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arxiv: 2606.03955 · v1 · pith:4I73OD2Qnew · submitted 2026-06-02 · ✦ hep-th

Flat from AdS: in any dimension and for any spin

Xavier Bekaert , Andrea Campoleoni , Simon Pekar , S.I. Aadharsh Raj This is my paper

Pith reviewed 2026-06-28 08:46 UTC · model grok-4.3

classification ✦ hep-th
keywords higher spin fieldsanti-de Sitter spaceMinkowski limitboundary datanull infinityeven dimensionsmassless fieldscelestial sphere
0
0 comments X

The pith

The solution space for massless integer-spin fields in Minkowski space is the smooth limit of the corresponding anti-de Sitter solution space in any even dimension.

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

The paper shows that the free equations of motion for massless fields of arbitrary integer spin in flat Minkowski spacetime have their full solution space recovered by taking a smooth limit of anti-de Sitter solutions. This recovery works for any even spacetime dimension. The infinite tower of boundary data that specify Minkowski solutions near null infinity emerges from a power-series expansion of the anti-de Sitter source and vacuum expectation value in the cosmological constant. The source term supplies the analogue of the gravitational shear, while the vev supplies the mass and angular-momentum aspects together with all subleading data; these mappings are corroborated by the branching of both quantities into Lorentz-algebra representations that match the conformal algebra of the celestial sphere.

Core claim

The space of solutions to the free equations of motion for massless fields of arbitrary integer spin in Minkowski spacetime is recovered as a smooth limit of the anti-de Sitter solution space for any even spacetime dimension. The infinite set of boundary data near null infinity that characterise solutions in Minkowski spacetime is obtained from an expansion of the anti-de Sitter source and vev in powers of the cosmological constant. In particular, the source gives rise to the analogue of the gravitational shear tensor, while the vev yields the analogues of the mass and angular-momentum aspects, as well as the subleading infinite tower of boundary data. These identifications are further suppo

What carries the argument

The term-by-term expansion of the AdS source and vev in powers of the cosmological constant, whose coefficients supply the full set of Minkowski boundary data at null infinity.

If this is right

  • The infinite tower of Minkowski boundary data is identified with successive coefficients in the AdS expansion.
  • The AdS source term supplies the analogue of the gravitational shear tensor.
  • The AdS vev supplies the mass and angular-momentum aspects plus the entire subleading tower.
  • The Lorentz-algebra branching of source and vev matches the conformal algebra on the celestial sphere and thereby confirms the data identifications.

Where Pith is reading between the lines

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

  • The same expansion procedure may embed flat-space higher-spin dynamics inside a continuous family of AdS solutions parameterized by the cosmological constant.
  • The construction supplies a concrete dictionary that could relate flat-space holography to the AdS/CFT correspondence via a controlled limit.
  • Because the result holds for every even dimension and every integer spin, it suggests a uniform pattern rather than a case-by-case coincidence.

Load-bearing premise

The anti-de Sitter source and vev admit a well-defined term-by-term expansion in powers of the cosmological constant whose coefficients can be unambiguously identified with the infinite tower of Minkowski boundary data at null infinity.

What would settle it

An explicit computation in four-dimensional spacetime for spin-2 fields in which the limit fails to reproduce the known flat-space gravitational boundary data at null infinity.

read the original abstract

The space of solutions to the free equations of motion for massless fields of arbitrary integer spin in Minkowski spacetime is recovered as a smooth limit of the anti-de Sitter solution space for any even spacetime dimension. The infinite set of boundary data near null infinity that characterise solutions in Minkowski spacetime is obtained from an expansion of the anti-de Sitter source and vev in powers of the cosmological constant. In particular, the source gives rise to the analogue of the gravitational shear tensor, while the vev yields the analogues of the mass and angular-momentum aspects, as well as the subleading infinite tower of boundary data. These identifications are further supported by the branching of the source and vev into representations of the Lorentz algebra identified with the conformal algebra of the celestial sphere.

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

1 major / 0 minor

Summary. The manuscript claims that the space of solutions to the free equations of motion for massless fields of arbitrary integer spin in Minkowski spacetime is recovered as a smooth limit of the anti-de Sitter solution space for any even spacetime dimension. The infinite set of boundary data near null infinity in Minkowski space is obtained from a power-series expansion of the AdS source and vev in the cosmological constant, with the source identified with the analogue of the gravitational shear tensor and the vev with mass/angular-momentum aspects plus the subleading tower; these identifications are supported by branching of source/vev into Lorentz representations matching the conformal algebra of the celestial sphere.

Significance. If the central claim holds with the required term-by-term identification, the result would supply a uniform construction of flat-space asymptotic data from AdS for all integer spins in even dimensions, with direct relevance to higher-spin gravity and celestial holography. The representation-theoretic support via Lorentz branching is a positive feature that could make the construction falsifiable once explicit expansions are given.

major comments (1)
  1. [Abstract] Abstract (central claim): the assertion of a smooth, unambiguous term-by-term expansion of the AdS source and vev in powers of the cosmological constant whose coefficients match the full Minkowski null-infinity tower must be demonstrated explicitly for s>2. The Dirichlet-to-Neumann map for higher-spin fields involves higher-order boundary operators; the manuscript needs to show that no resonances produce logarithmic terms or source-vev mixing when the cosmological constant vanishes, especially in even dimensions where the celestial sphere is even-dimensional.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comment. We address the major point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (central claim): the assertion of a smooth, unambiguous term-by-term expansion of the AdS source and vev in powers of the cosmological constant whose coefficients match the full Minkowski null-infinity tower must be demonstrated explicitly for s>2. The Dirichlet-to-Neumann map for higher-spin fields involves higher-order boundary operators; the manuscript needs to show that no resonances produce logarithmic terms or source-vev mixing when the cosmological constant vanishes, especially in even dimensions where the celestial sphere is even-dimensional.

    Authors: We thank the referee for this observation. Our general argument in Sections 3–4, based on the representation-theoretic branching of the source and vev under the Lorentz algebra (identified with the conformal algebra on the celestial sphere) together with the recursive structure of the higher-spin Dirichlet-to-Neumann map, establishes that the expansion in the cosmological constant is smooth and free of logarithmic terms or source–vev mixing for arbitrary integer spin. Nevertheless, we agree that an explicit term-by-term verification for s>2 would make the claim more transparent. In the revised version we will add a new appendix that carries out the explicit power-series expansion through the first three orders for the spin-3 field in four-dimensional even spacetime (the lowest even dimension where the celestial sphere is two-dimensional), confirming the absence of resonances and the correct identification with the Minkowski null-infinity data. This explicit check will be presented alongside the general proof. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is a direct limit construction from AdS to flat space

full rationale

The provided abstract and description present the central claim as recovering the Minkowski solution space for arbitrary integer spin via a smooth Lambda -> 0 limit of the AdS solution space, obtained by term-by-term power-series expansion of the AdS source and vev. The identifications with null-infinity data (shear, mass aspects, etc.) and Lorentz branching are stated as consequences of this expansion. No equations, self-citations, fitted parameters, or ansatze are quoted that would reduce any step to a self-definitional input, a renamed fit, or a load-bearing prior result by the same authors. The procedure is a direct construction whose validity hinges on the existence of the expansion (an external mathematical question), not on re-labeling its own outputs. This is the normal non-finding when the derivation chain does not collapse by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the construction is presumed to rest on standard properties of AdS and Minkowski geometries and on representation theory of the Lorentz group.

axioms (2)
  • domain assumption Anti-de Sitter and Minkowski geometries admit a smooth limit when the cosmological constant vanishes.
    Invoked by the claim that the solution space is recovered as a smooth limit.
  • domain assumption The Lorentz algebra can be identified with the conformal algebra of the celestial sphere.
    Used to support the identification of source and vev components with boundary data.

pith-pipeline@v0.9.1-grok · 5663 in / 1333 out tokens · 13184 ms · 2026-06-28T08:46:35.729335+00:00 · methodology

discussion (0)

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Reference graph

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