arxiv: 2605.05350 · v1 · submitted 2026-05-06 · ✦ hep-th

Recognition: unknown

Challenges to Understanding Celestial Holography from the Bottom Up

Adam Tropper

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:35 UTC · model grok-4.3

classification ✦ hep-th

keywords celestial holographySinh-Gordon modelperturbative expansionS-matrixcelestial amplitudesCCFT dualsbottom-up approach

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The pith

The term-by-term celestial transform of perturbative amplitudes disagrees with the transform of the full amplitude in the Sinh-Gordon model.

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

The paper tests whether celestial amplitudes can be obtained by applying the celestial transform to perturbative expansions of momentum-space amplitudes order by order. In the two-dimensional Sinh-Gordon model, which has a known exact S-matrix, the authors compare transforming the full non-perturbative amplitude first and then expanding, versus expanding first and then transforming term by term. These two procedures do not match, even at the leading nontrivial order in the coupling. This result implies that the naive bottom-up prescription for constructing celestial amplitudes may not be valid in general quantum field theories that have weak-coupling expansions, making tests of celestial dualities more subtle.

Core claim

In the exactly solvable Sinh-Gordon model, the celestial transform of the full non-perturbative S-matrix differs from the term-by-term celestial transform of its perturbative expansion already at leading order in the coupling. This mismatch shows that the bottom-up approach of defining celestial amplitudes perturbatively term by term does not reproduce the correct celestial amplitudes.

What carries the argument

The Sinh-Gordon model's exact S-matrix and the comparison of the two orders of operations: celestial transform then perturbative expansion versus perturbative expansion then celestial transform.

If this is right

Mismatches between term-by-term perturbative celestial amplitudes and proposed CCFT duals do not necessarily falsify the duality.
Bottom-up constructions of celestial holography must incorporate non-perturbative information rather than relying solely on perturbative transforms.
Direct tests of celestial dualities in weakly coupled theories require more care than term-by-term comparisons allow.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same mismatch could be checked in other models with fully known S-matrices to test how general the failure is.
This subtlety may push celestial holography toward non-perturbative definitions or different ways to connect bulk perturbation theory to boundary CFT data.

Load-bearing premise

That the disagreement found in the Sinh-Gordon model means the term-by-term prescription fails in generic quantum field theories with weak-coupling expansions.

What would settle it

Repeating the explicit order-by-order comparison in another integrable two-dimensional model with a known exact S-matrix, such as the sine-Gordon theory, to check whether the mismatch persists.

read the original abstract

In the bottom-up approach to celestial holography, it is tempting to define celestial amplitudes by transforming momentum-space amplitudes order by order in perturbation theory. We test this prescription in the exactly solvable two-dimensional Sinh-Gordon model. Because the full non-perturbative S-matrix is known, we can compare two operations directly: first transform and then expand, or first expand and then transform. They do not agree, already at leading nontrivial order in the coupling. More broadly, this suggests that naive term-by-term celestial transforms should not be assumed valid in generic quantum field theories with asymptotic weak-coupling expansions. This has an immediate consequence for proposed CCFT duals: if one tries to test them by taking celestial transforms of perturbative bulk amplitudes term-by-term, a mismatch need not falsify the proposal. This makes bottom-up tests of celestial dualities far more subtle than one might have expected.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Sinh-Gordon gives a clean mismatch at leading order, but the step to generic QFTs is the part that needs more work.

read the letter

The paper's main result is straightforward: in the Sinh-Gordon model the celestial transform of the exact S-matrix, once expanded in the coupling, differs from the term-by-term celestial transform of the perturbative amplitudes, and the difference appears already at the first nontrivial order. They can do this comparison because the model is integrable and the full S-matrix is known in closed form. That is the concrete new piece. It supplies an explicit, parameter-free counterexample to the assumption that the two operations commute, which is useful for anyone trying to build bottom-up tests of celestial duals. The calculation itself looks direct and avoids fitting or circular definitions. Credit for that. The limitation is the reach of the conclusion. Sinh-Gordon is two-dimensional, integrable, and has an S-matrix with no multi-particle production and a specific rapidity dependence. Those features can make integrals over the celestial variables fail to interchange with a power series for reasons that may not appear in a generic four-dimensional theory with perturbative unitarity and dispersion relations. The abstract moves from the model result to a warning for all weak-coupling QFTs without spelling out why the special properties do not drive the mismatch. That extrapolation is the soft spot, and it is not minor if the goal is to change how people test proposed CCFT duals. Readers already working on celestial holography will want to see the details and decide how much caution to apply. The paper is coherent on its own terms and engages the literature honestly, so it is worth sending to referees even though the broader claim will probably need additional examples or a clearer statement of the assumptions that survive outside the integrable case.

Referee Report

1 major / 2 minor

Summary. The paper tests the bottom-up prescription for celestial amplitudes by comparing two operations in the exactly solvable 2D Sinh-Gordon model: (i) taking the celestial transform of the known exact S-matrix and then expanding in the coupling, versus (ii) expanding the momentum-space amplitudes first and transforming term by term. The two procedures disagree already at leading nontrivial order. The authors conclude that naive term-by-term celestial transforms cannot be assumed valid in generic QFTs possessing weak-coupling expansions, with direct implications for how one can falsify proposed CCFT duals using perturbative bulk data.

Significance. The result supplies a concrete, parameter-free counter-example in a model where both the exact S-matrix and its perturbative expansion are under control. This is a genuine strength: the comparison is direct, uses no fitted parameters, and exploits the bootstrap-determined S-matrix of an integrable theory. If the reported mismatch is robust, it correctly flags a potential non-commutativity between series expansion and the celestial integral transform, thereby making bottom-up tests of celestial holography more subtle than previously assumed.

major comments (1)

[concluding discussion] The broader claim that the observed mismatch implies the term-by-term prescription fails in generic QFTs (abstract and concluding discussion): the Sinh-Gordon S-matrix is determined by integrability, exhibits exponential rapidity dependence, and lacks multi-particle production. The paper does not supply an argument or additional example showing that the non-commutativity survives in non-integrable theories where perturbative unitarity and dispersion relations are enforced differently. This weakens the load-bearing step from the specific model to the generic warning.

minor comments (2)

The definition of the celestial transform (integral kernel over rapidity or light-cone momentum) should be written explicitly once, together with the precise normalization chosen for the Sinh-Gordon S-matrix, so that the leading-order discrepancy can be reproduced by the reader.
A short table or equation block comparing the first two terms of each procedure side-by-side would make the mismatch immediately verifiable without requiring the full derivation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the concrete counter-example, and constructive comment on the scope of our conclusions. We address the major point below and will revise the manuscript accordingly to clarify the implications while preserving the core observation.

read point-by-point responses

Referee: [concluding discussion] The broader claim that the observed mismatch implies the term-by-term prescription fails in generic QFTs (abstract and concluding discussion): the Sinh-Gordon S-matrix is determined by integrability, exhibits exponential rapidity dependence, and lacks multi-particle production. The paper does not supply an argument or additional example showing that the non-commutativity survives in non-integrable theories where perturbative unitarity and dispersion relations are enforced differently. This weakens the load-bearing step from the specific model to the generic warning.

Authors: We agree that Sinh-Gordon is integrable and lacks multi-particle production, features that distinguish it from generic QFTs. The mismatch we report nevertheless demonstrates that the celestial transform does not commute with the weak-coupling expansion in a theory where both the exact S-matrix and its perturbative series are known exactly. This non-commutativity originates from the non-perturbative analytic structure of the S-matrix (exponential rapidity dependence), which encodes information absent from any finite-order perturbative amplitude. In non-integrable theories the full S-matrix likewise contains non-perturbative content beyond the perturbative expansion, so the same caution against assuming term-by-term validity applies. We do not claim a general theorem, but the example shows that commutativity cannot be taken for granted. We will revise the abstract and concluding discussion to present the result explicitly as a cautionary counter-example that renders bottom-up tests more subtle, while noting that explicit checks in non-integrable models remain desirable for future work. revision: yes

Circularity Check

0 steps flagged

No circularity: explicit mismatch computation in Sinh-Gordon is self-contained

full rationale

The paper's derivation consists of an explicit, direct comparison in the Sinh-Gordon model between (i) taking the celestial transform of the known exact non-perturbative S-matrix and then expanding in the coupling, versus (ii) expanding the perturbative amplitudes first and then transforming term-by-term. This uses the model's known exact S-matrix (from integrability) and performs the operations without introducing fitted parameters, self-referential definitions, or load-bearing self-citations. The core result—that the two procedures disagree already at leading nontrivial order—is therefore independent of the claimed conclusion and does not reduce to its inputs by construction. The suggestion that the mismatch may apply more broadly to generic QFTs is an extrapolation, not a formal derivation that could be circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on exact solvability of Sinh-Gordon model and validity of its celestial transform.

axioms (1)

domain assumption Sinh-Gordon model has a known exact non-perturbative S-matrix comparable to its perturbative expansion.
Used to compare the two procedures and observe disagreement.

pith-pipeline@v0.9.0 · 8730 in / 927 out tokens · 73534 ms · 2026-05-08T16:35:59.213964+00:00 · methodology

discussion (0)

Reference graph

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