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REVIEW 3 major objections 5 minor 15 cited by

On Carrollian and Celestial Correlators in General Dimensions

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2508.06602 v1 pith:PHGUOS7W submitted 2025-08-08 hep-th gr-qc

Harshal Kulkarni , Romain Ruzziconi , Akshay Yelleshpur Srikant This is my paper
classification hep-thgr-qc
keywords CarrollianholographyflatspacecelestialAdS/CFTcorrespondenceamplitudesmasslessscalarscatteringconformalprimariesgeneraldimensions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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

What would settle it

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).

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Extended reading notes

Core claim

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

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

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].

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 (3)
  1. [§5.2, Eqs. (5.13)–(5.14); abstract] 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.
  2. [§5.2 and App. A, Eqs. (5.9), (5.11)–(5.12), (A.1)] 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.
  3. [§5.3, Eqs. (5.29)–(5.36) and (3.22)] 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.
minor comments (5)
  1. [§3.3, §3.4, §5.3, App. A] Typos: 'Thee-point' in §3.3, 'F our-point' in §3.4, 'ofcourse', 'most easilt', 'Pocchammer' in App. A. Please proofread.
  2. [§5.3, Eq. (5.23)] 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.
  3. [§3.4, Eqs. (3.15)–(3.20)] 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.
  4. [§5.1, Eq. (5.2)] 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.
  5. [§6.3] 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.

Circularity Check

2 steps flagged · score 5.0 of 10

The 3- and 4-point boundary Carrollian limits are partly built into distributional ansätze (5.9) and (5.23), and the 3-point limit gives C3+C~3 rather than C3; otherwise the dictionary is a consistent set of definitions and normalizations.

  1. self definitional [Section 5.2, Eq. (5.9) (and Appendix A, Eq. (A.1))]
    "L = lim_{c→0} (1/c^D) e^{i Σ_{j<k} ε_j ε_k ω_j ω_k x^2_{jk}/c^2} = g(ω_i) |x_{12}|^{D−4} δ^{D−2}(x_{12}) δ^{D−2}(x_{13}) . The second equality is an ansatz motivated by the Carrollian amplitude (3.10)."

    The ansatz pre-inserts the exact kinematic support of C3 from (3.10): |x12|^{D−4} δ^{D−2}(x12) δ^{D−2}(x13). The subsequent computation only fixes g(ω_i); then the δ-function piece of the Sokhotsky split (5.13) is identified with C3. Thus the recovery of C3 is not independent of the assumed distributional form. Moreover (5.14) shows the actual limit is C3 + C~3, so the clean equality advertised in the abstract is obtained only by discarding the extra term.

  2. self definitional [Section 5.3, Eq. (5.23)]
    "this leads to the ansatz: lim_{c→0} c^α Φ̂^ls = ∫ Π_{j=1}^4 dc_j δ^{(D)}(Σ_{i=1}^4 c_i q_i^μ) R_D(c_i, q_i) ... Note that with c_i = ε_i ω_i (with ε_i = ±1 and ω_i ∈ R_+, this is precisely the structure that a D-dimensional 4-point Carrollian amplitude has!"

    The assumed δ^{(D)}(Σ c_i q_i) is the same momentum-conservation delta that defines the 4-point Carrollian amplitude in (3.20). The calculation then determines only the coefficient R, so the exact equality (5.36) is partially built into the ansatz. The subleading σ2|x_{4,n}|^4 term in (5.32) is dropped without proof, so the derivation does not independently establish the support either.

full rationale

Most of the paper is a consistent dictionary rather than a discovery: Section 3 defines Carrollian amplitudes as integral transforms of flat-space amplitudes (3.1) and as flat-space Witten diagrams (3.11), and Section 4's flat-space limit of AdS Witten diagrams (4.28), (4.34) is an identity with those definitions. That is not itself circular. The circularity is concentrated in the boundary Carrollian limit of Section 5. For the 3-point function, eq. (5.9) assumes the c→0 limit collapses to g(ω_i)|x12|^{D−4}δ^{D−2}(x12)δ^{D−2}(x13), explicitly 'an ansatz motivated by the Carrollian amplitude (3.10)'; C3 has exactly that support and prefactor. The remaining computation fixes g, and the δ-piece of the Sokhotsky split is identified with C3, yielding (5.14): C3 + C~3. Thus the advertised 'recovery' is partly built in, and the clean equality is not even what the limit gives. For 4 points, eq. (5.23) assumes a δ^{(D)}(Σ c_i q_i) structure that the text calls 'precisely the structure that a D-dimensional 4-point Carrollian amplitude has', so the exact match (5.36) is again partly by construction; the σ2|x4,n|^4 term is dropped without proof. The paper is candid about the limitations (C~3 'unclear how to interpret', the deferred branch point in footnote 9), and there is genuine computational content (g, R, C~3, celestial counterparts). Overall: partial circularity, score 5.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central derivation consumes several conventions and an ansatz. The normalization constants kappa2, beta3, beta4 and the exponent alpha are fixed for internal consistency, not fitted to data. No new particles, forces, or dimensions are introduced; the Carrollian CFT and operators Phi_epsilon, O_Delta are pre-existing framework objects.

free parameters (4)
  • kappa2 = i pi/2
    Chosen in (5.4) so the 2-point electric Carrollian limit of the CFT correlator equals the 2-point Carrollian amplitude (3.6).
  • beta3 = -(2 pi)^{D/2} / pi^3 epsilon1 epsilon2 epsilon3
    Fixed below (3.11) so the Feynman-diagram definition of the 3-point Carrollian amplitude equals the momentum-space integral definition (3.8).
  • beta4 = 16 (2 pi)^{D-4} epsilon1 epsilon2 epsilon3 epsilon4
    Fixed below (3.26) so the Feynman-diagram definition of the 4-point Carrollian amplitude equals (3.13).
  • alpha (electric-limit exponent) = Sigma_Delta - D
    Chosen in (5.33) so the c->0 limit of the 4-point CFT correlator is finite and non-zero, selecting the electric branch.
assumptions (6)
  • domain assumption AdS/CFT dictionary via Witten diagrams for boundary correlators
    Used throughout Section 4 to express AdS boundary correlators (4.25), (4.29) as bulk integrals over propagators.
  • domain assumption Flat limit in bulk infinity is equivalent to Carrollian limit c->0 at the boundary
    Section 4.1, eqs. (4.5)-(4.10): the AdS radius plays the role of 1/c in the boundary metric.
  • ad hoc to paper 3-point electric limit ansatz L = g(omega_i)|x12|^{D-4} delta^{D-2}(x12)delta^{D-2}(x13)
    Eq. (5.9) and Appendix A (A.1); motivated by the Carrollian amplitude (3.10), used to extract C3 and C~3.
  • domain assumption Leading singularity formula (5.17) for the Lorentzian 4-point D-function
    Imported without derivation in Section 5.3 to compute the 4-point Carrollian limit.
  • domain assumption Generic parameter regime for C~3: Delta1 > D/4, Sigma_Delta > D, Delta13 - (D-2)/2 not integer, Delta12 not integer
    Appendix A, stated to keep Mellin-Barnes poles simple; explicit closed form (A.15) valid only there.
  • domain assumption Standard Euclidean-to-Lorentzian analytic continuation of AdS boundary correlators
    Section 4.2 and 5.3, following [66]; needed to define the correlators whose limits are computed.

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Cite this review

Pith. "Pith review of On Carrollian and Celestial Correlators in General Dimensions." pith.science (2026). https://pith.science/paper/PHGUOS7W

@misc{pith2026250806602,
  author       = {Pith},
  title        = {Pith review of: On Carrollian and Celestial Correlators in General Dimensions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PHGUOS7W}},
  note         = {Machine review of arXiv:2508.06602}
}
abstract

Carrollian holography is a framework for flat space holography, suggesting that gravity in asymptotically flat spacetime in $D$ dimensions is dual to a conformal Carrollian field theory in $D - 1$ dimensions living at null infinity. In this work, we elaborate on the definition of Carrollian amplitudes for massless scalar fields in general dimensions and provide explicit expressions for the two-, three-, and four-point functions. We show that these amplitudes naturally arise from Lorentzian holographic correlators in AdS/CFT through a correspondence between the flat space limit in the bulk and the Carrollian limit at the boundary. Finally, we use the relation between Carrollian and celestial holography to derive explicit expressions for celestial amplitudes in $D$ dimensions, which are reinterpreted as correlators of the celestial CFT in $D - 2$ dimensions.

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Forward citations

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