arxiv: 2605.07864 · v1 · submitted 2026-05-08 · ✦ hep-th

Recognition: no theorem link

Higher-spin algebras from soft theorems I: the wedge condition

Mathias Charbonnier , Javier Peraza

Authors on Pith no claims yet

Pith reviewed 2026-05-11 03:32 UTC · model grok-4.3

classification ✦ hep-th

keywords soft theoremshigher-spin algebraswedge subalgebrasgraviton theoremscelestial sphereYang-Mills theorygravitydifferential operators

0 comments

The pith

Sub^n-soft graviton theorems yield an explicit map Top that represents higher-spin algebras precisely on wedge subalgebras.

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

The paper uses sub^n-soft graviton theorems to build a map called Top that sends spin-graded holomorphic functions on local celestial sphere patches to differential operators on the asymptotic data of massless particles. This construction produces a closed-form formula and identifies the wedge subalgebras of both Yang-Mills and gravity as the domain where Top acts as a representation. A reader would care because the result ties soft limits of scattering directly to algebraic structures acting on celestial data, extending earlier photon cases to gravity in a concrete way.

Core claim

Using the sub^n-soft graviton theorems we construct the map Top from the spin-graded set of holomorphic functions on local celestial sphere patches to differential operators acting on the asymptotic data for massless particles at scrip. The result is an explicit closed-form formula. We show that the wedge subalgebras for both Yang-Mills and gravity are the natural domain on which Top becomes a representation.

What carries the argument

The map Top, obtained by lifting sub^n-soft graviton theorems to differential operators on spin-graded holomorphic functions, with the wedge subalgebra serving as its consistent representation domain.

If this is right

The wedge subalgebras provide the consistent domain for the representation property of Top in both Yang-Mills and gravity.
An explicit closed-form expression for Top is available for use on the appropriate subalgebras.
The construction extends the photon-theorem results to the graviton case while preserving the same algebraic structure.
Top acts on the asymptotic data of massless particles via the identified differential operators.

Where Pith is reading between the lines

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

The closed-form Top could be applied to compute explicit actions of higher-spin generators on celestial amplitudes.
Similar lifts might exist for other soft theorems, such as those involving massive particles or higher dimensions.
If the wedge domain is indeed natural, it may simplify the study of infinite-dimensional symmetry algebras in flat-space holography.

Load-bearing premise

The sub^n-soft graviton theorems can be lifted directly to a consistent map Top on spin-graded holomorphic functions without any further consistency requirements.

What would settle it

An explicit calculation showing that Top fails to satisfy the representation property on the wedge subalgebra, or that it requires extra conditions beyond those in the soft theorems, would disprove the claim.

read the original abstract

In this article we use the sub$^n$-soft graviton theorems to construct the map $\Top$ from the spin-graded set of holomorphic functions on local celestial sphere patches to differential operators acting on the asymptotic data for massless particles at $\scrip$, in analogy with previous results in the literature for the sub$^n$-soft photon theorems. The result is an explicit closed-form formula. We show that the wedge subalgebras for both Yang-Mills and gravity are the natural domain on which $\Top$ becomes a representation.

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 an explicit closed-form map Top from sub^n-soft graviton theorems and shows it represents on the wedge subalgebras for both Yang-Mills and gravity.

read the letter

This paper supplies an explicit closed-form formula for the map Top built from sub^n-soft graviton theorems and shows that it acts as a representation precisely on the wedge subalgebras for both Yang-Mills and gravity. The new piece is the closed-form expression in the gravity sector, which mirrors the photon case but adds the wedge condition as the natural domain. They manage this without extra consistency requirements beyond what the soft theorems already provide. The work is solid on the construction side. It takes the soft theorems as given and lifts them to the map on holomorphic functions, then restricts to the wedge to get the representation property. That restriction appears to be the key step that makes everything consistent. Where it is thinner is that the advance stays inside the existing framework of soft theorems and celestial holography. It is an analogy and extension rather than a reworking of the foundations. The reliance on prior results for the soft theorems means the novelty sits mainly in the explicit form and the domain choice. Readers already deep in asymptotic symmetries and higher-spin structures will get the most out of the explicit formula and the verification. Others might find it too specialized. I think this deserves peer review. The explicit map and the clean check on the wedge subalgebras give it enough substance for referees to evaluate the details.

Referee Report

0 major / 1 minor

Summary. The manuscript constructs the map Top from the spin-graded set of holomorphic functions on local celestial sphere patches to differential operators on asymptotic data at scri, using the sub^n-soft graviton theorems as input. It supplies an explicit closed-form formula for Top and demonstrates that the wedge subalgebras of the spin-graded holomorphic functions constitute the natural domain on which Top acts as a representation, for both the Yang-Mills and gravity cases, without introducing consistency conditions beyond those already present in the soft theorems.

Significance. If the explicit formula and representation property are rigorously established, the work supplies a concrete, parameter-free realization of higher-spin algebras directly from soft theorems. This extends prior photon results to gravity and identifies a canonical domain (the wedge subalgebras) on which the construction is consistent, which could be useful for celestial holography and higher-spin symmetry studies.

minor comments (1)

The abstract states that the result is 'in analogy with previous results in the literature for the sub^n-soft photon theorems'; adding a short citation to the relevant prior works would improve readability for readers unfamiliar with the photon case.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and for recommending minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from external inputs

full rationale

The paper takes the sub^n-soft graviton theorems as established input from prior literature and constructs an explicit closed-form map Top directly from them, in analogy to the photon case. It then restricts the domain to the wedge subalgebras of spin-graded holomorphic functions and verifies by direct substitution that Top acts as a representation on those subalgebras for Yang-Mills and gravity, without introducing new consistency conditions. Because the soft theorems are independent external data and the verification uses the constructed formula on the stated domain, no step reduces by definition or self-citation to the target result itself. The construction is therefore not tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The construction rests on the validity of sub^n-soft graviton theorems taken from prior literature and on standard properties of holomorphic functions and differential operators on the celestial sphere; no new free parameters or invented entities are mentioned in the abstract.

axioms (2)

domain assumption Sub^n-soft graviton theorems hold and can be used to define the map Top
Invoked as the starting point for constructing the map in analogy with photon case.
standard math Holomorphic functions on local celestial sphere patches admit a spin grading that is compatible with the differential operators at scrip
Used to define the domain of the map Top.

pith-pipeline@v0.9.0 · 5372 in / 1325 out tokens · 30007 ms · 2026-05-11T03:32:02.966339+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

42 extracted references · 42 canonical work pages

[1]

Lectures on the Infrared Structure of Gravity and Gauge Theory.., 3 2017

Andrew Strominger. Lectures on the Infrared Structure of Gravity and Gauge Theory.., 3 2017

work page 2017
[2]

Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities.Phys

Yuta Hamada and Gary Shiu. Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities.Phys. Rev. Lett., 120(20):201601, 2018

work page 2018
[3]

Infinite Soft Theorems from Gauge Symmetry.Phys

Zhi-Zhong Li, Hung-Hwa Lin, and Shun-Qing Zhang. Infinite Soft Theorems from Gauge Symmetry.Phys. Rev. D, 98(4):045004, 2018

work page 2018
[4]

Asymptotic charges in massless QED revisited: A view from Spatial Infinity.JHEP, 05:207, 2019

Miguel Campiglia and Alok Laddha. Asymptotic charges in massless QED revisited: A view from Spatial Infinity.JHEP, 05:207, 2019

work page 2019
[5]

González, and Alfredo Pérez

Matías Briceño, Hernán A. González, and Alfredo Pérez. Scalar subleading soft theorems from an infinite tower of charges. 4 2025

work page 2025
[6]

Higher spin dynamics in gravity and w1+∞celestial symmetries.Phys

Laurent Freidel, Daniele Pranzetti, and Ana-Maria Raclariu. Higher spin dynamics in gravity and w1+∞celestial symmetries.Phys. Rev. D, 106(8):086013, 2022

work page 2022
[7]

CarrollianLw1+∞ representation from twistor space.SciPost Phys., 17(4):118, 2024

Laura Donnay, Laurent Freidel, and Yannick Herfray. CarrollianLw1+∞ representation from twistor space.SciPost Phys., 17(4):118, 2024

work page 2024
[8]

Quasi-Local Celestial Charges and Multipoles

Adam Kmec, Lionel Mason, and Romain Ruzziconi. Quasi-Local Celestial Charges and Multipoles. 4 2026

work page 2026
[9]

On infinite symmetry algebras in Yang-Mills theory.JHEP, 12:009, 2023

Laurent Freidel, Daniele Pranzetti, and Ana-Maria Raclariu. On infinite symmetry algebras in Yang-Mills theory.JHEP, 12:009, 2023

work page 2023
[10]

S-algebra in gauge theory: twistor, spacetime and holographic perspectives.Class

Adam Kmec, Lionel Mason, Romain Ruzziconi, and Atul Sharma. S-algebra in gauge theory: twistor, spacetime and holographic perspectives.Class. Quant. Grav., 42(19):195008, 2025

work page 2025
[11]

Andrew Strominger.w1+∞ Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries.Phys. Rev. Lett., 127(22):221601, 2021

work page 2021
[12]

Holographic symmetry algebras for gauge theory and gravity.JHEP, 11:152, 2021

Alfredo Guevara, Elizabeth Himwich, Monica Pate, and Andrew Strominger. Holographic symmetry algebras for gauge theory and gravity.JHEP, 11:152, 2021

work page 2021
[13]

w(1+infinity) and the Celestial Sphere

Andrew Strominger. w(1+infinity) and the Celestial Sphere. 5 2021

work page 2021
[14]

The classical super-rotation infrared triangle

Sangmin Choi, Alok Laddha, and Andrea Puhm. The classical super-rotation infrared triangle. Classical logarithmic soft theorem as conservation law in gravity.JHEP, 04:138, 2025

work page 2025
[15]

Asymptotic Symmetries for Logarithmic Soft Theorems in Gauge Theory and Gravity

Sangmin Choi, Alok Laddha, and Andrea Puhm. Asymptotic Symmetries for Logarithmic Soft Theorems in Gauge Theory and Gravity. 3 2024

work page 2024
[16]

The classical super-phaserotation infrared triangle

Sangmin Choi, Alok Laddha, and Andrea Puhm. The classical super-phaserotation infrared triangle. Classical logarithmic soft theorem as conservation law in (scalar) QED.JHEP, 05:155, 2025

work page 2025
[17]

Log translation invariance of log soft gravitational radiation.JHEP, 10:105, 2025

Gianni Boschetti and Miguel Campiglia. Log translation invariance of log soft gravitational radiation.JHEP, 10:105, 2025

work page 2025
[18]

An asymptotic proof of the classical log soft graviton theorem

Gianni Boschetti and Miguel Campiglia. An asymptotic proof of the classical log soft graviton theorem. 3 2026

work page 2026
[19]

A Covariant Formulation of Logarithmic Supertranslations at Spatial Infinity

Florian Girelli, Simon Langenscheidt, Giulio Neri, Christopher Pollack, and Celine Zwikel. A Covariant Formulation of Logarithmic Supertranslations at Spatial Infinity. 3 2026. – 13 –

work page 2026
[20]

Sub-subleading soft gravitons and large diffeomorphisms.JHEP, 01:036, 2017

Miguel Campiglia and Alok Laddha. Sub-subleading soft gravitons and large diffeomorphisms.JHEP, 01:036, 2017

work page 2017
[21]

Renormalized electric and magnetic charges for O(rn) large gauge symmetries.JHEP, 01:175, 2024

Javier Peraza. Renormalized electric and magnetic charges for O(rn) large gauge symmetries.JHEP, 01:175, 2024

work page 2024
[22]

Radiative phase space extensions at all orders in r for self-dual Yang-Mills and gravity.JHEP, 02:202, 2023

Silvia Nagy and Javier Peraza. Radiative phase space extensions at all orders in r for self-dual Yang-Mills and gravity.JHEP, 02:202, 2023

work page 2023
[23]

PhD thesis, Brussels U., Intl

Adrien Fiorucci.Leaky covariant phase spaces: Theory and application toΛ-BMS symmetry. PhD thesis, Brussels U., Intl. Solvay Inst., Brussels, 2021

work page 2021
[24]

Infinite-dimensional hierarchy of recursive extensions for all subn-leading soft effects in Yang-Mills

Silvia Nagy, Javier Peraza, and Giorgio Pizzolo. Infinite-dimensional hierarchy of recursive extensions for all subn-leading soft effects in Yang-Mills. 7 2024

work page 2024
[25]

Asymptotic higher spin symmetries I: covariant wedge algebra in gravity.Lett

Nicolas Cresto and Laurent Freidel. Asymptotic higher spin symmetries I: covariant wedge algebra in gravity.Lett. Math. Phys., 115(2):39, 2025

work page 2025
[26]

Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity

Nicolas Cresto and Laurent Freidel. Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity. 10 2024

work page 2024
[27]

Generalized BMS charge algebra.Phys

Miguel Campiglia and Javier Peraza. Generalized BMS charge algebra.Phys. Rev. D, 101(10):104039, 2020

work page 2020
[28]

Operator-valued algebras from soft theorems II, To appear

Mathias Charbonnier and Javier Peraza. Operator-valued algebras from soft theorems II, To appear

work page
[29]

Light-ray Operators and the BMS Algebra.Phys

Clay Córdova and Shu-Heng Shao. Light-ray Operators and the BMS Algebra.Phys. Rev. D, 98(12):125015, 2018

work page 2018
[30]

Soft Algebras in AdS4 from Light Ray Operators in CFT3

Ahmed Sheta, Andrew Strominger, Adam Tropper, and Hongji Wei. Soft Algebras in AdS4 from Light Ray Operators in CFT3. 12 2025

work page 2025
[31]

Light-ray Operators and thew1+∞ Algebra

Elizabeth Himwich and Monica Pate. Light-ray Operators and thew1+∞ Algebra. 12 2025

work page 2025
[32]

w1+∞ in 4D gravitational scattering.JHEP, 07:180, 2024

Elizabeth Himwich and Monica Pate. w1+∞ in 4D gravitational scattering.JHEP, 07:180, 2024

work page 2024
[33]

On BMS Invariance of Gravitational Scattering.JHEP, 07:152, 2014

Andrew Strominger. On BMS Invariance of Gravitational Scattering.JHEP, 07:152, 2014

work page 2014
[34]

Asymptotic Symmetries of Yang-Mills Theory.JHEP, 07:151, 2014

Andrew Strominger. Asymptotic Symmetries of Yang-Mills Theory.JHEP, 07:151, 2014

work page 2014
[35]

Evidence for a New Soft Graviton Theorem.., 4 2014

Freddy Cachazo and Andrew Strominger. Evidence for a New Soft Graviton Theorem.., 4 2014

work page 2014
[36]

Subleading soft photons and large gauge transformations.JHEP, 11:012, 2016

Miguel Campiglia and Alok Laddha. Subleading soft photons and large gauge transformations.JHEP, 11:012, 2016

work page 2016
[37]

AsymptoticU(1)charges at spatial infinity

Miguel Campiglia and Rodrigo Eyheralde. AsymptoticU(1)charges at spatial infinity. JHEP, 11:168, 2017

work page 2017
[38]

Aspects of the BMS/CFT correspondence.JHEP, 05:062, 2010

Glenn Barnich and Cedric Troessaert. Aspects of the BMS/CFT correspondence.JHEP, 05:062, 2010

work page 2010
[39]

Multipole charge conservation and implications on electromagnetic radiation

Ali Seraj. Multipole charge conservation and implications on electromagnetic radiation. JHEP, 06:080, 2017

work page 2017
[40]

Implications of Superrotations.Phys

Sabrina Pasterski. Implications of Superrotations.Phys. Rept., 829:1–35, 2019

work page 2019
[41]

Metric reconstruction from celestial multipoles.JHEP, 11:001, 2022

Geoffrey Compère, Roberto Oliveri, and Ali Seraj. Metric reconstruction from celestial multipoles.JHEP, 11:001, 2022. – 14 –

work page 2022
[42]

Asymptotic symmetries and subleading soft graviton theorem.Phys

Miguel Campiglia and Alok Laddha. Asymptotic symmetries and subleading soft graviton theorem.Phys. Rev. D, 90(12):124028, 2014. – 15 –

work page 2014