From AdS Propagators to Celestial Propagators

Pongwit Srisangyingcharoen

Authors on Pith no claims yet

Pith reviewed 2026-05-15 03:20 UTC · model grok-4.3

classification ✦ hep-th

keywords celestialpropagatorspropagatorbasisboundary-to-boundarybulk-to-boundarycaseconformal

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The pith

AdS scalar propagators are mapped to celestial basis expressions, yielding a two-dimensional boundary object for massless fields dependent on Delta and a Bessel-function kernel for massive fields.

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

The authors start from the bulk-to-boundary propagator in Euclidean AdS space. They apply a Schwinger parametrization to obtain the boundary-to-boundary version, then convert both to the celestial basis using special wavefunctions suited to massless and massive scalars. For massless fields the result simplifies to an effectively two-dimensional object living on the celestial sphere that depends on the AdS/CFT conformal dimension Delta. For massive fields the expression keeps a nontrivial kernel built from modified Bessel functions that mirrors the radial structure already present in the original AdS propagators. The work therefore supplies a concrete translation rule between the two propagator languages.

Core claim

The results suggest a structural translation from AdS propagators and celestial propagators.

Load-bearing premise

That the chosen conformal primary wavefunctions and Schwinger parametrization produce the correct celestial propagators without missing correction terms or boundary contributions that would alter the claimed reductions.

read the original abstract

In this paper, we investigate how AdS scalar propagators are represented in the celestial basis. Starting from the standard bulk-to-boundary propagator in Euclidean AdS space, we express the propagator in a Schwinger parametrization and construct the corresponding boundary-to-boundary propagator. We then transform the resulting propagators to the celestial basis using conformal primary wavefunctions for both massless and massive scalar fields. For the massless case, the celestial propagator reduces to an effectively two-dimensional boundary-to-boundary object on the celestial sphere dependent on the AdS/CFT conformal dimension $\Delta$. For the massive case, the celestial propagator exhibits a nontrivial kernel involving modified Bessel functions, closely resembling the momentum-space radial structure of AdS bulk-to-boundary propagators. The results suggest a structural translation from AdS propagators and celestial propagators.

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.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work relies on standard mathematical tools from AdS/CFT and celestial holography. No new free parameters beyond the known conformal dimension Delta are introduced, and no new entities are postulated.

free parameters (1)

Delta
Conformal dimension that parametrizes the massless celestial propagator; treated as an input from AdS/CFT rather than fitted here.

axioms (2)

standard math Standard bulk-to-boundary propagator in Euclidean AdS and its Schwinger parametrization
Invoked at the start to express the propagator before celestial transformation.
domain assumption Properties and completeness of conformal primary wavefunctions for scalars
Used to perform the basis change to celestial coordinates.

pith-pipeline@v0.9.0 · 5428 in / 1270 out tokens · 46927 ms · 2026-05-15T03:20:16.201216+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

For the massless case, the celestial propagator reduces to an effectively two-dimensional boundary-to-boundary object... For the massive case, the celestial propagator exhibits a nontrivial kernel involving modified Bessel functions
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We then transform the resulting propagators to the celestial basis using conformal primary wavefunctions

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.