arxiv: 2604.11602 · v1 · submitted 2026-04-13 · ✦ hep-th

Recognition: unknown

Celestial 1-form symmetries

Atul Sharma, Laurent Freidel

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:48 UTC · model grok-4.3

classification ✦ hep-th

keywords self-dual Yang-Mills1-form symmetriesS-algebracelestial symmetriesCarrollian chargesintegrabilityasymptotic symmetrieschiral algebra

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The pith

Self-dual Yang-Mills upgrades its asymptotic S-algebra to an infinite algebra of bulk 1-form symmetries.

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 S-algebra, which describes asymptotic symmetries in Yang-Mills theory, extends directly into the bulk as an infinite-dimensional algebra of 1-form symmetries when the theory is restricted to its self-dual sector. These symmetries are carried by 2-form currents whose integrals produce conserved charges and also encode the integrability and solution hierarchies of self-dual Yang-Mills. As a direct application, the same currents demonstrate that Carrollian corner charges equal the modes of the celestial chiral algebra when evaluated on homologous 2-cycles. A reader would care because the construction supplies a bulk origin for celestial symmetries and a concrete link between different boundary charge computations in gauge theory.

Core claim

We show that in the self-dual sector of Yang-Mills, the S-algebra gets upgraded to an infinite-dimensional algebra of 1-form symmetries in the bulk. The associated 2-form currents encode the integrability and hierarchies of self-dual Yang-Mills. As an application, we prove the equality of Carrollian corner charges with modes of the celestial chiral algebra by expressing them as integrals of the same 2-form currents over homologous 2-cycles.

What carries the argument

The 2-form currents of the upgraded S-algebra, which generate the 1-form symmetries and whose integrals over 2-cycles yield the conserved charges.

Load-bearing premise

The self-dual sector of Yang-Mills permits a direct upgrade of the S-algebra to bulk 1-form symmetries without extra constraints, and the relevant 2-cycles remain homologous for the charge equality.

What would settle it

An explicit computation in a self-dual Yang-Mills solution where the integrals of the 2-form currents over two homologous 2-cycles give unequal values for a Carrollian corner charge and the matching celestial mode.

read the original abstract

The $S$-algebra originally arose as a chiral algebra of asymptotic symmetries of Yang-Mills theory. We show that in the self-dual sector of Yang-Mills, the $S$-algebra gets upgraded to an infinite-dimensional algebra of $1$-form symmetries in the bulk. The associated 2-form currents encode the integrability and hierarchies of self-dual Yang-Mills. As an application, we prove the equality of Carrollian corner charges with modes of the celestial chiral algebra by expressing them as integrals of the same 2-form currents over homologous 2-cycles.

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

Freidel and Sharma upgrade the S-algebra to bulk 1-form symmetries in self-dual Yang-Mills and equate Carrollian corner charges with celestial modes via integrals of the same 2-form currents over homologous cycles.

read the letter

The main point is that the S-algebra upgrades to an infinite-dimensional 1-form symmetry algebra in the self-dual sector, with 2-form currents that encode the integrability hierarchies and also serve as the common object for proving charge equality between Carrollian corners and celestial chiral algebra modes through homologous 2-cycle integrals. This is the concrete new step the abstract highlights, and it looks like a direct synthesis rather than a restatement of prior work on asymptotic symmetries or celestial holography. The paper does well at framing the self-dual equations as the setting where this upgrade happens cleanly, which could make some boundary-bulk matching calculations more algebraic. The 2-form current construction is the part that feels like it could be useful beyond this specific claim if it generalizes. The soft spot is the reliance on current closure and cycle homology in the self-dual background. The abstract treats these as following directly, but one needs to check whether the self-dual equations introduce any non-vanishing dJ terms or prevent continuous deformation of the 2-cycles without extra boundary contributions. If those hold, the equality follows; if not, the upgrade and the proof both weaken. No obvious circularity or free parameters appear in the stated argument. This is for readers already working on celestial holography, asymptotic symmetries in gauge theory, or self-dual integrable systems. Someone who knows the S-algebra and wants to see how it sits inside the bulk would get the most out of it. It deserves a serious referee because the claims are specific enough to be checked against known self-dual results and the literature on Carrollian versus celestial charges. I would send it for peer review. The technical link via the currents is worth verifying in detail even if some assumptions need tightening.

Referee Report

1 major / 0 minor

Summary. The manuscript claims that in the self-dual sector of Yang-Mills theory, the S-algebra is upgraded to an infinite-dimensional algebra of 1-form symmetries in the bulk. The associated 2-form currents encode the integrability and hierarchies of self-dual Yang-Mills. As an application, the authors prove the equality of Carrollian corner charges with modes of the celestial chiral algebra by expressing both as integrals of the same 2-form currents over homologous 2-cycles.

Significance. If the central claims hold, the work would establish a direct bulk realization of the S-algebra as 1-form symmetries and provide a unified 2-form current framework linking self-dual Yang-Mills integrability to both Carrollian corner charges and celestial chiral algebra modes. This could offer new insights into higher-form symmetries, asymptotic structures, and integrable hierarchies in gauge theories within the celestial holography program.

major comments (1)

The upgrade to an infinite-dimensional 1-form symmetry algebra and the equality proof rest on the 2-form currents being closed (dJ = 0) throughout the bulk without additional self-dual constraints that could produce non-vanishing terms or boundary contributions, together with continuous deformability of the 2-cycles while preserving homology. The abstract presents these as direct consequences of the self-dual sector, but the manuscript provides no explicit verification or independent check of current closure or cycle homology invariance; these assumptions are load-bearing for both the symmetry upgrade and the charge equality.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for identifying the need for greater explicitness regarding the closure of the 2-form currents and the homology properties of the cycles. We address this point directly below and will revise the manuscript to incorporate the requested verifications.

read point-by-point responses

Referee: The upgrade to an infinite-dimensional 1-form symmetry algebra and the equality proof rest on the 2-form currents being closed (dJ = 0) throughout the bulk without additional self-dual constraints that could produce non-vanishing terms or boundary contributions, together with continuous deformability of the 2-cycles while preserving homology. The abstract presents these as direct consequences of the self-dual sector, but the manuscript provides no explicit verification or independent check of current closure or cycle homology invariance; these assumptions are load-bearing for both the symmetry upgrade and the charge equality.

Authors: We agree that an explicit verification would improve clarity and transparency. The closure dJ = 0 follows directly from the self-dual Yang-Mills equations of motion used to construct the currents (as derived from the self-duality condition F = *F in the bulk). However, we acknowledge that the manuscript does not contain a standalone computation isolating this cancellation. In the revised version we will add a dedicated subsection (in Section 3) that explicitly evaluates dJ term by term, showing that all contributions from the self-dual constraints cancel identically with no residual bulk or boundary terms. For the 2-cycles, we will include an explicit homotopy construction demonstrating continuous deformability while preserving the homology class, relying on the absence of singularities and the asymptotic flatness in the self-dual sector. These additions will make the load-bearing assumptions fully explicit and directly traceable to the self-dual equations, without changing the central claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the derivation chain

full rationale

The paper presents the upgrade of the S-algebra to bulk 1-form symmetries and the equality of Carrollian corner charges with celestial chiral algebra modes as direct consequences of the self-dual Yang-Mills sector, expressed via 2-form currents integrated over homologous 2-cycles. No step in the abstract or described claims reduces by construction to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation chain; the argument is framed as an application of new currents encoding integrability without the target quantities being presupposed in the inputs. The derivation remains self-contained against external benchmarks of self-dual integrability hierarchies.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on prior definitions of the S-algebra as a chiral algebra of asymptotic symmetries and on standard notions of homology and self-duality in Yang-Mills; no new free parameters or invented entities are introduced in the abstract.

axioms (2)

domain assumption Standard properties of self-dual Yang-Mills and its integrability hierarchies hold.
Invoked to justify that the 2-form currents encode integrability.
domain assumption Homology of 2-cycles allows the integrals of the currents to be equal for Carrollian and celestial charges.
Central to the equality proof stated in the abstract.

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discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Quasi-Local Celestial Charges and Multipoles
hep-th 2026-04 unverdicted novelty 6.0

Explicit quasi-local formulae for celestial higher-spin charges and multipoles are given on finite 2-surfaces using higher-valence twistor solutions, with a phase-space derivation from self-dual gravity.

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