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Celestial dual of conformal gravity MHV amplitudes: an OPE analysis

T0 review · 2 major / 2 minor · reviewed 2026-05-08 · grok-4.3

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Pith's one-line read A free-field 2d CFT realizes the celestial dual to conformal gravity MHV amplitudes through matching OPEs.

desk verdict This paper builds an explicit free-field 2d CFT with three scalars and ghost pairs that realizes the chiral bms4 algebra and whose vertex operators give OPEs matching the authors' earlier bulk MHV extraction. read the letter →

arxiv 2605.05363 v1 submitted 2026-05-06 hep-th

Nirmal Ghorai , Partha Paul , Nemani V. Suryanarayana This is my paper · ORCID
classification hep-th
keywords celestialCFTconformalgravityMHVamplitudesOPEbms4algebrafreefieldrealizationvertexoperatorsdual
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 aims to provide an explicit two-dimensional chiral conformal field theory description for the celestial dual of the MHV sector in conformal gravity. It builds a free-field model with three scalars and ghost pairs that realizes the chiral bms4 algebra. Vertex operators are proposed for the primary operators corresponding to positive-helicity gravitons and scalars. Their operator product expansions exactly reproduce the ones derived from the bulk theory's Mellin-transformed MHV amplitudes. This matters because it gives a concrete CFT picture for the symmetries and amplitudes in this gravitational theory on the celestial sphere.

What carries the argument

The 2d free-field realization of the chiral bms4 algebra using three scalars and three ghost pairs, with vertex operators for the graviton and scalar primaries that allow explicit OPE computation matching the bulk results.

What would settle it

Explicit computation of the OPEs in the proposed 2d CFT yielding coefficients or structures that differ from those extracted from the bulk MHV amplitudes would disprove the duality proposal.

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Extended reading notes

Core claim

We construct a 2d chiral CFT free-field realisation of the relevant chiral bms4 algebra in terms of three free scalars and three ghost pairs, and propose vertex operators for the positive-helicity graviton primary G++_Δ(z, z-bar) as well as the scalar primary Φ_Δ(z, z-bar). We compute their OPEs. These OPEs reproduce exactly those obtained from the bulk conformal gravity MHV amplitudes, providing a concrete celestial dual description of its MHV sector.

Load-bearing premise

That the proposed free-field realization using three scalars and ghost pairs, together with the chosen vertex operators, correctly identifies the primaries and captures the full celestial CFT dual to the bulk theory.

Editorial extensions

If this is right

  • The MHV sector of conformal gravity admits a concrete 2d CFT dual that can be used to compute amplitudes via standard CFT methods.
  • The chiral bms4 symmetry, including its non-trivial central extension, is realized explicitly in the free-field theory.
  • Correlation functions of the celestial operators can be evaluated directly from the vertex operators and free fields.
  • The construction confirms the soft theorem analysis of the bulk symmetries for this extended gravity theory.

Reading between the lines

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

  • This free-field model could be extended to describe non-MHV amplitudes or other sectors in conformal gravity.
  • Similar realizations might connect to celestial duals of Einstein gravity or other modified gravity theories.
  • The central extension could be used to derive constraints on higher-point functions or anomalies in the celestial CFT.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript constructs a free-field realization of the chiral bms_4 algebra in a two-dimensional CFT using three free scalar fields φ_i and three (β_i, γ_i) ghost pairs. It proposes explicit vertex operators for the positive-helicity graviton primary G^{++}_Δ(z,¯z) and the scalar primary Φ_Δ(z,¯z), computes their OPEs, and demonstrates that these OPEs exactly reproduce the coefficients extracted from the Mellin-transformed MHV amplitudes of conformal gravity in the authors' prior work.

Significance. If the free-field realization is shown to be independent and the vertex operators are verified to be the correct primaries, the work supplies a concrete 2d CFT model for the celestial dual of the MHV sector of conformal gravity, including the chiral bms_4 symmetry with its non-trivial central extension. The explicit construction and exact OPE matching constitute a clear strength for celestial holography.

major comments (2)
  1. [§2] §2: The free-field realization must be shown to reproduce the full chiral bms_4 algebra, including the central extension of the sl(2,R) current algebra. Explicit computation of the OPEs or commutation relations among the realized generators (supertranslations, superrotations, and currents) is required to confirm the central charge matches the bulk value; without this, the claim that the construction realizes the symmetry algebra remains unverified.
  2. [§3] §3: The vertex operators for G^{++}_Δ and Φ_Δ are proposed in a form that yields the desired OPEs, but it is not demonstrated that these operators are primaries transforming correctly under the full set of realized bms_4 generators (including the central extension). The operators appear selected to match the known bulk OPE data from arXiv:2511.03669 rather than being fixed by requiring the correct transformation laws; an explicit check of their conformal dimensions, charges, and OPEs with the generators is needed to establish them as the correct celestial duals.
minor comments (2)
  1. The abstract refers to the 'bosonic subsector of the Berkovits-Witten theory' without a brief reminder of its relation to conformal gravity; adding one sentence of context would improve accessibility.
  2. [§4] Notation for the ghost pairs (β_i, γ_i) and the precise form of the vertex operators should be cross-checked for consistency between the algebra realization in §2 and the OPE computations in §4.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below, providing clarifications on the existing construction and committing to explicit verifications in the revised version.

read point-by-point responses

  1. Referee: [§2] §2: The free-field realization must be shown to reproduce the full chiral bms_4 algebra, including the central extension of the sl(2,R) current algebra. Explicit computation of the OPEs or commutation relations among the realized generators (supertranslations, superrotations, and currents) is required to confirm the central charge matches the bulk value; without this, the claim that the construction realizes the symmetry algebra remains unverified.

    Authors: In §2 we define the free scalar and ghost fields and construct the generators of the chiral bms_4 algebra (supertranslations, superrotations, and the sl(2,R) currents) explicitly in terms of these fields. The algebra relations, including the non-trivial central extension of the sl(2,R) currents, follow directly from the canonical OPEs of the free fields and are arranged to reproduce the central charge extracted from the bulk conformal gravity analysis in our prior work. To make the verification fully explicit, we will expand §2 with a complete tabulation of the relevant OPEs among all generators. revision: yes

  2. Referee: [§3] §3: The vertex operators for G^{++}_Δ and Φ_Δ are proposed in a form that yields the desired OPEs, but it is not demonstrated that these operators are primaries transforming correctly under the full set of realized bms_4 generators (including the central extension). The operators appear selected to match the known bulk OPE data from arXiv:2511.03669 rather than being fixed by requiring the correct transformation laws; an explicit check of their conformal dimensions, charges, and OPEs with the generators is needed to establish them as the correct celestial duals.

    Authors: The vertex operators are fixed by the celestial dictionary to carry the conformal dimensions and charges appropriate to the positive-helicity graviton and scalar primaries. Their OPEs with the full set of bms_4 generators (including the action of the central extension) are computed in the manuscript and confirm the expected primary transformation laws. These checks are consistent with the dimensions and charges obtained from the bulk MHV amplitudes. We will add the explicit OPE computations with the generators to the revised manuscript to demonstrate the primary property directly. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

Independent 2d free-field realization computes OPEs that match prior bulk extraction

full rationale

The paper constructs a chiral bms4 algebra realization using three free scalars and ghost pairs, proposes vertex operators for G^{++}_Δ and Φ_Δ based on the algebra, and computes their OPEs. These are shown to reproduce the OPEs extracted from bulk conformal gravity MHV amplitudes in the authors' prior work. The 2d construction relies on standard CFT free-field methods and the algebra generators rather than being defined in terms of or fitted to the target OPE coefficients. The self-citation supplies an external benchmark for the match but does not reduce the derivation to its inputs by construction. No self-definitional steps, fitted predictions, or load-bearing uniqueness theorems from self-citation are present.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

No free parameters are introduced. The construction relies on standard 2d CFT axioms and the bms4 algebra taken from prior work; no new entities are postulated.

assumptions (2)
  • standard math Standard axioms and OPE rules of 2d conformal field theory for free scalars and ghost systems
    Invoked to define the free-field realization and compute the OPEs of the vertex operators.
  • domain assumption The chiral bms4 algebra with non-trivial central extension as derived from soft theorem analysis in prior work
    This is the target symmetry that the 2d CFT must realize.

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Cite this review

Pith. "Pith review of Celestial dual of conformal gravity MHV amplitudes: an OPE analysis." pith.science (2026). https://pith.science/paper/2605.05363

@misc{pith2026260505363,
  author       = {Pith},
  title        = {Pith review of: Celestial dual of conformal gravity MHV amplitudes: an OPE analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2605.05363}},
  note         = {Machine review of arXiv:2605.05363}
}
abstract

In an earlier paper [arXiv:2511.03669] we extracted the OPE of celestial CFT operator duals of positive helicity graviton and scalar particles from the Mellin transformed relevant MHV amplitudes of conformal gravity, realised as the bosonic subsector of the Berkovits-Witten theory. A soft theorem analysis of bulk MHV amplitudes established that this conformal gravity exhibits a chiral $\mathfrak{bms}_4$ symmetry on the celestial sphere with the associated $\mathfrak{sl}(2,\mathbb{R})$ current algebra, which acquires a non-trivial central extension, unlike the Einstein gravity. Here we construct a $2d$ chiral CFT free-field realisation of the relevant chiral $\mathfrak{bms}_4$ algebra in terms of three free scalars ($\phi_i$) and three $(\beta_i,\gamma_i)$ ghost pairs, and propose vertex operators for the positive-helicity graviton primary $G^{++}_{\Delta}(z,\bar{z})$ as well as the scalar primary $\Phi_{\Delta}(z,\bar{z})$, and compute their OPEs. These OPEs reproduce exactly those obtained from the bulk conformal gravity MHV amplitudes, providing a concrete celestial dual description of its MHV sector.

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