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arxiv: 2503.15607 · v3 · submitted 2025-03-19 · ✦ hep-th

Operator Product Expansion in Carrollian CFT

Kevin Nguyen , Jakob Salzer This is my paper

Pith reviewed 2026-05-22 23:08 UTC · model grok-4.3

classification ✦ hep-th
keywords carrollian conformal field theoryoperator product expansionconformal correlatorsscattering amplitudescarrollian symmetriescomposite operatorsrepresentation theoryshort-distance expansion
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0 comments X

The pith

Carrollian conformal field theories admit operator product expansions compatible with their symmetries that control short-distance expansions of correlators and amplitudes.

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

The paper constructs operator product expansions that respect Carrollian conformal symmetries and shows they dictate the short-distance behavior of Carrollian correlators and amplitudes. It extends the representation theory to handle composite operators such as the stress tensor and operators creating multiparticle states. The work classifies two- and three-point correlators and amplitudes under complex kinematics and determines the general symmetry-allowed form of four-point functions. This approach unifies earlier results and supplies a predictive structure for Carrollian CFT as an alternative description of massless scattering.

Core claim

We construct operator product expansions (OPEs) compatible with carrollian symmetries. These OPEs unify and extend preliminary works on the subject, and demonstrate that the carrollian OPEs indeed control the short-distance expansion of carrollian correlators and amplitudes. In the process, we extend the representation theory of carrollian conformal fields such as to account for composite operators like the carrollian stress tensor or those creating multiparticle states. In addition we classify 2- and 3-point carrollian correlators and amplitudes with complex kinematics, and give the general form of the 4-point function allowed by symmetry.

What carries the argument

Carrollian operator product expansions (OPEs) compatible with the Carrollian symmetry algebra

If this is right

  • Short-distance expansions of Carrollian correlators and amplitudes are governed by the constructed OPEs.
  • Composite operators including the Carrollian stress tensor fit consistently into the representation theory.
  • Two- and three-point Carrollian correlators and amplitudes are fully classified for complex kinematics.
  • Four-point functions take a specific form dictated by Carrollian symmetry.
  • The OPE framework unifies and extends earlier preliminary results on Carrollian CFT.

Where Pith is reading between the lines

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

  • The OPE construction could enable systematic calculations of higher-point functions and amplitudes in Carrollian theories.
  • This approach may offer new constraints on massless scattering processes through the holographic Carrollian description.
  • The extended representation theory might apply to other composite structures or different kinematic regimes not covered in the paper.

Load-bearing premise

The constructed OPEs remain compatible with the full Carrollian symmetry algebra when extended to composite operators and higher-point functions without introducing extra constraints or inconsistencies.

What would settle it

Explicit computation of the short-distance limit of a four-point Carrollian correlator using the constructed OPE and comparison against the symmetry-allowed general form.

read the original abstract

Carrollian conformal field theory offers an alternative description of massless scattering amplitudes, that is holographic in nature. In an effort to build a framework that is both predictive and constraining, we construct operator product expansions (OPE) that are compatible with carrollian symmetries. In this way, we unify and extend preliminary works on the subject, and demonstrate that the carrollian OPEs indeed control the short-distance expansion of carrollian correlators and amplitudes. In the process, we extend the representation theory of carrollian conformal fields such as to account for composite operators like the carrollian stress tensor or those creating multiparticle states. In addition we classify 2- and 3-point carrollian correlators and amplitudes with complex kinematics, and give the general form of the 4-point function allowed by symmetry.

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.

Referee Report

0 major / 3 minor

Summary. The manuscript constructs operator product expansions (OPEs) compatible with Carrollian conformal symmetries, unifying and extending prior results on the subject. It demonstrates that these OPEs control the short-distance expansion of Carrollian correlators and amplitudes, extends the representation theory of Carrollian fields to composite operators (including the stress tensor and multiparticle states), classifies 2- and 3-point correlators and amplitudes with complex kinematics, and derives the general symmetry-allowed form of the 4-point function.

Significance. If the central constructions hold, the work supplies a symmetry-constrained, predictive framework for Carrollian CFT with direct relevance to holographic descriptions of massless scattering. The explicit OPEs, their verification against classified correlators, and the treatment of composite operators constitute concrete technical progress that can be used in further amplitude and correlator calculations.

minor comments (3)
  1. [§2] §2: the definition of the Carrollian conformal algebra generators is given without an explicit comparison table to the standard BMS or Poincaré limits; adding such a table would clarify the extension to composite operators.
  2. [§4.2] §4.2, Eq. (4.12): the OPE coefficient for the stress-tensor insertion is stated to be fixed by symmetry, but the normalization convention relative to the 2-point function is not restated; a one-line reminder would prevent ambiguity when extending to higher-point functions.
  3. [Figure 3] Figure 3: the contour choices for the complex-kinematics integrals are shown but the branch-cut conventions are only described in the caption; moving the conventions into the main text would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our work on Carrollian OPEs, representation theory extensions, and correlator classifications. We appreciate the recommendation for minor revision and will address any editorial or presentational points in the revised version.

Circularity Check

0 steps flagged

No significant circularity; direct symmetry construction independent of inputs

full rationale

The paper presents a direct construction of Carrollian OPEs from symmetry compatibility, extending representation theory for composites and classifying correlators/amplitudes, with an explicit demonstration that the OPEs reproduce short-distance expansions. No step reduces by the paper's own equations to a fitted parameter, self-definition, or load-bearing self-citation chain; preliminary works are unified/extended rather than serving as unverified premises for the central result. The derivation remains self-contained against external symmetry benchmarks, warranting only a minimal score for routine citation of prior literature.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The work rests on the domain assumption of Carrollian conformal symmetry but provides no further ledger details.

axioms (1)
  • domain assumption Carrollian conformal symmetries define the allowed operator algebra and correlator structures
    Invoked throughout the abstract as the basis for constructing OPEs and classifying functions.

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On Carrollian Loop Amplitudes for Gauge Theory and Gravity

    hep-th 2026-04 unverdicted novelty 6.0

    Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.

  2. The gravitational S-matrix from the path integral: asymptotic symmetries and soft theorems

    hep-th 2026-03 unverdicted novelty 6.0

    A path integral with asymptotic boundary conditions produces the gravitational S-matrix and derives soft graviton theorems from extended BMS symmetry Ward identities.

  3. On Carrollian Loop Amplitudes for Gauge Theory and Gravity

    hep-th 2026-04 unverdicted novelty 5.0

    Loop-level Carrollian amplitudes in gauge theory and gravity preserve tree-level structures, show logarithmic dependence in the eikonal regime, and factorize to yield an IR-safe definition.

  4. The Carrollian Kaleidoscope

    hep-th 2025-06 unverdicted novelty 1.0

    A review summarizing Carrollian symmetries, CCFT constructions, and applications in AFS holography, Carroll hydrodynamics, and condensed matter phenomena such as fractons and flat bands.

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