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arxiv: 2607.00864 · v1 · pith:DL5OYVXJnew · submitted 2026-07-01 · ✦ hep-th

Soft Algebras via Bulk Double Soft Limits

Sruthi A. Narayanan This is my paper

Pith reviewed 2026-07-02 09:21 UTC · model grok-4.3

classification ✦ hep-th
keywords celestial amplitudessoft limitscollinear limitsgravitational scatteringcelestial CFTsymmetry algebrasbulk amplitudes
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0 comments X

The pith

Bulk gravitational amplitudes do not inherit recursive soft expansions from celestial algebras without subtleties from combined limits.

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

Soft and collinear limits of celestial amplitudes produce infinite-dimensional symmetry algebras acting on two-dimensional celestial CFTs. A small subset of operators generates the full set recursively through commutation relations, and inserting this subset into correlators reproduces the first three terms of the soft expansion for the corresponding four-dimensional bulk gravitational amplitude. The paper establishes that the same recursive mechanism does not allow the entire soft expansion of bulk amplitudes to be recovered from those first three terms. The combined action of soft and collinear limits creates subtleties in bulk amplitudes that are absent from the boundary celestial description. A sympathetic reader would care because this shows that boundary symmetries do not translate directly into a complete recursive control over bulk scattering data.

Core claim

A bulk analog of the recursive determination of the full soft expansion via celestial algebras does not follow trivially. The interplay of soft and collinear limits produces subtleties for bulk amplitudes that do not appear in the boundary description.

What carries the argument

The interplay of soft and collinear limits when applied directly to bulk amplitudes, which blocks a direct lift of the recursive commutation relations from celestial algebras.

If this is right

  • The full soft expansion of a gravitational amplitude cannot be determined from the first three terms alone using the celestial algebra recursions.
  • Combined soft and collinear limits must be treated separately when moving from boundary to bulk amplitudes.
  • The recursive generation of the algebra via commutation relations requires additional modifications in the bulk setting.

Where Pith is reading between the lines

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

  • The boundary celestial description may therefore omit bulk-specific constraints that appear only when soft and collinear limits act together.
  • Explicit examples of higher-order bulk soft factors could be computed to isolate the precise form of the missing contributions.

Load-bearing premise

The recursive action generated by commutation relations in celestial algebras extends directly to bulk amplitudes without additional modifications arising from the combined soft and collinear limits.

What would settle it

An explicit computation of a four-dimensional gravitational scattering amplitude to soft orders beyond the third term, followed by checking whether those higher terms match the output of the celestial recursion applied to the first three terms.

read the original abstract

Soft and collinear limits of "celestial amplitudes" give rise to infinite dimensional symmetry algebras for two-dimensional (2D) "celestial" conformal field theories (CFTs). A small subset of these operators generates the action of the entire set recursively via the commutation relations. Insertion of this subset into celestial CFT correlators gives the boundary version of the first three terms in a soft expansion of the corresponding 4D bulk gravitational scattering amplitude. In this paper, we find that a bulk analog of this, which would allow the entire soft expansion of a gravitational amplitude to be determined via just the first three terms, does not follow trivially from the celestial algebras. We show how the interplay of soft and collinear limits results in subtleties for bulk amplitudes that do not show up in the boundary description.

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 / 2 minor

Summary. The manuscript examines soft algebras arising from soft and collinear limits of celestial amplitudes in 4D gravity. It shows that a small subset of operators in the celestial CFT algebra recursively generates the full set via commutation relations, reproducing the first three terms of the soft expansion on the boundary; however, the analogous bulk construction for gravitational scattering amplitudes does not follow trivially, owing to additional subtleties generated by the simultaneous imposition of soft and collinear limits.

Significance. The result clarifies a concrete obstruction to lifting boundary celestial symmetries directly to bulk soft theorems. By isolating the role of combined soft-collinear limits, the work supplies a diagnostic that future attempts to reconstruct higher-order soft factors from celestial algebras must address. This distinction between boundary and bulk is a substantive contribution to the celestial holography program.

minor comments (2)
  1. The abstract states that the bulk analog 'does not follow trivially' but does not preview the concrete mechanism (e.g., a specific failure of a commutation relation or an extra collinear pole). Adding one sentence would improve readability.
  2. Notation for the soft operators and their commutation relations is introduced without an explicit reference to the earlier celestial-algebra literature; a single sentence citing the relevant prior works would help readers.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. The referee's summary accurately captures the central result: that the recursive generation of the full soft algebra via commutation relations works on the boundary but encounters additional subtleties in the bulk due to the simultaneous soft and collinear limits. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central claim is a negative result: a bulk analog allowing the entire soft expansion to be determined from the first three terms does not follow trivially from celestial algebras, due to subtleties arising from the interplay of soft and collinear limits in bulk amplitudes (absent in the boundary description). This is presented as an observation about distinctions between boundary celestial CFTs and 4D bulk gravitational amplitudes, not a derivation or prediction that reduces to its own inputs by construction. No self-definitional steps, fitted inputs renamed as predictions, load-bearing self-citations, or ansatzes smuggled via citation are quoted or evident. The derivation chain relies on external celestial algebra commutation relations and known soft expansions, remaining self-contained against those benchmarks without internal reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, invented entities, or paper-specific axioms; the claim rests on standard domain assumptions of celestial CFT and soft theorems in gravity that are not detailed here.

axioms (1)
  • domain assumption Standard assumptions of celestial conformal field theory and soft/collinear theorems in gravity
    The abstract invokes these without introducing or deriving new ones.

pith-pipeline@v0.9.1-grok · 5658 in / 1188 out tokens · 33593 ms · 2026-07-02T09:21:59.115843+00:00 · methodology

discussion (0)

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Reference graph

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