point single-valued graviton correlators could be built as KLT products of single-valued gluon correlators, which would provide a bootstrap route to gravity correlators.","Generalizing the single-valued completion beyond the conformally soft shadow limit (general $\\lambda_1$) would test whether the integer-spin spectrum and the $J=-1$ operator persist or are special to the soft point.","The analogy with minimal-model Coulomb-gas integrals raises the possibility that the single-valued graviton correlator satisfies a null-vector differential equation, which could link the construction to Liouville-type descriptions of celestial gravity."],"forward_implications":["The single-valued correlator (3.5) is crossing symmetric and blocks-expands with integer spins only in all three channels, so continuous-spin states are an artifact of naively continuing the uncompleted shadow correlator.","The leading OPEs reproduce the standard celestial graviton OPEs, so the single-valued completion is consistent with the known celestial CFT operator algebra; the only new ingredient is the $J=-1$ operator in the opposite-helicity channel.","The inverse shadow yields a single-valued celestial graviton amplitude proportional to $\\bar{z}/(z(1-z))$, a double copy of the gluon result, providing a graviton analogue of the single-valued gluon correlator.","The integral representation opens the way to applying Coulomb-gas/Dotsenko-Fateev techniques to graviton correlators and to constructing more general graviton correlators from gluon ones via the double copy."],"supporting_citations":[{"why":"Supplies the celestial MHV four-graviton amplitude with the conformally soft behavior that the shadow transform acts on.","marker":"[10]"},{"why":"Provides the standard celestial graviton OPEs that the single-valued correlator must reproduce.","marker":"[12]"},{"why":"Introduces the shadow-correlator method for gluon amplitudes that this paper adapts to gravitons.","marker":"[55]"},{"why":"Supplies the single-valued completion template and the single-valued gluon amplitude whose double copy appears here.","marker":"[56]"},{"why":"Provides the explicit four-graviton celestial amplitude used as the starting input for the shadow transform.","marker":"[83]"},{"why":"Provide the Coulomb-gas integral representation used to write the single-valued correlator and invert the shadow transform.","marker":"[76, 77]"},{"why":"Establish the KLT/BCJ double-copy relations that identify $\\bar{z}/(z(1-z))$ as a double copy of gluon amplitudes.","marker":"[87, 88]"}],"fun_headline_variants":["Single-valued graviton correlator from shadow completion","Shadow transform yields analytic celestial graviton amplitude","Graviton correlator becomes gluon double copy when single-valued","Conformal blocks from single-valued shadow correlator","Shadow trick completes graviton correlator to analytic form"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the particular single-valued completion chosen to cancel the branch cut—selected by following the gluon template—is the physically correct celestial correlator, not just one ad hoc completion.","fun_headline_variants_meta":{"raw":{"variants":["Single-valued graviton correlator from shadow completion","Shadow transform yields analytic celestial graviton amplitude","Graviton correlator becomes gluon double copy when single-valued","Conformal blocks from single-valued shadow correlator","Shadow trick completes graviton correlator to analytic form"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000153,"raw_usage":{"total_tokens":1191,"prompt_tokens":913,"completion_tokens":278,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":529,"completion_tokens_details":{"reasoning_tokens":203}},"tokens_in":529,"tokens_out":278,"duration_ms":2980,"temperature":1.0,"reasoning_tokens":203,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:05:26.268704+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the four-graviton celestial amplitude in a concrete bulk theory with broken translation invariance, such as gravity coupled to photons on a nontrivial background, and check whether its conformally soft shadow limit reproduces (3.5) and the $\\bar{z}/(z(1-z))$ amplitude, including the $J=-1$ OPE term; if no bulk process produces that operator, the completion is not physical.","supporting_citations":[],"review_version":1}