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Higher-spins on Taub-NUT and higher-spin Taub-NUT

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Taub-NUT instantons admit higher-spin extensions; in self-dual gravity the perturbation series converges for each spin and is governed by a commutative non-associative algebra.

desk verdict New Taub-NUT higher-spin instantons with a terminating perturbation theory; the positive-helicity construction is solid, the negative-helicity side is honestly flagged as a conjecture. read the letter →

arxiv 2508.18804 v1 pith:XS4WJHFE submitted 2025-08-26 hep-th

Evgeny Skvortsov , Yihao Yin This is my paper
classification hep-th
keywords higher-spingravityself-dualYang-MillsTaub-NUTgravitationalinstantonschiralnon-associativealgebra
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Massless fields of any spin are notoriously hard to put on curved backgrounds—the usual symmetric-tensor description fails away from maximally symmetric spaces—but this paper works with self-dual higher-spin theories, which are flexible enough to live on self-dual gravitational instantons. It constructs explicit free higher-spin solutions on the Taub-NUT instanton, shows they remain exact solutions when the interactions are of Yang-Mills type (HS-SDYM), and shows that in the gravitational version (HS-SDGR) nonlinear corrections build a genuine higher-spin generalization of Taub-NUT. The central positive result is that for any chosen spin the perturbation series terminates after finitely many steps, with every step bookkept by a commutative non-associative algebra whose product encodes the source structure; negative-helicity fields form a representation of that algebra, with full all-orders consistency left as a conjecture. If correct, this provides a concrete higher-spin instanton and a template for how higher-spin corrections organize around non-trivial backgrounds.

What carries the argument

The machinery is a commutative but non-associative algebra on basis elements V^m_s, where s indexes the weight s-2 of a spin-s field and m counts extra inverse powers of V beyond the free solution. Its product (3.43), V^{m1}_{s1} circle V^{m2}_{s2} = f^1 V^{m1+m2+1}_{s1+s2} + f^2 V^{m1+m2+2}_{s1+s2}, with the structure constants f^1 and f^2 given in (3.44), is exactly the rule for what one interaction step does to two monomial sources. The product is non-associative, so different bracketings of the same initial fields yield genuinely different intermediate corrections; the full solution therefore requires summing over all binary-tree bracketings, which is what makes the expansion intricate.

What would settle it

Calculate the third-order HS-SDGR source from three free monomials in (B.1), or run the third-order negative-helicity consistency check (3.63) with unequal spins: any departure from the two allowed V-power terms, or any mismatch between the two equations (3.58), would overturn the claimed convergence.

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Extended reading notes

Core claim

The paper's central claim is that Taub-NUT, the classic self-dual gravitational instanton, can be consistently embedded into the higher-spin extensions of self-dual Yang-Mills and self-dual gravity. For free fields, negative-helicity solutions take the form Psi = kappa_s(rho) u^s with kappa_s ~ rho^{-s-1/2}, and positive-helicity potentials are Phi = u^{s-1} w sigma_s with sigma_s = V^{-1/2}, where V is the harmonic function defining the Taub-NUT geometry in the Gibbons-Hawking ansatz. In HS-SDYM these linearized solutions solve the full nonlinear equations because the Yang-Mills-type interaction source vanishes. In HS-SDGR the source does not vanish; the paper solves the equations order by

Load-bearing premise

The construction rests on the assumption that every nonlinear correction stays inside the same simple power-of-V ansatz as the free solution—no new functional forms ever appear—and separately on the conjecture that the two negative-helicity equations remain consistent to all orders.

Editorial extensions

If this is right

  • Every free higher-spin solution found on Taub-NUT is automatically a solution of the full HS-SDYM equations, so in the Yang-Mills-type sector the higher-spin Taub-NUT is exact with no backreaction.
  • In HS-SDGR, for any fixed spin the perturbative series terminates at finite order: higher spins receive contributions only from lower-weight sources, never the reverse.
  • The entire positive-helicity solution space is parameterized by the free coefficients c_{s,0}, and the generating function F(t) obeys the flow equation dF/dt = F circle F, giving a combinatorial handle on solutions.
  • Because HS-SDYM and HS-SDGR are truncations of chiral higher-spin gravity, the solutions lie in its self-dual sector and are candidates for an uplift to the full theory.
  • Negative-helicity fields in HS-SDGR form a representation of the same algebra; first- and second-order consistency checks pass, and proving all-orders consistency of the two defining equations (3.58) is the remaining open step.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the same ansatz closes, the algebraic scheme is a natural testbed for other Gibbons-Hawking instantons such as Eguchi-Hanson or multi-center geometries; the basis elements would remain powers of the harmonic function V, but that closure is not automatic and would have to be checked.
  • The flow equation dF/dt = F circle F suggests treating the full solution as a formal non-associative exponential of F; an enveloping associative algebra, if one exists, could resum the binary-tree series into a closed-form field profile.
  • The sharpest test of the negative-helicity representation is third-order consistency with unequal source spins: any mismatch between the two equations (3.58) would signal that the representation needs extra generators or that the two helicity sectors decouple beyond leading order.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper constructs higher-spin fields on the Taub-NUT gravitational instanton within the HS-SDYM and HS-SDGR truncations of chiral higher-spin gravity. After setting up the Gibbons-Hawking ansatz and free higher-spin equations, the authors find explicit free-field solutions: positive-helicity potentials with σ_s = V^{-1/2} and negative-helicity fields κ_s ~ ρ^{-s-1/2}. For HS-SDYM they show that these free solutions remain exact because the nonlinear source vanishes by the structure identities (3.23). For HS-SDGR the positive-helicity part is developed as a perturbation series: the equation (3.40) is sourced by pairs of lower-spin fields, the weight hierarchy implies convergence/termination for each spin, and the one-step monomial response (3.42) is promoted to a commutative algebra with product (3.43)-(3.44). Negative-helicity fields are treated via a representation action (3.62), with consistency of the two equations (3.58) verified only at low orders and left as a conjecture. The paper concludes that HS-SDGR admits higher-spin Taub-NUT solutions governed by a commutative non-associative algebra.

Significance. If the constructions are fully established, the paper gives the first explicit nonlinear higher-spin instantons on a non-trivial self-dual background and cleanly demonstrates the different roles of Yang-Mills-type versus gravitational-type interactions in the chiral higher-spin framework. The positive-helicity part is explicit and structurally credible: the source recursion (3.40), the monomial response (3.42), the closed-form recursion in Appendix B.1, and the weight-hierarchy termination argument are all written out. The HS-SDYM exactness is a concrete vanishing computation. The proposed algebra (3.43) is a suggestive and potentially useful organizational device. However, two load-bearing points are not proven: the all-orders closure of the monomial ansatz, and the higher-order consistency of the negative-helicity system. The claim of non-associativity is also asserted without demonstration. These gaps currently prevent the paper from fully supporting its abstract claims, though they appear fixable within the manuscript's scope.

major comments (3)
  1. The all-orders closure of the monomial ansatz is asserted but not proved. Equation (3.42) is a one-step computation for two generic monomials, and the sentence 'It can easily be checked that the pattern persists' is not a proof. The termination argument ('each tree has at most ŝ leaves') and the algebra description (3.43) both inherit their validity from this closure. The gap is avoidable: Eq. (B.1) is a first-order linear ODE for σ_s whose source is quadratic in lower-weight σ's. If, by induction, every lower-spin σ is a finite sum of monomials V^{-1/2-m}, the source is V^{-3/2} times a polynomial in V^{-1}, and the integrating-factor solution (B.4) preserves that class. Please replace the 'easily checked' statement with this induction, or an equivalent proof.
  2. The algebra is called 'commutative non-associative', but no associator is computed and non-associativity is not demonstrated. This is part of the abstract's headline claim. Please provide a concrete associator evaluation, e.g. (V^0_1 ◦ V^0_1) ◦ V^0_1 versus V^0_1 ◦ (V^0_1 ◦ V^0_1), or a general proof. If the product turns out to be associative in some sector, the claim should be adjusted accordingly.
  3. The negative-helicity solution rests on a conjecture that is explicitly flagged in the text: 'We leave the higher order consistency as a conjecture.' The two equations (3.58) are verified to agree at first order, and the text says that second-order consistency 'supports, but does not prove' the general statement. Since the full HS-SDGR solution includes negative-helicity fields, this conjecture is load-bearing for the central claim. Please either supply an induction argument for consistency of the two equations for all orders, or clearly delimit the main theorem as requiring that assumption. If consistency can fail at some order, the representation action (3.62) would need revision.
minor comments (4)
  1. The phrase 'It can easily be checked that the pattern persists' should be replaced by the actual induction argument; this is both a mathematical gap and a presentation issue.
  2. The hatted spin notation (ŝ = s-2) is used before being explicitly defined. Please define it at first use, e.g. after Eq. (3.40), to avoid confusion when reading (3.45).
  3. Minor typos: 'It is then can be checked' should be 'It can then be checked'; in Eq. (3.61) the expression for κ_{s-n+2} omits the dependence on g_{s,n} in the displayed prefactor but includes it in (3.62), so the notation should be made consistent.
  4. Since the product is claimed to be non-associative, the expansion (3.48) relies on an arbitrarily chosen bracketing convention for the higher-order terms. Specify that the displayed sums include all distinct bracketings, or state a bracketing convention explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the perturbative solution is derived from the equations of motion; the algebra (3.43) is a bookkeeping formalization of the derived recursion, and the explicit conjectures/limitations are about missing proofs, not circular inputs.

full rationale

The paper's central derivation is self-contained. The free solution σ_s = V^{-1/2} is obtained by solving Eq. (2.22), giving Eq. (2.23). The nonlinear positive-helicity equation (3.40) is reduced to the linear ODE (B.1), whose solution is given in closed form (B.4); feeding two monomials σ_{s_i} ∝ V^{-1/2-m_i} produces exactly the two monomials displayed in (3.42). The algebra (3.43) is introduced explicitly to "formalize what happens in the perturbation theory," with structure constants copied from (3.42); it is a repackaging of the derived recursion, not an independent input, so there is no self-definitional or fitted-input circularity. The termination of the series for fixed spin follows from the additive weight ŝ = ŝ1 + ŝ2: any binary tree building spin ŝ has at most ŝ leaves, and each tree contribution is a finite monomial by the induction supplied by (B.1). The HS-SDYM exactness is a direct vanishing computation, Eq. (3.23). The paper explicitly flags the places where it is not proving something: Section 3.3.1 asserts "It can easily be checked that the pattern persists" rather than spelling out the induction, and Section 3.3.2 states "We leave the higher order consistency as a conjecture" for the two negative-helicity equations (3.58). These are limitations or omitted proofs, not circularity. Prior self-citations ([24], [35], [46]) supply the theory definitions and earlier examples, but the Taub-NUT construction itself is computed here from those equations; none of the load-bearing steps reduces to a self-citation. Score 0 reflects the absence of circularity while noting the unproven induction/conjecture flags.

Assumptions & free parameters 2 free parameters · 6 assumptions · 2 invented entities

No parameter is fitted to data and relabeled as a prediction. The c_{s,0} are honest moduli of the solution family; α is a bookkeeping coupling introduced in (3.40). The load-bearing assumptions are: the self-dual background framework that makes higher-spin propagation consistent at all (Section 2), the monomial ansatz closure on which the entire perturbative construction rests ((3.34), (3.42)), the source-weight hierarchy s = s1 + s2 − 2 that yields termination, the Chan-Paton color restriction that makes the HS-SDYM negative-helicity source vanish, and the conjectural higher-order consistency of the negative-helicity equations (3.58). The Taub-NUT background data (m, v0, a) are inputs, and the normalizations (Appendix A: α_s = 1, β_s = −1/4, a_{s1,s2} = 1) are conventions inherited from the chiral theory.

free parameters (2)
  • c_{s,0}: coefficients in front of the free solutions = arbitrary; infinitely many
    Equation (3.47): F = Σ c_{s,0}V^0_s. These are the moduli of the higher-spin Taub-NUT family, chosen by hand to select a solution, not fitted to data.
  • α: formal coupling constant = unspecified; α^{-1} small
    Introduced at (3.40) to organize perturbation theory over the fixed background. Its value does not affect the termination or algebra structure.
assumptions (6)
  • domain assumption Free higher-spin equations (2.1)-(2.3) and the action (2.8) are gauge-invariant on any self-dual background with Ψ_ABCD = 0.
    Section 2, after (2.4): gauge invariance requires ∇AM'∇AM'χA ∼ ΨAAABχB. Taub-NUT satisfies this (Ψ_AAAA = 0, Section 1). The whole construction lives in the self-dual sector.
  • domain assumption HS-SDYM (3.17)-(3.18) and HS-SDGR (3.25) with couplings a_{s1,s2} = a_{2,s} = 1, fixed by Appendix A to match chiral higher-spin gravity.
    The objects of study are defined by these actions, taken from prior work [24], [25]. The specific normalization (α_s = 1, β_s = -1/4, Appendix A) is a convention; the paper's claims concern these specific theories.
  • ad hoc to paper The single-radial-function ansatz: positive-helicity potentials take the form Φ = u^{s-1}wσ_s(ρ) (3.34), u = (yξy), w = (ȳy).
    The free solution (2.23) is found within this ansatz, and the nonlinear construction (3.34)-(3.42) assumes the corrections stay in the same class ('nothing else pops up', Section 3.3.1). This is the load-bearing structural assumption; see also (2.19) and (2.14).
  • domain assumption The source hierarchy s = s1 + s2 − 2, with spin-2 frozen as the background, so a weight-ŝ field is sourced only by fields of strictly smaller weight.
    Section 3.3.1 and positive-helicity EOM (3.30)-(3.31). The termination of the perturbation theory for each spin rests on this grading. The spin-2 freeze is argued in Section 3.1 via the Stueckelberg and diffeomorphism link (3.15)-(3.16).
  • domain assumption For HS-SDYM negative helicity, the field Ψ must commute with all ω's (Chan-Paton color with the graviton as the unit matrix) for the source to vanish.
    Section 3.2, negative helicity: the source tensor structure is incompatible with the free field, so the paper requires Ψ to live in the subspace commuting with all ωs. This restricts the solution class.
  • ad hoc to paper Higher-order consistency of the two negative-helicity equations (3.58) is assumed (verified at first order, checked at second order).
    Section 3.3.2: the paper explicitly leaves higher-order consistency as a conjecture ('We leave the higher order consistency as a conjecture.'). The representation (3.62) and the Ψ-side of the story depend on it.
invented entities (2)
  • Commutative non-associative algebra A (basis V^m_s, product ◦)
    purpose: Encodes one round of the HS-SDGR perturbation theory as a product of generators; ∂_tF = F◦F packages all orders (3.43)-(3.50).
    The product is defined to reproduce the derived monomial response (3.42), so it is a reformulation of the recursion rather than an independently evidenced object. Its non-associativity is asserted but not demonstrated.
  • Negative-helicity representation action U^k_s ⊲ V^m_j (3.62)
    purpose: Bookkeeping for the negative-helicity response to positive-helicity sources.
    Defined to match the first-order solution (3.61); consistent through second order, conjectural at higher orders per the paper's own statement.

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Pith. "Pith review of Higher-spins on Taub-NUT and higher-spin Taub-NUT." pith.science (2026). https://pith.science/paper/XS4WJHFE

@misc{pith2026250818804,
  author       = {Pith},
  title        = {Pith review of: Higher-spins on Taub-NUT and higher-spin Taub-NUT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XS4WJHFE}},
  note         = {Machine review of arXiv:2508.18804}
}
read the original abstract

We consider higher-spin extensions of self-dual Yang-Mills (HS-SDYM) and self-dual Gravity (HS-SDGR), which are also truncations of chiral higher-spin gravity. Higher-spin fields can consistently propagate on gravitational instantons and we construct solutions to the higher-spin equations on the Taub-NUT background. We show that these solutions remain exact solutions of HS-SDYM. For HS-SDGR the perturbation theory converges for any given spin to give a higher-spin generalization of Taub-NUT and we identify a commutative non-associative algebra that governs the structure of the perturbation theory.

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Forward citations

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Reference graph

Works this paper leans on

72 extracted references · 29 canonical work pages · cited by 5 Pith papers

  1. [1]

    Interacting Higher Spin Gauge Fields on the Light Front,

    A. K. H. Bengtsson, I. Bengtsson, and N. Linden, “Interacting Higher Spin Gauge Fields on the Light Front,” Class. Quant. Grav.4 (1987) 1333

    work page 1987

  2. [2]

    Light-cone gauge cubic interaction vertices for massless fields in AdS(4),

    R. R. Metsaev, “Light-cone gauge cubic interaction vertices for massless fields in AdS(4),” Nucl. Phys. B936 (2018) 320–351, arXiv:1807.07542 [hep-th]

    arXiv 2018

  3. [3]

    A Consistent Interacting Massless Higher Spin Field Theory in D = (2+1),

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

    work page 1989

  4. [4]

    Area Preserving Diffeomorphisms and Higher Spin Algebra,

    E. Bergshoeff, M. P. Blencowe, and K. S. Stelle, “Area Preserving Diffeomorphisms and Higher Spin Algebra,” Commun. Math. Phys.128 (1990) 213

    work page 1990

  5. [5]

    Conformal Higher Spin in (2+1)-dimensions,

    C. N. Pope and P. K. Townsend, “Conformal Higher Spin in (2+1)-dimensions,” Phys. Lett.B225 (1989) 245–250

    work page 1989

  6. [6]

    A Superconformal Theory of Massless Higher Spin Fields in D = (2+1),

    E. S. Fradkin and V. Ya. Linetsky, “A Superconformal Theory of Massless Higher Spin Fields in D = (2+1),” Mod. Phys. Lett.A4 (1989) 731. [Annals Phys.198,293(1990)]

    work page 1989

  7. [7]

    New Conformal Higher Spin Gravities in 3 d,

    M. Grigoriev, I. Lovrekovic, and E. Skvortsov, “New Conformal Higher Spin Gravities in 3 d,” JHEP 01 (2020) 059, arXiv:1909.13305 [hep-th]. 27

    arXiv 2020

  8. [8]

    Matter-free higher spin gravities in 3D: Partially-massless fields and general structure,

    M. Grigoriev, K. Mkrtchyan, and E. Skvortsov, “Matter-free higher spin gravities in 3D: Partially-massless fields and general structure,” Phys. Rev. D102 no. 6, (2020) 066003, arXiv:2005.05931 [hep-th]

    arXiv 2020

Show all 72 references
  1. [9]

    Conformal higher spin theory,

    A. Y. Segal, “Conformal higher spin theory,” Nucl. Phys. B664 (2003) 59–130, arXiv:hep-th/0207212 [hep-th]

    2003 arXiv

  2. [10]

    On limits of superstring in AdS5 × S5,

    A. A. Tseytlin, “On limits of superstring in AdS5 × S5,” Theor. Math. Phys.133 (2002) 1376–1389, arXiv:hep-th/0201112 [hep-th]. [Teor. Mat. Fiz.133,69(2002)]

    2002 arXiv

  3. [11]

    Effective action in a higher-spin background,

    X. Bekaert, E. Joung, and J. Mourad, “Effective action in a higher-spin background,” JHEP 02 (2011) 048, arXiv:1012.2103 [hep-th]

    2011 arXiv

  4. [12]

    Poincare invariant dynamics of massless higher spins: Fourth order analysis on mass shell,

    R. R. Metsaev, “Poincare invariant dynamics of massless higher spins: Fourth order analysis on mass shell,” Mod. Phys. Lett.A6 (1991) 359–367

    1991

  5. [13]

    S matrix approach to massless higher spins theory. 2: The Case of internal symmetry,

    R. R. Metsaev, “ S matrix approach to massless higher spins theory. 2: The Case of internal symmetry,” Mod. Phys. Lett.A6 (1991) 2411–2421

    1991

  6. [14]

    Light-Front Higher-Spin Theories in Flat Space,

    D. Ponomarev and E. D. Skvortsov, “Light-Front Higher-Spin Theories in Flat Space,” J. Phys. A50 no. 9, (2017) 095401, arXiv:1609.04655 [hep-th]

    2017 arXiv

  7. [15]

    Quantum Chiral Higher Spin Gravity,

    E. D. Skvortsov, T. Tran, and M. Tsulaia, “Quantum Chiral Higher Spin Gravity,” Phys. Rev. Lett.121 no. 3, (2018) 031601, arXiv:1805.00048 [hep-th]

    2018 arXiv

  8. [16]

    More on Quantum Chiral Higher Spin Gravity,

    E. Skvortsov, T. Tran, and M. Tsulaia, “More on Quantum Chiral Higher Spin Gravity,” Phys. Rev. D101 no. 10, (2020) 106001, arXiv:2002.08487 [hep-th]

    2020 arXiv

  9. [17]

    Chiral higher spin gravity in (A)dS4 and secrets of Chern–Simons matter theories,

    A. Sharapov and E. Skvortsov, “Chiral higher spin gravity in (A)dS4 and secrets of Chern–Simons matter theories,” Nucl. Phys. B985 (2022) 115982, arXiv:2205.15293 [hep-th]

    2022 arXiv

  10. [18]

    Snowmass White Paper: Higher Spin Gravity and Higher Spin symmetry,

    X. Bekaert, N. Boulanger, A. Campoleoni, M. Chiodaroli, D. Francia, M. Grigoriev, E. Sezgin, and E. Skvortsov, “Snowmass White Paper: Higher Spin Gravity and Higher Spin symmetry,” arXiv:2205.01567 [hep-th]

    arXiv

  11. [19]

    Photons and Gravitons in S Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass,

    S. Weinberg, “Photons and Gravitons in S Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass,” Phys. Rev.135 (1964) B1049–B1056

    1964

  12. [20]

    Constraining higher-spin S-matrices,

    T. Tran, “Constraining higher-spin S-matrices,” JHEP 02 (2023) 001, arXiv:2212.02540 [hep-th]

    2023 arXiv

  13. [21]

    Higher-spin Yang–Mills, amplitudes and self-duality,

    T. Adamo and T. Tran, “Higher-spin Yang–Mills, amplitudes and self-duality,” Lett. Math. Phys.113 no. 3, (2023) 50, arXiv:2210.07130 [hep-th]

    2023 arXiv

  14. [22]

    Massless fields with integer spin,

    C. Fronsdal, “Massless fields with integer spin,” Phys. Rev.D18 (1978) 3624

    1978

  15. [23]

    Consistency Problems of Hypergravity,

    C. Aragone and S. Deser, “Consistency Problems of Hypergravity,” Phys. Lett.B86 (1979) 161

    1979

  16. [24]

    Actions for Self-dual Higher Spin Gravities,

    K. Krasnov, E. Skvortsov, and T. Tran, “Actions for Self-dual Higher Spin Gravities,” arXiv:2105.12782 [hep-th]

    arXiv

  17. [25]

    Chiral Higher Spin Theories and Self-Duality,

    D. Ponomarev, “Chiral Higher Spin Theories and Self-Duality,” JHEP 12 (2017) 141, arXiv:1710.00270 [hep-th]

    2017 arXiv

  18. [26]

    From Moyal deformations to chiral higher-spin theories and to celestial algebras,

    R. Monteiro, “From Moyal deformations to chiral higher-spin theories and to celestial algebras,” JHEP 03 (2023) 062, arXiv:2212.11266 [hep-th]

    2023 arXiv

  19. [27]

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

    Y. Neiman, “Higher-spin self-dual General Relativity: 6d and 4d pictures, covariant vs. lightcone,” JHEP 07 (2024) 178, arXiv:2404.18589 [hep-th]. 28

    2024 arXiv

  20. [28]

    Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills,

    T. Tran, “Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills,” JHEP 11 (2021) 117, arXiv:2107.04500 [hep-th]

    2021 arXiv

  21. [29]

    Toward a twistor action for chiral higher-spin gravity,

    T. Tran, “Toward a twistor action for chiral higher-spin gravity,” Phys. Rev. D107 no. 4, (2023) 046015, arXiv:2209.00925 [hep-th]

    2023 arXiv

  22. [30]

    Anomaly-free twistorial higher-spin theories,

    T. Tran, “Anomaly-free twistorial higher-spin theories,” arXiv:2505.13785 [hep-th]

  23. [31]

    Chiral higher-spin theories from twistor space,

    L. Mason and A. Sharma, “Chiral higher-spin theories from twistor space,” arXiv:2505.09419 [hep-th]

    arXiv

  24. [32]

    Hidden sectors of Chern-Simons matter theories and exact holography,

    S. Jain, D. K. S, and E. Skvortsov, “Hidden sectors of Chern-Simons matter theories and exact holography,” Phys. Rev. D111 no. 10, (2025) 106017, arXiv:2405.00773 [hep-th]

    2025

  25. [33]

    A chiral limit for Chern-Simons-matter theories,

    O. Aharony, R. R. Kalloor, and T. Kukolj, “A chiral limit for Chern-Simons-matter theories,” JHEP 10 (2024) 051, arXiv:2405.01647 [hep-th]

    2024 arXiv

  26. [34]

    Higher-spin self-dual Yang-Mills and gravity from the twistor space,

    Y. Herfray, K. Krasnov, and E. Skvortsov, “Higher-spin self-dual Yang-Mills and gravity from the twistor space,” JHEP 01 (2023) 158, arXiv:2210.06209 [hep-th]

    2023 arXiv

  27. [35]

    Low spin solutions of higher spin gravity: BPST instanton,

    E. Skvortsov and Y. Yin, “Low spin solutions of higher spin gravity: BPST instanton,” JHEP 07 (2024) 032, arXiv:2403.17148 [hep-th]

    2024 arXiv

  28. [36]

    Pseudoparticle Solutions of the Yang-Mills Equations,

    A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Y. S. Tyupkin, “Pseudoparticle Solutions of the Yang-Mills Equations,” Phys. Lett. B59 (1975) 85–87

    1975

  29. [37]

    Self-dual pp-wave solutions in chiral higher-spin gravity,

    T. Tran, “Self-dual pp-wave solutions in chiral higher-spin gravity,” arXiv:2501.06445 [hep-th]

  30. [38]

    Empty space-times admitting a three parameter group of motions,

    A. H. Taub, “Empty space-times admitting a three parameter group of motions,” Annals Math. 53 (1951) 472–490

    1951

  31. [39]

    Empty space generalization of the Schwarzschild metric,

    E. Newman, L. Tamburino, and T. Unti, “Empty space generalization of the Schwarzschild metric,” J. Math. Phys. 4 (1963) 915

    1963

  32. [40]

    Bulk interactions and boundary dual of higher-spin-charged particles,

    A. David and Y. Neiman, “Bulk interactions and boundary dual of higher-spin-charged particles,” JHEP 03 (2021) 264, arXiv:2009.02893 [hep-th]

    2021 arXiv

  33. [41]

    Bulk locality and gauge invariance for boundary-bilocal cubic correlators in higher-spin gravity,

    V. Lysov and Y. Neiman, “Bulk locality and gauge invariance for boundary-bilocal cubic correlators in higher-spin gravity,” JHEP 12 (2022) 142, arXiv:2209.00854 [hep-th]

    2022 arXiv

  34. [42]

    Higher-spin gravity’s “string

    V. Lysov and Y. Neiman, “Higher-spin gravity’s “string”: new gauge and proof of holographic duality for the linearized Didenko-Vasiliev solution,” JHEP 10 (2022) 054, arXiv:2207.07507 [hep-th]

    2022 arXiv

  35. [43]

    Families of exact solutions to Vasiliev’s 4D equations with spherical, cylindrical and biaxial symmetry,

    C. Iazeolla and P. Sundell, “Families of exact solutions to Vasiliev’s 4D equations with spherical, cylindrical and biaxial symmetry,” JHEP 12 (2011) 084, arXiv:1107.1217 [hep-th]

    2011 arXiv

  36. [44]

    Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity,

    Y. Herfray, “Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity,” J. Math. Phys.58 no. 11, (2017) 112505, arXiv:1610.02343 [hep-th]

    2017 arXiv

  37. [45]

    Self-Dual Gravity,

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

    2017 arXiv

  38. [46]

    Flat self-dual gravity,

    K. Krasnov and E. Skvortsov, “Flat self-dual gravity,” JHEP 08 (2021) 082, arXiv:2106.01397 [hep-th]

    2021 arXiv

  39. [47]

    Gravitational Multi - Instantons,

    G. W. Gibbons and S. W. Hawking, “Gravitational Multi - Instantons,” Phys. Lett. B78 (1978) 430

    1978

  40. [48]

    Rod Structures and Patching Matrices: a review,

    P. Tod, “Rod Structures and Patching Matrices: a review,” arXiv:2411.02096 [math.DG]. 29

  41. [49]

    Zero rest mass fields including gravitation: Asymptotic behavior,

    R. Penrose, “Zero rest mass fields including gravitation: Asymptotic behavior,” Proc. Roy. Soc. Lond. A284 (1965) 159

    1965

  42. [50]

    Selfdual Solutions to Euclidean Gravity,

    T. Eguchi and A. J. Hanson, “Selfdual Solutions to Euclidean Gravity,” Annals Phys. 120 (1979) 82

    1979

  43. [51]

    Asymptotically Flat Selfdual Solutions to Euclidean Gravity,

    T. Eguchi and A. J. Hanson, “Asymptotically Flat Selfdual Solutions to Euclidean Gravity,” Phys. Lett. B 74 (1978) 249–251

    1978

  44. [52]

    Linear field equations on selfdual spaces,

    N. J. Hitchin, “Linear field equations on selfdual spaces,” Proc. Roy. Soc. Lond.A370 (1980) 173–191

    1980

  45. [53]

    Real methods in twistor theory,

    N. M. J. Woodhouse, “Real methods in twistor theory,” Class. Quant. Grav.2 (1985) 257–291

    1985

  46. [54]

    The Selfdual sector of QCD amplitudes,

    G. Chalmers and W. Siegel, “The Selfdual sector of QCD amplitudes,” Phys. Rev.D54 (1996) 7628–7633, arXiv:hep-th/9606061 [hep-th]

    1996 arXiv

  47. [55]

    Selfdual N=8 supergravity as closed N=2 (N=4) strings,

    W. Siegel, “Selfdual N=8 supergravity as closed N=2 (N=4) strings,” Phys. Rev.D47 (1993) 2504–2511, arXiv:hep-th/9207043 [hep-th]

    1993 arXiv

  48. [56]

    On classification of (self-dual) higher-spin gravities in flat space,

    M. Serrani, “On classification of (self-dual) higher-spin gravities in flat space,” JHEP 08 (2025) 032, arXiv:2505.12839 [hep-th]

    2025 arXiv

  49. [57]

    Extended higher spin superalgebras and their massless representations,

    S. E. Konstein and M. A. Vasiliev, “Extended higher spin superalgebras and their massless representations,” Nucl. Phys. B331 (1990) 475–499

    1990

  50. [58]

    Coagulation, non-associative algebras and binary trees,

    S. J. Malham, “Coagulation, non-associative algebras and binary trees,” Physica D: Nonlinear Phenomena 460 (2024) 134054. https://www.sciencedirect.com/science/article/pii/S0167278924000058

    2024

  51. [59]

    Spacetime Geometry in Higher Spin Gravity,

    M. Ammon, M. Gutperle, P. Kraus, and E. Perlmutter, “Spacetime Geometry in Higher Spin Gravity,” JHEP 10 (2011) 053, arXiv:1106.4788 [hep-th]

    2011 arXiv

  52. [60]

    Geometry and Observables in Vasiliev’s Higher Spin Gravity,

    E. Sezgin and P. Sundell, “Geometry and Observables in Vasiliev’s Higher Spin Gravity,” JHEP 07 (2012) 121, arXiv:1103.2360 [hep-th]

    2012 arXiv

  53. [61]

    Inconsistency of point-particle dynamics on higher-spin backgrounds,

    V. Ivanovskiy and D. Ponomarev, “Inconsistency of point-particle dynamics on higher-spin backgrounds,” JHEP 07 (2025) 040, arXiv:2503.11546 [hep-th]

    2025 arXiv

  54. [62]

    Inconsistency of point-particle dynamics on higher-spin backgrounds: massive particles,

    V. Ivanovskiy and D. Ponomarev, “Inconsistency of point-particle dynamics on higher-spin backgrounds: massive particles,” arXiv:2506.13976 [hep-th]

    arXiv

  55. [63]

    Real forms of complex higher spin field equations and new exact solutions,

    C. Iazeolla, E. Sezgin, and P. Sundell, “Real forms of complex higher spin field equations and new exact solutions,” Nucl. Phys. B791 (2008) 231–264, arXiv:0706.2983 [hep-th]

    2008 arXiv

  56. [64]

    Light-Front Bootstrap for Chern-Simons Matter Theories,

    E. Skvortsov, “Light-Front Bootstrap for Chern-Simons Matter Theories,” JHEP 06 (2019) 058, arXiv:1811.12333 [hep-th]

    2019 arXiv

  57. [65]

    AdS dual of the critical O(N ) vector model,

    I. R. Klebanov and A. M. Polyakov, “AdS dual of the critical O(N ) vector model,” Phys. Lett.B550 (2002) 213–219, arXiv:hep-th/0210114

    2002 arXiv

  58. [66]

    Massless higher spins and holography,

    E. Sezgin and P. Sundell, “Massless higher spins and holography,” Nucl.Phys. B644 (2002) 303–370, arXiv:hep-th/0205131 [hep-th]

    2002 arXiv

  59. [67]

    Holography of the N=1 higher spin theory on AdS(4),

    R. G. Leigh and A. C. Petkou, “Holography of the N=1 higher spin theory on AdS(4),” JHEP 0306 (2003) 011, arXiv:hep-th/0304217 [hep-th]

    2003 arXiv

  60. [68]

    Chern-Simons Theory with Vector Fermion Matter,

    S. Giombi, S. Minwalla, S. Prakash, S. P. Trivedi, S. R. Wadia, and X. Yin, “Chern-Simons Theory with Vector Fermion Matter,” Eur. Phys. J.C72 (2012) 2112, arXiv:1110.4386 [hep-th]. 30

    2012 arXiv

  61. [69]

    Moyal deformations, W 1+∞ and celestial holography,

    W. Bu, S. Heuveline, and D. Skinner, “Moyal deformations, W 1+∞ and celestial holography,” JHEP 12 (2022) 011, arXiv:2208.13750 [hep-th]

    2022 arXiv

  62. [70]

    The celestial chiral algebra of self-dual gravity on Eguchi-Hanson space,

    R. Bittleston, S. Heuveline, and D. Skinner, “The celestial chiral algebra of self-dual gravity on Eguchi-Hanson space,” JHEP 09 (2023) 008, arXiv:2305.09451 [hep-th]

    2023 arXiv

  63. [71]

    Scattering on self-dual Taub-NUT,

    T. Adamo, G. Bogna, L. Mason, and A. Sharma, “Scattering on self-dual Taub-NUT,” Class. Quant. Grav. 41 no. 1, (2024) 015030, arXiv:2309.03834 [hep-th]

    2024 arXiv

  64. [72]

    Graviton scattering on self-dual black holes,

    T. Adamo, G. Bogna, L. Mason, and A. Sharma, “Graviton scattering on self-dual black holes,” arXiv:2507.18605 [hep-th]. 31

    arXiv

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