arxiv: 2604.09771 · v1 · submitted 2026-04-10 · ✦ hep-th · gr-qc

Recognition: 2 theorem links

· Lean Theorem

Towards a Carrollian Description of Yang-Mills

Jeffrey Opreij , David Skinner , Hangzhi Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:40 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords Yang-Mills theorynull infinityCarrollian dynamicsMHV amplitudestree-level scatteringcelestial sphereboundary formulation

0 comments

The pith

A theory on null infinity with a Carrollian kinetic term and MHV interactions reproduces Yang-Mills tree amplitudes.

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

The paper constructs a field theory whose degrees of freedom are the characteristic data of a gauge field living purely on null infinity of Minkowski space. Its action pairs an electric Carrollian kinetic term with non-local MHV-type interactions that connect points on the celestial sphere. Explicit calculations show that the model's Feynman rules generate all MHV and NMHV tree amplitudes of bulk Yang-Mills theory, with a new closed-form expression for the NMHV case. The authors outline how the same diagram expansion yields arbitrary higher-point trees. A reader would care because the construction offers a boundary-only description that might simplify amplitude computations or expose hidden structures in gauge-theory scattering.

Core claim

We provide a theory defined purely on null infinity that describes Yang-Mills in the Minkowski space bulk. The dynamical field of our model is the characteristic data of the bulk gauge field, and the action combines an electric branch Carrollian kinetic term with non-local interactions of MHV type that link different points on the celestial sphere. We explicitly show how this theory recovers all MHV and NMHV tree amplitudes in Yang-Mills, and outline how arbitrary tree amplitudes may be obtained from its Feynman diagram expansion. The detailed expression we find for the NMHV amplitude appears to be new.

What carries the argument

The electric-branch Carrollian kinetic term for the null-infinity gauge-field data together with non-local MHV-type interaction vertices on the celestial sphere.

If this is right

All MHV tree amplitudes are recovered exactly from the boundary action.
NMHV amplitudes are given by a new explicit expression derived from the Carrollian model.
Arbitrary tree-level amplitudes follow from the Feynman diagram expansion of the boundary theory.
The complete set of Yang-Mills tree-level interactions is encoded in the combination of Carrollian kinetics and MHV vertices on null infinity.

Where Pith is reading between the lines

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

The non-local character of the interactions may allow direct derivation of amplitude relations without reference to bulk diagrams.
Similar Carrollian constructions on null infinity could be tested for gravity or other gauge theories.
The boundary-only formulation might simplify the extraction of soft theorems or factorization properties at tree level.

Load-bearing premise

The assumption that the chosen Carrollian kinetic term plus the non-local MHV-type interactions are sufficient to capture the full Yang-Mills dynamics without missing vertices or extra constraints.

What would settle it

Explicit computation of the five-gluon NMHV amplitude from the boundary theory's Feynman rules and direct comparison with the known Yang-Mills result; any mismatch would show the model is incomplete.

read the original abstract

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.

Desk Editor's Note private letter to a colleague

The paper gives a Carrollian action on null infinity that explicitly recovers MHV and NMHV Yang-Mills amplitudes with a new NMHV expression, but only outlines the general case.

read the letter

The main takeaway is that the authors construct a Carrollian theory purely on null infinity, with a kinetic term and non-local MHV interactions, that explicitly recovers the MHV and NMHV tree amplitudes of Yang-Mills, and they provide what appears to be a new detailed expression for the NMHV amplitude. They do well in defining the dynamical field from the bulk gauge field's characteristic data and showing how the action leads to those amplitudes through Feynman diagram expansions. The link to Carrollian limits and celestial holography is clear, and the explicit low-point matches give some concrete evidence that the setup works at least for those cases. Where it is softer is in the extension to arbitrary tree amplitudes. The paper outlines how they might arise from the Feynman expansion but does not provide explicit computations or a general argument for N²MHV or higher. This means we cannot yet confirm that the specific combination of terms fully reproduces the complete Yang-Mills dynamics without missing interactions or extra constraints. There is also some circularity risk since the interactions are chosen to be of MHV type to match known results, though the Carrollian kinetic term provides independent input. This paper is for people working on boundary descriptions in flat space holography or looking for alternative ways to generate gauge theory amplitudes. Someone in that area could get value from the new NMHV formula and the overall framing, and it might spark ideas for further development. I think it deserves a serious referee. The work is grounded enough with the explicit checks to warrant review, even if the general claim needs more support. So, my recommendation is to send it out for peer review.

Referee Report

1 major / 1 minor

Summary. The manuscript proposes a Carrollian Yang-Mills theory defined purely on null infinity, with the dynamical field given by the characteristic data of the bulk gauge field. The action combines an electric-branch Carrollian kinetic term with non-local MHV-type interactions linking points on the celestial sphere. It explicitly recovers all MHV and NMHV tree amplitudes from the Feynman expansion and outlines how arbitrary tree amplitudes may be obtained, presenting what appears to be a new detailed expression for the NMHV amplitude.

Significance. If the action is shown to be complete, the work would supply a novel boundary formulation of bulk Yang-Mills dynamics, potentially useful for celestial holography and amplitude calculations. The explicit derivations for the MHV and NMHV sectors, together with the new NMHV formula, constitute a concrete technical contribution even if the general case requires further development.

major comments (1)

[Abstract and main results] Abstract and main results: the central claim that the Carrollian kinetic term plus the chosen non-local MHV-type interactions generate the complete set of Yang-Mills tree amplitudes is supported by explicit calculations only for MHV and NMHV; the extension to arbitrary amplitudes is described only as an outline without a general proof, explicit N²MHV example, or demonstration that no additional vertices are required. This sufficiency question is load-bearing for the assertion of a complete description.

minor comments (1)

The manuscript would benefit from an explicit listing of the Feynman rules derived from the action to facilitate independent verification of the amplitude computations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the key point regarding the scope of our results. We address the major comment below.

read point-by-point responses

Referee: [Abstract and main results] Abstract and main results: the central claim that the Carrollian kinetic term plus the chosen non-local MHV-type interactions generate the complete set of Yang-Mills tree amplitudes is supported by explicit calculations only for MHV and NMHV; the extension to arbitrary amplitudes is described only as an outline without a general proof, explicit N²MHV example, or demonstration that no additional vertices are required. This sufficiency question is load-bearing for the assertion of a complete description.

Authors: We agree that explicit derivations are given only for the MHV and NMHV sectors, with the general case presented as an outline of the Feynman expansion. This matches the manuscript's abstract and the 'Towards' framing of the title, which does not assert a fully proven complete description but rather a framework verified in the first non-trivial cases. The outline indicates that arbitrary tree amplitudes arise from iterated use of the Carrollian propagator together with the MHV-type vertices, without new interaction terms. To strengthen the presentation we will revise the relevant section to include a more detailed step-by-step description of the general construction and an explicit N²MHV example computed from the existing vertices. This will illustrate that no additional vertices are needed for the checked cases and clarify the pattern for higher amplitudes. A rigorous inductive proof for all n remains outside the present scope. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the proposed Carrollian model for Yang-Mills

full rationale

The paper constructs an action on null infinity consisting of an electric Carrollian kinetic term plus non-local MHV-type interactions, then derives the tree amplitudes via its Feynman rules and verifies they match known Yang-Mills MHV and NMHV results (with an apparently new NMHV expression). This is a self-contained construction: the amplitudes are computed from the action rather than presupposed, the interaction choice is part of the model definition rather than a post-hoc fit, and no load-bearing step reduces by definition or self-citation to the target result. The outline for higher amplitudes is presented as a direction for future verification rather than a completed claim.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The claim rests on standard Yang-Mills asymptotics at null infinity and the validity of the Carrollian limit for the kinetic term; no explicit free parameters are fitted, but the precise form of the non-local interactions is selected to match known amplitudes.

axioms (2)

domain assumption Standard Yang-Mills theory in Minkowski space with appropriate fall-off at null infinity
The bulk theory whose amplitudes are to be reproduced is ordinary Yang-Mills.
domain assumption Carrollian geometry governs the kinetic term on null infinity
The electric-branch Carrollian kinetic term is taken as the correct boundary dynamics.

invented entities (1)

Carrollian Yang-Mills theory on null infinity no independent evidence
purpose: Boundary theory whose Feynman expansion reproduces bulk Yang-Mills tree amplitudes
New model introduced by the paper; no independent falsifiable evidence outside the amplitude matching is provided.

pith-pipeline@v0.9.0 · 5383 in / 1450 out tokens · 42402 ms · 2026-05-10T16:40:24.703979+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.

The action combines an electric branch Carrollian kinetic term with non-local interactions of MHV type... S_kin[a,¯a] = ∫_{I_C} tr(∂a ¯∂¯a)
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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

good cuts C_x = E^+(x) ∩ I^+ obeying the good-cut equation (D_A D_B u)_tf = 0

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.

Reference graph

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