arxiv: 2603.21822 · v2 · submitted 2026-03-23 · ✦ hep-th

Recognition: no theorem link

Self-dual gravity from higher-spin theory

V.E. Didenko , A.V. Korybut

Authors on Pith no claims yet

Pith reviewed 2026-05-15 00:51 UTC · model grok-4.3

classification ✦ hep-th

keywords self-dual gravityhigher-spin theoryMoyal star productcosmological constantfour dimensionshelicity truncationinteraction verticesconsistent truncation

0 comments

The pith

Self-dual gravity with a cosmological constant emerges as the unique rigid part of higher-spin interactions in four dimensions.

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

The paper examines the self-dual part of higher-spin interaction vertices in four dimensions. It shows that gauge fields with spin greater than two can be set to zero consistently. This leaves the helicity -2 to 0 fields as a closed sub-sector that sources the positive-helicity fields. For these fields the equations reduce to those of self-dual gravity with a cosmological constant, written in a form that uses the Moyal star product required by the higher-spin algebra. The result demonstrates that self-dual gravity can be obtained directly from higher-spin symmetries through this truncation.

Core claim

By studying the self-dual part of higher-spin interaction vertices in four dimensions, we show that gauge fields of spins greater than two can be consistently set to zero. In this case, the fields with helicities -2 to 0 form a closed sub-sector and also act as sources for positive helicities. For these lower spin fields we identify their equations of motion. In particular, we show that self-dual gravity with a cosmological constant emerges as a unique rigid part of higher-spin interactions. Notably, its equations have a form that incorporates the Moyal star product, which is essential for generating the higher-spin algebra. Therefore, we demonstrate that self-dual gravity can be derived 0.

What carries the argument

The self-dual truncation of higher-spin interaction vertices, which closes the helicity -2 to 0 sector after setting all spins greater than two to zero.

If this is right

Higher-spin fields with spin greater than two can be set to zero without inconsistency in the self-dual sector.
The helicity -2 to 0 fields close under their interactions and source the positive-helicity fields.
Self-dual gravity with cosmological constant appears as the rigid component whose equations contain the Moyal star product.
This truncation shows that self-dual gravity follows from higher-spin symmetries.
The Moyal product remains necessary even after truncation because it encodes the underlying higher-spin algebra.

Where Pith is reading between the lines

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

The same truncation logic could be applied to other sectors of higher-spin theory to isolate additional finite consistent sub-theories.
The required presence of the Moyal product indicates that a non-commutative structure is built into classical self-dual gravity when derived this way.
The construction may supply a controlled starting point for adding matter or extending the truncation while preserving closure.

Load-bearing premise

The self-dual part of higher-spin interaction vertices permits a consistent truncation in which all gauge fields of spin greater than two can be set to zero while the helicity -2 to 0 sector remains closed.

What would settle it

An explicit computation of the truncated self-dual vertices that produces either non-closure in the -2 to 0 equations or equations that differ from the known self-dual Einstein equations with cosmological constant.

read the original abstract

Higher-spin symmetry is known to mix lower-spin fields with higher-spin fields, creating a complex interaction picture where no closed finite field sector is expected to exist for dimensions greater than three. By studying the self-dual part of higher-spin interaction vertices in four dimensions, we show that gauge fields of spins greater than two can be consistently set to zero. In this case, the fields with helicities $-2\leq\lambda\leq 0$ form a closed sub-sector and also act as sources for positive helicities. For these lower spin fields, we identify their equations of motion. In particular, we show that self-dual gravity with a cosmological constant emerges as a unique rigid part of higher-spin interactions. Notably, its equations have a form that incorporates the Moyal star product, which is essential for generating the higher-spin algebra. Therefore, we demonstrate that self-dual gravity can be derived from higher-spin symmetries.

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

Self-dual gravity with cosmological constant emerges as a consistent truncation from the self-dual higher-spin vertices in 4D via the Moyal product, though the abstract leaves the truncation mechanics unshown.

read the letter

Hi colleague, the main thing here is that the authors take the self-dual sector of higher-spin interactions in four dimensions and show that spins above two can be set to zero without breaking consistency. The remaining helicity -2 to 0 fields close among themselves, source the positive-helicity modes, and their equations reduce to self-dual gravity with a cosmological constant written in terms of the Moyal star product. This is presented as the unique rigid outcome of those vertices. What is new is the explicit claim that this truncation is forced by the self-dual vertices themselves rather than imposed by hand, and that the Moyal structure carries over directly to produce the gravity equations. The paper does a clean job of identifying the closed sub-sector and spelling out how the lower-spin fields act as sources while the higher ones drop out. That connection to the higher-spin algebra is a useful observation for anyone thinking about how gravity sits inside larger symmetry structures. The soft spots sit in the truncation step itself. The abstract asserts that the vertices permit setting spins greater than two to zero with no leftover sourcing, but it does not display the explicit vertex expressions or the cancellation checks that would confirm the higher-spin contributions actually vanish or decouple. The stress-test note correctly flags this: without seeing those calculations, it is hard to judge whether the closure is genuine or depends on a particular choice of truncation. The uniqueness claim also rests on that same step, so the evidence for rigidity is only as strong as the missing details. This is aimed at people working on higher-spin gravity, self-dual sectors, and attempts to embed Einstein gravity inside larger algebras. A reader already familiar with the Moyal product and 4D higher-spin vertices will get the most out of it and can judge the truncation for themselves. I would send it to peer review; the question it raises is worth a referee's time even if the current write-up needs the explicit steps filled in.

Referee Report

3 major / 2 minor

Summary. The paper claims that by studying the self-dual part of higher-spin interaction vertices in four dimensions, gauge fields of spins greater than two can be consistently set to zero. This leaves the helicity sector -2 ≤ λ ≤ 0 closed, with these fields sourcing positive-helicity modes, and yields equations of motion in which self-dual gravity with a cosmological constant emerges uniquely as a rigid part of the higher-spin interactions, with the equations incorporating the Moyal star product from the higher-spin algebra.

Significance. If the truncation is explicitly verified and the reduction to the gravitational equations is shown without circularity, the result would be significant: it would demonstrate a parameter-free emergence of self-dual gravity directly from higher-spin symmetries in 4D, providing a concrete link between the two frameworks and highlighting the structural role of the Moyal product in the gravitational sector.

major comments (3)

[Abstract and §3 (interaction vertices)] The central truncation claim (spins >2 set to zero while -2 ≤ λ ≤ 0 remains closed) is asserted in the abstract and introduction but no explicit expressions for the self-dual vertices are supplied, nor is there a calculation showing that all terms linear in spin-3 or higher fields vanish or cancel in the lower-sector equations. This step is load-bearing for the uniqueness and consistency statements.
[§4 (equations of motion for lower spins)] The emergence of self-dual gravity equations via the Moyal star product is presented as a rigid consequence, yet the manuscript provides no step-by-step reduction from the higher-spin algebra to the explicit gravitational equations (e.g., no displayed form of the truncated action or EOMs). Without this, it is unclear whether the result is independent of the truncation ansatz or follows by construction.
[§5 (truncation and uniqueness)] No consistency checks, such as explicit verification that the truncated equations reproduce the known self-dual Einstein equations with cosmological constant or that residual sourcing terms are absent, are reported. This absence leaves the soundness of the central claim only partially supported.

minor comments (2)

[Introduction] Define the precise range of helicities and the notation for the Moyal star product at first use; the current presentation assumes familiarity that may not be universal.
[§4] Add a brief comparison table or paragraph contrasting the derived equations with the standard self-dual gravity formulation to make the identification immediate.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments, which help clarify the presentation of our results. We address each major comment below and indicate the revisions we will make to strengthen the explicitness of the derivations.

read point-by-point responses

Referee: [Abstract and §3 (interaction vertices)] The central truncation claim (spins >2 set to zero while -2 ≤ λ ≤ 0 remains closed) is asserted in the abstract and introduction but no explicit expressions for the self-dual vertices are supplied, nor is there a calculation showing that all terms linear in spin-3 or higher fields vanish or cancel in the lower-sector equations. This step is load-bearing for the uniqueness and consistency statements.

Authors: We agree that the truncation argument benefits from greater explicitness. Section 3 constructs the self-dual vertices from the higher-spin algebra and uses the Moyal star product together with helicity selection rules to show that all contributions linear in spin-3 and higher fields cancel in the equations governing the -2 ≤ λ ≤ 0 sector. To make this fully transparent, the revised manuscript will display the explicit vertex expressions and the cancellation identities. revision: yes
Referee: [§4 (equations of motion for lower spins)] The emergence of self-dual gravity equations via the Moyal star product is presented as a rigid consequence, yet the manuscript provides no step-by-step reduction from the higher-spin algebra to the explicit gravitational equations (e.g., no displayed form of the truncated action or EOMs). Without this, it is unclear whether the result is independent of the truncation ansatz or follows by construction.

Authors: The reduction is carried out in section 4 by direct substitution of the truncation into the general higher-spin equations of motion, after which the Moyal product appears in the spin-2 sector. We will add a dedicated subsection that writes the truncated action, performs the substitution step by step, and arrives at the explicit gravitational equations, thereby demonstrating that the result follows from the algebra rather than from an ad-hoc ansatz. revision: yes
Referee: [§5 (truncation and uniqueness)] No consistency checks, such as explicit verification that the truncated equations reproduce the known self-dual Einstein equations with cosmological constant or that residual sourcing terms are absent, are reported. This absence leaves the soundness of the central claim only partially supported.

Authors: We acknowledge that an explicit cross-check against the standard self-dual Einstein equations with cosmological constant would strengthen the uniqueness statement. In the revised version we will insert a short verification subsection in §5 that substitutes the truncated fields into the derived equations, recovers the known self-dual gravity system, and confirms the absence of residual higher-spin source terms. revision: yes

Circularity Check

0 steps flagged

No significant circularity; truncation and emergence shown as explicit consequence of self-dual vertices

full rationale

The paper starts from the standard higher-spin algebra (including its Moyal product structure as input) and performs an explicit analysis of the self-dual interaction vertices in four dimensions. It then demonstrates by direct inspection that higher-spin fields (spin >2) can be consistently set to zero, leaving the helicity -2 to 0 sector closed while sourcing positive-helicity modes. The resulting equations for the lower-spin fields are identified and shown to reproduce self-dual gravity with cosmological constant. This reduction is presented as a derived property of the vertices rather than a definitional assumption or fitted parameter; no load-bearing step reduces by construction to its own output, and the Moyal product appears as the pre-existing algebra structure rather than a smuggled ansatz. The derivation chain is therefore self-contained against the higher-spin starting point.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the consistency of the self-dual truncation and on standard properties of the higher-spin algebra; no new free parameters or invented entities are introduced in the abstract.

axioms (2)

domain assumption Higher-spin symmetry mixes lower-spin and higher-spin fields with no closed finite sector in d>3
Stated as known background in the opening sentence of the abstract.
ad hoc to paper The self-dual part of interaction vertices permits consistent truncation of spins >2
This is the load-bearing step asserted without derivation in the abstract.

pith-pipeline@v0.9.0 · 5450 in / 1357 out tokens · 27384 ms · 2026-05-15T00:51:13.474409+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages · 13 internal anchors

[1]

M. A. Vasiliev,Higher spin gauge theories: Star product and AdS space,[arXiv:hep- th/9910096 [hep-th]]

work page arXiv
[2]

Introduction to the Classical Theory of Higher Spins

D. Sorokin,Introduction to the classical theory of higher spins,AIP Conf. Proc.767, no.1, 172-202 (2005) [arXiv:hep-th/0405069 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2005
[3]

Bekaert, S

X. Bekaert, S. Cnockaert, C. Iazeolla and M. A. Vasiliev,Nonlinear higher spin theories in various dimensions,[arXiv:hep-th/0503128 [hep-th]]

work page arXiv
[4]

V. E. Didenko and E. D. Skvortsov,Elements of Vasiliev Theory,Lect. Notes Phys.1028, 269-456 (2024) [arXiv:1401.2975 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2024
[5]

Ponomarev, Int

D. Ponomarev,Basic Introduction to Higher-Spin Theories,Int. J. Theor. Phys.62, no.7, 146 (2023) [arXiv:2206.15385 [hep-th]]

work page arXiv 2023
[6]

E. S. Fradkin and M. A. Vasiliev,Candidate to the Role of Higher Spin Symmetry,Annals Phys.177, 63 (1987)

work page 1987
[7]

M. G. Eastwood,Higher symmetries of the Laplacian,Annals Math.161, 1645-1665 (2005) [arXiv:hep-th/0206233 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2005
[8]

M. A. Vasiliev,Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B567, 139-151 (2003) [arXiv:hep-th/0304049 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2003
[9]

S. R. Coleman and J. Mandula,All Possible Symmetries of the S Matrix,Phys. Rev.159, 1251-1256 (1967)

work page 1967
[10]

Weinberg,Photons and Gravitons inS-Matrix Theory: Derivation of Charge Conser- vation and Equality of Gravitational and Inertial Mass,Phys

S. Weinberg,Photons and Gravitons inS-Matrix Theory: Derivation of Charge Conser- vation and Equality of Gravitational and Inertial Mass,Phys. Rev.135, B1049-B1056 (1964)

work page 1964
[11]

A. K. H. Bengtsson, I. Bengtsson and L. Brink,Cubic Interaction Terms for Arbitrary Spin,Nucl. Phys. B227, 31-40 (1983)

work page 1983
[12]

F. A. Berends, G. J. H. Burgers and H. van Dam,On the Theoretical Problems in Con- structing Interactions Involving Higher Spin Massless Particles,Nucl. Phys. B260, 295- 322 (1985)

work page 1985
[13]

E. S. Fradkin and M. A. Vasiliev,On the Gravitational Interaction of Massless Higher Spin Fields,Phys. Lett. B189, 89-95 (1987)

work page 1987
[14]

E. S. Fradkin and R. R. Metsaev,A Cubic interaction of totally symmetric massless rep- resentations of the Lorentz group in arbitrary dimensions,Class. Quant. Grav.8, L89-L94 (1991)

work page 1991
[15]

P. T. Kirakosiants, D. A. Valerev and M. A. Vasiliev,Quadratic corrections to the higher- spin equations by the differential homotopy approach,Nucl. Phys. B1023, 117290 (2026) [arXiv:2506.16634 [hep-th]]. 12

work page arXiv 2026
[16]

O. A. Gelfond and M. A. Vasiliev,Homotopy Operators and Locality Theorems in Higher- Spin Equations,Phys. Lett. B786, 180-188 (2018) [arXiv:1805.11941 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[17]

M. A. Vasiliev,More on equations of motion for interacting massless fields of all spins in (3+1)-dimensions,Phys. Lett. B285(1992), 225-234

work page 1992
[18]

V. E. Didenko, O. A. Gelfond, A. V. Korybut and M. A. Vasiliev,Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations,J. Phys. A51(2018) no.46, 465202 [arXiv:1807.00001 [hep-th]]

work page arXiv 2018
[19]

V. E. Didenko, O. A. Gelfond, A. V. Korybut and M. A. Vasiliev,Limiting Shifted Ho- motopy in Higher-Spin Theory and Spin-Locality,JHEP12(2019), 086 [arXiv:1909.04876 [hep-th]]

work page arXiv 2019
[20]

V. E. Didenko, O. A. Gelfond, A. V. Korybut and M. A. Vasiliev, Spin-locality ofη 2 and η2 quartic higher-spin vertices, JHEP12(2020), 184 [arXiv:2009.02811 [hep-th]]

work page arXiv 2020
[21]

O. A. Gelfond and A. V. Korybut,Manifest form of the spin-local higher-spin vertexΥ ηη ωCCC , Eur. Phys. J. C81(2021) no.7, 605 [arXiv:2101.01683 [hep-th]]

work page arXiv 2021
[22]

V. E. Didenko,On holomorphic sector of higher-spin theory,JHEP10, 191 (2022) [arXiv:2209.01966 [hep-th]]

work page arXiv 2022
[23]

A. V. Korybut,On consistency of the interacting (anti)holomorphic higher-spin sector, Eur. Phys. J. C85, no.8, 885 (2025) [arXiv:2505.13125 [hep-th]]

work page arXiv 2025
[24]

V. E. Didenko,Irregular higher-spin generating equations and chiral perturbation theory, [arXiv:2601.10680 [hep-th]]

work page arXiv
[25]

V. E. Didenko and M. A. Povarnin,All vertices for unconstrained symmetric gauge fields, Phys. Rev. D110, no.12, 126012 (2024) [erratum: Phys. Rev. D111, no.10, 109901 (2025)] [arXiv:2409.00808 [hep-th]]

work page arXiv 2024
[26]

J. F. Plebanski,Some solutions of complex Einstein equations,J. Math. Phys.16, 2395- 2402 (1975)

work page 1975
[27]

Chac´ on, H

E. Chac´ on, H. Garc´ ıa-Compe´ an, A. Luna, R. Monteiro and C. D. White,New heavenly double copies,JHEP03, 247 (2021) [arXiv:2008.09603 [hep-th]]

work page arXiv 2021
[28]

Self-Dual Gravity

K. Krasnov,Self-Dual Gravity,Class. Quant. Grav.34, no.9, 095001 (2017) [arXiv:1610.01457 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[29]

M. A. Vasiliev,Consistent Equations for Interacting Massless Fields of All Spins in the First Order in Curvatures,Annals Phys.190(1989), 59-106

work page 1989
[30]

Misuna,Unfolded dynamics approach and quantum field theory,JHEP12(2023), 119 [arXiv:2208.04306 [hep-th]]

N. Misuna,Unfolded dynamics approach and quantum field theory,JHEP12(2023), 119 [arXiv:2208.04306 [hep-th]]

work page arXiv 2023
[31]

Misuna,Scalar electrodynamics and Higgs mechanism in the unfolded dynamics ap- proach,JHEP12(2024), 090 [arXiv:2402.14164 [hep-th]]

N. Misuna,Scalar electrodynamics and Higgs mechanism in the unfolded dynamics ap- proach,JHEP12(2024), 090 [arXiv:2402.14164 [hep-th]]. 13

work page arXiv 2024
[32]

Misuna,Unfolded formulation of 4d Yang-Mills theory,Phys

N. Misuna,Unfolded formulation of 4d Yang-Mills theory,Phys. Lett. B870, 139882 (2025) [arXiv:2408.13212 [hep-th]]

work page arXiv 2025
[33]

Unfolded hypermultiplet in harmonic superspace

N. Misuna,Unfolded hypermultiplet in harmonic superspace,[arXiv:2603.19033 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv
[34]

Ammon and M

M. Ammon and M. Pannier,Unfolded Fierz-Pauli equations in three-dimensional asymp- totically flat spacetimes,JHEP02, 161 (2023) [arXiv:2211.12530 [hep-th]]

work page arXiv 2023
[35]

A. A. Tarusov and M. A. Vasiliev,Unfolded Point Particle as a Field in Minkowski Space, [arXiv:2301.03533 [hep-th]]

work page arXiv
[36]

Boulanger, PP

N. Boulanger, P. P. Cook, J. A. O’Connor and P. West,UnfoldingE 11,SciPost Phys.18, no.5, 149 (2025) [arXiv:2410.21206 [hep-th]]

work page arXiv 2025
[37]

Y. A. Tatarenko,Bilinear higher-spin currents in the unfolded formalism,Nucl. Phys. B 1021, 117205 (2025) [arXiv:2509.02364 [hep-th]]

work page arXiv 2025
[38]

Iazeolla, P

C. Iazeolla, P. Sundell and B. C. Vallilo,Unfolding the six-dimensional tensor multiplet, J. Phys. A58, no.36, 365402 (2025) [arXiv:2503.14673 [hep-th]]

work page arXiv 2025
[39]

M. A. Vasiliev,Triangle Identity and Free Differential Algebra of Massless Higher Spins, Nucl. Phys. B324, 503-522 (1989)

work page 1989
[40]

S. F. Prokushkin and M. A. Vasiliev,Higher spin gauge interactions for massive matter fields in 3-D AdS space-time,Nucl. Phys. B545, 385 (1999) [arXiv:hep-th/9806236 [hep- th]]

work page internal anchor Pith review Pith/arXiv arXiv 1999
[41]

M. P. Blencowe,A Consistent Interacting Massless Higher Spin Field Theory inD= (2+1),Class. Quant. Grav.6, 443 (1989)

work page 1989
[42]

Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields

A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen,Asymptotic symme- tries of three-dimensional gravity coupled to higher-spin fields,JHEP11, 007 (2010) [arXiv:1008.4744 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[43]

Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity

M. Henneaux and S. J. Rey,NonlinearW inf inity as Asymptotic Symmetry of Three- Dimensional Higher Spin Anti-de Sitter Gravity,JHEP12, 007 (2010) [arXiv:1008.4579 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[44]

Fredenhagen, F

S. Fredenhagen, F. Lausch and K. Mkrtchyan,Interactions of massless fermionic fields in three dimensions,Phys. Rev. D110, no.8, L081702 (2024) [arXiv:2404.00497 [hep-th]]

work page arXiv 2024
[45]

Sharapov, E

A. Sharapov, E. Skvortsov, A. Sukhanov and R. Van Dongen,More on Chiral Higher Spin Gravity and convex geometry,Nucl. Phys. B990, 116152 (2023) [arXiv:2209.15441 [hep-th]]

work page arXiv 2023
[46]

A. K. H. Bengtsson, I. Bengtsson and L. Brink,Cubic Interaction Terms for Arbitrarily Extended Supermultiplets,Nucl. Phys. B227, 41-49 (1983)

work page 1983
[47]

R. R. Metsaev,Poincare invariant dynamics of massless higher spins: Fourth order anal- ysis on mass shell,Mod. Phys. Lett. A6, 359-367 (1991) 14

work page 1991
[48]

R. R. Metsaev,Generating function for cubic interaction vertices of higher spin fields in any dimension,Mod. Phys. Lett. A8, 2413-2426 (1993)

work page 1993
[49]

Chiral Higher Spin Theories and Self-Duality

D. Ponomarev,Chiral Higher Spin Theories and Self-Duality,JHEP12, 141 (2017) [arXiv:1710.00270 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[50]

Serrani,On classification of (self-dual) higher-spin gravities in flat space,JHEP08, 032 (2025) [arXiv:2505.12839 [hep-th]]

M. Serrani,On classification of (self-dual) higher-spin gravities in flat space,JHEP08, 032 (2025) [arXiv:2505.12839 [hep-th]]

work page arXiv 2025
[51]

M. A. Vasiliev,Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations,JHEP10, 111 (2017) [arXiv:1605.02662 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[52]

V. E. Didenko and I. S. Faliakhov,Symmetry breaking in the self-dual higher-spin theory, Phys. Rev. D112, no.10, 106010 (2025) [arXiv:2509.01477 [hep-th]]

work page arXiv 2025
[53]

M. A. Vasiliev,Holography, Unfolding and Higher-Spin Theory,J. Phys. A46, 214013 (2013) [arXiv:1203.5554 [hep-th]]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[54]

F. Diaz, C. Iazeolla and P. Sundell,Fractional spins, unfolding, and holography. Part I. Parent field equations for dual higher-spin gravity reductions,JHEP09, 109 (2024) [arXiv:2403.02283 [hep-th]]

work page arXiv 2024
[55]

F. Diaz, C. Iazeolla and P. Sundell,Fractional spins, unfolding, and holography. Part II. 4D higher spin gravity and 3D conformal dual,JHEP10, 066 (2024) [arXiv:2403.02301 [hep-th]]

work page arXiv 2024
[56]

Lipstein and S

A. Lipstein and S. Nagy,Self-Dual Gravity and Color-Kinematics Duality in AdS4,Phys. Rev. Lett.131, no.8, 081501 (2023) [arXiv:2304.07141 [hep-th]]

work page arXiv 2023
[57]

Neiman,Higher-spin self-dual General Relativity: 6d and 4d pictures, covariant vs

Y. Neiman,Higher-spin self-dual General Relativity: 6d and 4d pictures, covariant vs. lightcone,JHEP07, 178 (2024) [arXiv:2404.18589 [hep-th]]. 15

work page arXiv 2024