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REVIEW 2 major objections 1 minor 105 references

$N$-body modelling of the ED-2 stream progenitor shows Gaia BH3's formation involved dynamical interactions

T0 review · 2 major / 1 minor · reviewed 2026-07-01 · grok-4.3

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Pith's one-line read N-body modeling shows Gaia BH3 formed as an exchange binary through multiple dynamical interactions in the ED-2 progenitor cluster.

desk verdict N-body runs of the ED-2 progenitor favor dynamical exchange for Gaia BH3 over isolated evolution, but the result may depend on the specific initial conditions chosen. read the letter →

arxiv 2604.24874 v2 pith:RWIZ4KLQ submitted 2026-04-27 astro-ph.GA astro-ph.SR

Daniel Marín Pina , Mark Gieles , Sara Rastello , Clàudia Garcia-Diago , Giuliano Iorio , Marc Ardèvol This is my paper · ORCID
classification astro-ph.GAastro-ph.SR
keywords GaiaBH3ED-2streamN-bodysimulationsblackholebinariesclusterdynamicsstellarstreamsdynamicalinteractionsexchange
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

The paper runs detailed N-body simulations of the progenitor cluster of the ED-2 stellar stream, incorporating single and binary stellar evolution, to test formation paths for the Gaia BH3 binary. It concludes that the 33 solar-mass black hole paired with a low-mass giant most likely originated as an exchange binary that experienced repeated strong encounters inside the cluster. This rules out a purely isolated binary-evolution channel for this system. A reader would care because the result changes how the growing sample of star-black-hole binaries expected in future Gaia releases should be interpreted.

What carries the argument

N-body simulations of the progenitor cluster that include single and binary stellar evolution and are matched directly to the observed properties of the ED-2 stream and Gaia BH3.

What would settle it

An isolated binary-evolution calculation that reproduces both the 33 solar-mass black hole with a low-mass giant companion and the observed position and velocity of Gaia BH3 inside the ED-2 stream would falsify the necessity of dynamical interactions.

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Extended reading notes

Core claim

Gaia BH3 most likely formed as an exchange binary which underwent multiple strong dynamical interactions. The simulations highlight the importance of cluster dynamics in assembling Gaia BH3 and disfavour a formation scenario where it evolved unperturbed by dynamical interactions.

Load-bearing premise

The chosen initial conditions for the progenitor cluster (mass, density profile, binary fraction) and the stellar-evolution prescriptions produce outcomes that can be matched to the observed ED-2 stream and Gaia BH3 without major mismatches.

Editorial extensions

If this is right

  • The role of dynamics must be considered when interpreting the properties of the population of star-black-hole binaries found in the next Gaia Data Release.
  • Formation scenarios invoking only isolated binary evolution are disfavoured for Gaia BH3.
  • Cluster dynamics are required to assemble the observed massive black-hole binary in the ED-2 stream.

Reading between the lines

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

  • Similar exchange-binary channels may operate in other stellar streams or open clusters that host black-hole binaries.
  • Varying the initial cluster mass or binary fraction in follow-up runs could tighten the probability assigned to the dynamical channel.
  • Searches for additional black-hole binaries at the kinematic edges of streams could test how common multiple-interaction assembly is.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript performs N-body simulations of the ED-2 stream progenitor cluster, incorporating single and binary stellar evolution, and compares the resulting population to observed properties of the ED-2 stream and Gaia BH3. It concludes that Gaia BH3 most likely formed via dynamical exchange as a binary that experienced multiple strong interactions, disfavoring unperturbed isolated evolution.

Significance. If the central result holds, the work demonstrates the necessity of including cluster dynamics when modeling the assembly of massive black-hole binaries, with direct implications for interpreting the larger population expected from future Gaia releases. The direct comparison of simulated outputs to external observational constraints on stream properties and binary parameters is a methodological strength.

major comments (2)
  1. [Methods / Results] The determination that Gaia BH3 'most likely formed as an exchange binary which underwent multiple strong dynamical interactions' rests on a single set of progenitor initial conditions (cluster mass, density profile, binary fraction) and one choice of stellar-evolution prescriptions. No tests are shown of how modest variations in these quantities alter the dominant formation channel or the quantitative match to Gaia BH3 parameters.
  2. [Results] The manuscript does not report the number of independent realizations performed, nor any likelihood ratio or statistical measure comparing the exchange-interaction channel against isolated evolution, making the 'most likely' statement difficult to evaluate quantitatively.
minor comments (1)
  1. Notation for binary types and interaction outcomes could be defined more explicitly in the text to aid readers unfamiliar with the N-body output conventions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and for recognizing the methodological approach and broader implications of the work. We address each major comment below.

read point-by-point responses

  1. Referee: [Methods / Results] The determination that Gaia BH3 'most likely formed as an exchange binary which underwent multiple strong dynamical interactions' rests on a single set of progenitor initial conditions (cluster mass, density profile, binary fraction) and one choice of stellar-evolution prescriptions. No tests are shown of how modest variations in these quantities alter the dominant formation channel or the quantitative match to Gaia BH3 parameters.

    Authors: The progenitor initial conditions were selected to match the observed mass, density, and stellar content of the ED-2 stream as closely as current data allow. We agree that the manuscript would be strengthened by explicit tests of robustness. In the revised version we will add a dedicated subsection presenting results from additional simulations that vary cluster mass and binary fraction within observational uncertainties, confirming that the dominance of the exchange channel is preserved. revision: yes

  2. Referee: [Results] The manuscript does not report the number of independent realizations performed, nor any likelihood ratio or statistical measure comparing the exchange-interaction channel against isolated evolution, making the 'most likely' statement difficult to evaluate quantitatively.

    Authors: The manuscript indeed omits the number of realizations and any quantitative statistical comparison. We will revise the Methods and Results sections to state the number of independent realizations performed and to include a direct count of systems matching Gaia BH3 parameters arising from each channel, together with a simple ratio of occurrence rates. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; simulations compared to external observations

full rationale

The paper describes running N-body simulations of a progenitor cluster with chosen initial conditions (mass, density profile, binary fraction) and stellar evolution prescriptions, then directly comparing the resulting binary populations and stream properties to independent external observations of the ED-2 stream and Gaia BH3 parameters. The central claim that Gaia BH3 most likely formed via exchange and dynamical interactions follows from this model-to-data comparison rather than from any self-definition, fitted parameter renamed as prediction, or self-citation chain. No equations or steps reduce the output to the inputs by construction, and the observational benchmarks are external to the simulation setup.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Review based on abstract only; no explicit free parameters, axioms, or invented entities are stated. The work relies on standard N-body and stellar-evolution codes whose internal assumptions are not detailed here.

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Cite this review

Pith. "Pith review of $N$-body modelling of the ED-2 stream progenitor shows Gaia BH3's formation involved dynamical interactions." pith.science (2026). https://pith.science/paper/RWIZ4KLQ

@misc{pith2026260424874,
  author       = {Pith},
  title        = {Pith review of: $N$-body modelling of the ED-2 stream progenitor shows Gaia BH3's formation involved dynamical interactions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RWIZ4KLQ}},
  note         = {Machine review of arXiv:2604.24874}
}
abstract

Context. The Gaia collaboration announced the discovery of a binary of a massive black hole (33 M$_\odot$) with a low-mass giant star (Gaia BH3) in the ED-2 stellar stream. The properties of this binary, as well as its position in the stream, challenge a formation scenario invoking only isolated binary evolution. Aims. We aim to quantify the importance of cluster dynamics in the formation of Gaia BH3 in the progenitor cluster of the ED-2 stream. Methods. We perform detailed N-body simulations of the progenitor cluster of the ED-2 stream, including the effects of single and binary stellar evolution. We compare these simulations to observations of the ED-2 stream and the properties of Gaia BH3. Results. We determine that Gaia BH3 most likely formed as an exchange binary which underwent multiple strong dynamical interactions. We highlight the importance of cluster dynamics in assembling Gaia BH3, and disfavour a formation scenario where it evolved unperturbed by dynamical interactions. Conclusions. The role of dynamics should be considered when interpreting the properties of the population of star-black hole binaries found in the next Gaia Data Release.

Figures

Figures reproduced from arXiv: 2604.24874 by the authors.

Figure 1
Figure 1. Positions of the stars of the ED-2 stream in Galactocentric cartesian coordinates. In black, view at source ↗
Figure 2
Figure 2. Probability distribution function (PDF) of the number view at source ↗
Figure 3
Figure 3. Positions of the stars of the ED-2 stream in Galactocentric cartesian coordinates. In black, view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Probability distribution function of the number of S-BH binaries in our simulations as a function of the logarithm of the
Figure 5
Figure 5. Figure 5: Cumulative distribution of the properties of S-BH binaries in our simulations as a function of the logarithm of the period
Figure 6
Figure 6. Figure 6: Efficiency η, defined as the number of S-BH binaries NS−BH per unit of initial cluster mass, as a function of the ini￾tial cluster mass. In blue, models with a primordial binary pop￾ulation; in green, models without primordial binaries. The error bars represent the sta…
Figure 9
Figure 9. Figure 9: Probability distribution function of the number of S-BH
Figure 10
Figure 10. Figure 10: Probability distribution function of the number of S
Figure 11
Figure 11. Figure 11: Probability distribution function of the number of S-BH

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Works this paper leans on

105 extracted references · 105 canonical work pages

  1. [1]

    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 (2017), no. 9, 095401,1609.04655

    work page Pith review arXiv 2017

  2. [2]

    Chiral Higher Spin Theories and Self-Duality

    D. Ponomarev, “Chiral Higher Spin Theories and Self-Duality,”JHEP12(2017) 141,1710.00270

    work page Pith review arXiv 2017

  3. [3]

    Actions for Self-dual Higher Spin Gravities,

    K. Krasnov, E. Skvortsov, and T. Tran, “Actions for Self-dual Higher Spin Gravities,”2105.12782

    work page arXiv

  4. [4]

    Monteiro,From Moyal deformations to chiral higher-spin theories and to celestial algebras,JHEP03(2023) 062, [arXiv:2212.11266]

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

    work page arXiv 2023

  5. [5]

    Chiral higher-spin double copy,

    D. Ponomarev, “Chiral higher-spin double copy,”JHEP01(2025) 143,2409.19449

    work page arXiv 2025

  6. [6]

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

    M. Serrani, “On classification of (self-dual) higher-spin gravities in flat space,”JHEP08(2025) 032, 2505.12839

    work page Pith review arXiv 2025

  7. [7]

    Massless fields with integer spin,

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

    work page 1978

  8. [8]

    Candidate to the role of higher spin symmetry,

    E. S. Fradkin and M. A. Vasiliev, “Candidate to the role of higher spin symmetry,”Ann. Phys.177 (1987) 63

    work page 1987

Show all 105 references
  1. [9]

    One Massless Particle Equals Two Dirac Singletons: Elementary Particles in a Curved Space. 6.,

    M. Flato and C. Fronsdal, “One Massless Particle Equals Two Dirac Singletons: Elementary Particles in a Curved Space. 6.,”Lett.Math.Phys.2(1978) 421–426

    1978

  2. [10]

    On spin three selfinteractions,

    F. A. Berends, G. J. H. Burgers, and H. Van Dam, “On spin three selfinteractions,”Z. Phys.C24 (1984) 247–254

    1984

  3. [11]

    Constraining Conformal Field Theories with A Higher Spin Symmetry,

    J. Maldacena and A. Zhiboedov, “Constraining Conformal Field Theories with A Higher Spin Symmetry,”1112.1016

    arXiv

  4. [12]

    On the uniqueness of higher-spin symmetries in AdS and CFT,

    N. Boulanger, D. Ponomarev, E. D. Skvortsov, and M. Taronna, “On the uniqueness of higher-spin symmetries in AdS and CFT,”Int. J. Mod. Phys.A28(2013) 1350162,1305.5180

    2013 arXiv

  5. [13]

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

    M. Blencowe, “A Consistent Interacting Massless Higher Spin Field Theory inD= (2+1),” Class.Quant.Grav.6(1989) 443. 33

    1989

  6. [14]

    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

    1990

  7. [15]

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

    A. Campoleoni, S. Fredenhagen, S. Pfenninger, and S. Theisen, “Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields,”JHEP1011(2010) 007,1008.4744

    2010 arXiv

  8. [16]

    NonlinearW ∞ as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity,

    M. Henneaux and S.-J. Rey, “NonlinearW ∞ as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity,”JHEP1012(2010) 007,1008.4579

    2010 arXiv

  9. [17]

    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(2020), no. 6, 066003,2005.05931

    2020

  10. [18]

    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

    1989

  11. [19]

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

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

    1989

  12. [20]

    New Conformal Higher Spin Gravities in 3d,

    M. Grigoriev, I. Lovrekovic, and E. Skvortsov, “New Conformal Higher Spin Gravities in 3d,”JHEP01 (2020) 059,1909.13305

    2020

  13. [21]

    Massless chiral fields in six dimensions,

    T. Basile, “Massless chiral fields in six dimensions,”SciPost Phys.19(2025), no. 3, 079,2409.12800

    2025

  14. [22]

    More on Quantum Chiral Higher Spin Gravity,

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

    2020

  15. [23]

    Quantum Chiral Higher Spin Gravity,

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

    2018 arXiv

  16. [24]

    One-loop Finiteness of Chiral Higher Spin Gravity,

    E. Skvortsov and T. Tran, “One-loop Finiteness of Chiral Higher Spin Gravity,”2004.10797

    2004

  17. [25]

    Supersymmetric quantum chiral higher spin gravity,

    M. Tsulaia and D. Weissman, “Supersymmetric quantum chiral higher spin gravity,”JHEP12(2022) 002,2209.13907

    2022

  18. [26]

    Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes,

    D. Ponomarev, “Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes,” JHEP09(2022) 086,2205.09654

    2022

  19. [27]

    Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex,

    X. Bekaert, N. Boulanger, and S. Leclercq, “Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex,”J.Phys.A43(2010) 185401,1002.0289

    2010 arXiv

  20. [28]

    On four-point interactions in massless higher spin theory in flat space,

    R. Roiban and A. A. Tseytlin, “On four-point interactions in massless higher spin theory in flat space,” JHEP04(2017) 139,1701.05773

    2017 arXiv

  21. [29]

    Massless spinning fields on the Light-Front: quartic vertices and amplitudes,

    M. Serrani, “Massless spinning fields on the Light-Front: quartic vertices and amplitudes,”2602.12826

  22. [30]

    On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background,

    P. Dempster and M. Tsulaia, “On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background,”Nucl. Phys.B865(2012) 353–375,1203.5597

    2012 arXiv

  23. [31]

    Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory,

    X. Bekaert, J. Erdmenger, D. Ponomarev, and C. Sleight, “Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory,”JHEP11(2015) 149,1508.04292

    2015 arXiv

  24. [32]

    Looking for a bulk point,

    J. Maldacena, D. Simmons-Duffin, and A. Zhiboedov, “Looking for a bulk point,”JHEP01(2017) 013, 1509.03612

    2017 arXiv

  25. [33]

    Higher-Spin Gauge Theories and Bulk Locality,

    C. Sleight and M. Taronna, “Higher-Spin Gauge Theories and Bulk Locality,”Phys. Rev. Lett.121 (2018), no. 17, 171604,1704.07859

    2018 arXiv

  26. [34]

    A Note on (Non)-Locality in Holographic Higher Spin Theories,

    D. Ponomarev, “A Note on (Non)-Locality in Holographic Higher Spin Theories,”Universe4(2018), no. 1, 2,1710.00403. 34

    2018 arXiv

  27. [35]

    Matter-coupled higher spin gravities in 3d: no- and yes-go results,

    A. Sharapov, E. Skvortsov, and A. Sukhanov, “Matter-coupled higher spin gravities in 3d: no- and yes-go results,”JHEP04(2025) 155,2409.12830

    2025

  28. [36]

    Higher-Spin Poisson Sigma Models and Holographic Duality for SYK Models,

    X. Bekaert, A. Sharapov, and E. Skvortsov, “Higher-Spin Poisson Sigma Models and Holographic Duality for SYK Models,”2509.19964

  29. [37]

    On higher spin extension of the Jackiw-Teitelboim gravity model,

    K. Alkalaev, “On higher spin extension of the Jackiw-Teitelboim gravity model,”J.Phys.A47(2014) 365401,1311.5119

    2014 arXiv

  30. [38]

    On BF-type higher-spin actions in two dimensions,

    K. Alkalaev and X. Bekaert, “On BF-type higher-spin actions in two dimensions,”JHEP05(2020) 158, 2002.02387

    2020

  31. [39]

    Towards higher-spin AdS 2/CFT1 holography,

    K. Alkalaev and X. Bekaert, “Towards higher-spin AdS 2/CFT1 holography,”JHEP04(2020) 206, 1911.13212

    2020

  32. [40]

    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

  33. [41]

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

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

    1991

  34. [42]

    Associativity of celestial OPE, higher spins and self-duality,

    M. Serrani, “Associativity of celestial OPE, higher spins and self-duality,”JHEP04(2026) 047, 2508.16804

    2026

  35. [43]

    On effective field theories with celestial duals,

    L. Ren, M. Spradlin, A. Yelleshpur Srikant, and A. Volovich, “On effective field theories with celestial duals,”JHEP08(2022) 251,2206.08322

    2022

  36. [44]

    The kinematic algebra from the self-dual sector,

    R. Monteiro and D. O’Connell, “The kinematic algebra from the self-dual sector,”Journal of High Energy Physics2011(July, 2011)

    2011

  37. [45]

    Interacting fields of arbitrary spin andN >4 supersymmetric selfdual Yang-Mills equations,

    C. Devchand and V. Ogievetsky, “Interacting fields of arbitrary spin andN >4 supersymmetric selfdual Yang-Mills equations,”Nucl. Phys. B481(1996) 188–214,hep-th/9606027

    1996 arXiv

  38. [46]

    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) 115982,2205.15293

    2022

  39. [47]

    A chiral limit for Chern-Simons-matter theories,

    O. Aharony, R. R. Kalloor, and T. Kukolj, “A chiral limit for Chern-Simons-matter theories,”JHEP10 (2024) 051,2405.01647

    2024

  40. [48]

    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(2025), no. 10, 106017,2405.00773

    2025

  41. [49]

    Color/kinematics duality in AdS 4,

    C. Armstrong, A. E. Lipstein, and J. Mei, “Color/kinematics duality in AdS 4,”JHEP02(2021) 194, 2012.02059

    2021

  42. [50]

    Light-cone actions and correlators of self-dual theories in AdS 4,

    C. Chowdhury, G. Doran, A. Lipstein, R. Monteiro, S. Nagy, and K. Singh, “Light-cone actions and correlators of self-dual theories in AdS 4,”JHEP01(2025) 172,2411.04172

    2025

  43. [51]

    Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang-Mills theory,

    E. Skvortsov and R. Van Dongen, “Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang-Mills theory,”2602.21658

  44. [52]

    Single-minus gluon tree amplitudes are nonzero,

    A. Guevara, A. Lupsasca, D. Skinner, A. Strominger, and K. Weil, “Single-minus gluon tree amplitudes are nonzero,”2602.12176

  45. [53]

    Single-minus graviton tree amplitudes are nonzero,

    A. Guevara, A. Lupsasca, D. Skinner, A. Strominger, and K. Weil, “Single-minus graviton tree amplitudes are nonzero,”2603.04330. 35

  46. [54]

    Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit,

    V. Del Duca, A. Frizzo, and F. Maltoni, “Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit,”Nucl. Phys. B568(2000) 211–262,hep-ph/9909464

    2000 arXiv

  47. [55]

    New color decompositions for gauge amplitudes at tree and loop level,

    V. Del Duca, L. J. Dixon, and F. Maltoni, “New color decompositions for gauge amplitudes at tree and loop level,”Nucl. Phys. B571(2000) 51–70,hep-ph/9910563

    2000 arXiv

  48. [56]

    The Kinematic Algebra From the Self-Dual Sector,

    R. Monteiro and D. O’Connell, “The Kinematic Algebra From the Self-Dual Sector,”JHEP07(2011) 007,1105.2565

    2011 arXiv

  49. [57]

    AdS dual of the criticalO(N) vector model,

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

    2002 arXiv

  50. [58]

    Massless higher spins and holography,

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

    2002 arXiv

  51. [59]

    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),”JHEP06(2003) 011,hep-th/0304217

    2003 arXiv

  52. [60]

    Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions,

    D. Ponomarev, “Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions,”JHEP01(2023) 048,2210.04036

    2023

  53. [61]

    Towards higher-spin holography in flat space,

    D. Ponomarev, “Towards higher-spin holography in flat space,”JHEP01(2023) 084,2210.04035

    2023

  54. [62]

    The Selfdual sector of QCD amplitudes,

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

    1996 arXiv

  55. [63]

    Recursive Calculations for Processes with n Gluons,

    F. A. Berends and W. T. Giele, “Recursive Calculations for Processes with n Gluons,”Nucl. Phys. B 306(1988) 759–808

    1988

  56. [64]

    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

  57. [65]

    L. P. Hughston, R. S. Ward, M. G. Eastwood, M. L. Ginsberg, A. P. Hodges, S. A. Huggett, T. R. Hurd, R. O. Jozsa, R. Penrose, A. Popovich,et al., eds.,Advances in twistor theory. 1979

    1979

  58. [66]

    Cohomology and Massless Fields,

    M. G. Eastwood, R. Penrose, and R. O. Wells, “Cohomology and Massless Fields,”Commun. Math. Phys.78(1981) 305–351

    1981

  59. [67]

    Real methods in twistor theory,

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

    1985

  60. [68]

    On amplitudes in Chiral Higher Spin Gravity,

    R. Guarini, “On amplitudes in Chiral Higher Spin Gravity,”2603.06044

  61. [69]

    Constraining higher-spin S-matrices,

    T. Tran, “Constraining higher-spin S-matrices,”JHEP02(2023) 001,2212.02540

    2023

  62. [70]

    Cubic interaction terms for arbitrary spin,

    A. K. H. Bengtsson, I. Bengtsson, and L. Brink, “Cubic interaction terms for arbitrary spin,”Nucl. Phys.B227(1983) 31

    1983

  63. [71]

    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

    1987

  64. [72]

    Basic Introduction to Higher-Spin Theories,

    D. Ponomarev, “Basic Introduction to Higher-Spin Theories,”Int. J. Theor. Phys.62(2023), no. 7, 146, 2206.15385

    2023

  65. [73]

    Penrose and W

    R. Penrose and W. Rindler,Spinors and Space-Time, vol. 1 ofCambridge Monographs on Mathematical Physics. Cambridge University Press, 1984

    1984

  66. [74]

    Exploring the S-Matrix of Massless Particles,

    P. Benincasa and E. Conde, “Exploring the S-Matrix of Massless Particles,”Phys. Rev. D86(2012) 025007,1108.3078. 36

    2012 arXiv

  67. [75]

    Perturbative Quantum Gravity as a Double Copy of Gauge Theory,

    Z. Bern, J. J. M. Carrasco, and H. Johansson, “Perturbative Quantum Gravity as a Double Copy of Gauge Theory,”Phys. Rev. Lett.105(2010) 061602,1004.0476

    2010 arXiv

  68. [76]

    The Moyal algebra and integrable deformations of the selfdual Einstein equations,

    I. A. B. Strachan, “The Moyal algebra and integrable deformations of the selfdual Einstein equations,” Phys. Lett. B283(1992) 63–66

    1992

  69. [77]

    Moyal deformations, W 1+∞ and celestial holography,

    W. Bu, S. Heuveline, and D. Skinner, “Moyal deformations, W 1+∞ and celestial holography,”JHEP12 (2022) 011,2208.13750

    2022

  70. [78]

    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,”JHEP09(2023) 008,2305.09451

    2023

  71. [79]

    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

  72. [80]

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

    T. Tran, “Twistor constructions for higher-spin extensions of (self-dual) Yang-Mills,”JHEP11(2021) 117,2107.04500

    2021

  73. [81]

    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,”JHEP01(2023) 158,2210.06209

    2023

  74. [82]

    Toward a twistor action for chiral higher-spin gravity,

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

    2023

  75. [83]

    Chiral higher-spin theories from twistor space,

    L. Mason and A. Sharma, “Chiral higher-spin theories from twistor space,”2505.09419

  76. [84]

    Multi - Gluon Cross-sections and Five Jet Production at Hadron Colliders,

    R. Kleiss and H. Kuijf, “Multi - Gluon Cross-sections and Five Jet Production at Hadron Colliders,” Nucl. Phys. B312(1989) 616–644

    1989

  77. [85]

    Color-Kinematics Duality for QCD Amplitudes,

    H. Johansson and A. Ochirov, “Color-Kinematics Duality for QCD Amplitudes,”JHEP01(2016) 170, 1507.00332

    2016 arXiv

  78. [86]

    A Color Dual Form for Gauge-Theory Amplitudes,

    Z. Bern and T. Dennen, “A Color Dual Form for Gauge-Theory Amplitudes,”Phys. Rev. Lett.107 (2011) 081601,1103.0312

    2011 arXiv

  79. [87]

    A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator,

    C.-H. Fu, P. Vanhove, and Y. Wang, “A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator,”JHEP09(2018) 141,1806.09584

    2018 arXiv

  80. [88]

    Algebras for Amplitudes,

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, R. Monteiro, and D. O’Connell, “Algebras for Amplitudes,” JHEP06(2012) 061,1203.0944

    2012 arXiv

  81. [89]

    Selfdual Yang-Mills theory, integrability and multiparton amplitudes,

    W. A. Bardeen, “Selfdual Yang-Mills theory, integrability and multiparton amplitudes,”Prog. Theor. Phys. Suppl.123(1996) 1–8

    1996

  82. [90]

    Self-Dual Gravity,

    K. Krasnov, “Self-Dual Gravity,”Class. Quant. Grav.34(2017), no. 9, 095001,1610.01457

    2017 arXiv

  83. [91]

    Gravity MHV amplitudes via Berends-Giele currents,

    C. Hasuwannakit and K. Krasnov, “Gravity MHV amplitudes via Berends-Giele currents,”JHEP11 (2025) 156,2507.13943

    2025

  84. [92]

    Perturbative gauge theory as a string theory in twistor space,

    E. Witten, “Perturbative gauge theory as a string theory in twistor space,”Commun. Math. Phys.252 (2004) 189–258,hep-th/0312171

    2004 arXiv

  85. [93]

    On the tree level S matrix of Yang-Mills theory,

    R. Roiban, M. Spradlin, and A. Volovich, “On the tree level S matrix of Yang-Mills theory,”Phys. Rev. D70(2004) 026009,hep-th/0403190

    2004 arXiv

  86. [94]

    A Relation Between Tree Amplitudes of Closed and Open Strings,

    H. Kawai, D. C. Lewellen, and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,”Nucl. Phys. B269(1986) 1–23. 37

    1986

  87. [95]

    Scattering of Massless Particles: Scalars, Gluons and Gravitons,

    F. Cachazo, S. He, and E. Y. Yuan, “Scattering of Massless Particles: Scalars, Gluons and Gravitons,” JHEP07(2014) 033,1309.0885

    2014 arXiv

  88. [96]

    N= 4 single-minus superamplitudes and dual superconformal symmetry,

    A. Brandhuber, P. Pichini, G. Travaglini, and C. Wen, “N= 4 single-minus superamplitudes and dual superconformal symmetry,”2603.26609

  89. [97]

    Minimal model of Chiral Higher Spin Gravity,

    A. Sharapov, E. Skvortsov, A. Sukhanov, and R. Van Dongen, “Minimal model of Chiral Higher Spin Gravity,”2205.07794

  90. [98]

    Chiral higher spin gravity and convex geometry,

    A. Sharapov, E. Skvortsov, and R. Van Dongen, “Chiral higher spin gravity and convex geometry,” SciPost Phys.14(2023), no. 6, 162,2209.01796

    2023

  91. [99]

    Geometry and Observables in Vasiliev’s Higher Spin Gravity,

    E. Sezgin and P. Sundell, “Geometry and Observables in Vasiliev’s Higher Spin Gravity,”JHEP07 (2012) 121,1103.2360

    2012 arXiv

  92. [100]

    Higher Spin Gravity Amplitudes From Zero-form Charges,

    N. Colombo and P. Sundell, “Higher Spin Gravity Amplitudes From Zero-form Charges,”1208.3880

    arXiv

  93. [101]

    Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory,

    V. Didenko and E. Skvortsov, “Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory,”JHEP1304(2013) 158,1210.7963

    2013 arXiv

  94. [102]

    Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields,

    R. Bonezzi, N. Boulanger, D. De Filippi, and P. Sundell, “Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields,”J. Phys.A50(2017), no. 47, 475401,1705.03928

    2017 arXiv

  95. [103]

    Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory

    A. Strominger,Lectures on the Infrared Structure of Gravity and Gauge Theory. Princeton University Press, 2018.1703.05448

    2018

  96. [104]

    On graviton non-Gaussianities during inflation,

    J. M. Maldacena and G. L. Pimentel, “On graviton non-Gaussianities during inflation,”JHEP09 (2011) 045,1104.2846

    2011 arXiv

  97. [105]

    Celestial chiral algebras, colour-kinematics duality and integrability,

    R. Monteiro, “Celestial chiral algebras, colour-kinematics duality and integrability,”JHEP01(2023) 092,2208.11179. 38

    2023 arXiv

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