Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

The Double Copy of Maximal Supersymmetry in $D=4$

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that N=8 supergravity in four dimensions is, to cubic order in fields, the off-shell double copy of N=4 super Yang-Mills theory, with N=8 supersymmetry and SU(8) R-symmetry emerging from two copies of N=4.

desk verdict A genuinely new off-shell double-copy construction, but the cubic-order identification with N=8 supergravity is asserted from free-theory data, not demonstrated. read the letter →

arxiv 2501.02058 v2 pith:JJFJBI5F submitted 2025-01-03 hep-th

Roberto Bonezzi , Giuseppe Casale , Olaf Hohm This is my paper · ORCID
classification hep-th MSC 81T6081T1317B5583E50
keywords doublecopyN=8supergravityN=4superYang-MillshomotopyalgebrasL-infinitykinematiccolor-kinematicsdualityR-symmetry
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 aims to turn the old slogan that N=8 supergravity is the square of N=4 super Yang-Mills into an off-shell, local, and gauge-invariant statement, at least to cubic order in fields. It constructs the kinematic algebra of N=4 SYM in a redundant fermionic formulation so that a purely algebraic b operator exists, then tensors two copies to build an L-infinity algebra on a level-matched subspace. On that double-copy space the two N=4 supersymmetries combine into one N=8 supersymmetry, and the R-symmetry enhances from SU(4) times SU(4) to SU(8). If correct, this gives a first-principle, field-level route from maximal gauge theory to maximal supergravity, going beyond on-shell scattering amplitudes.

What carries the argument

The load-bearing object is the kinematic algebra $K$ of N=4 super Yang-Mills: a $C_\infty$ algebra (homotopy commutative associative algebra) with products $m_1,m_2,m_3$, together with a degree-shift operator $b$ satisfying $b^2=0$ and $bm_1+m_1b=\square$. The paper adds a redundant fermionic chain complex, motivated by the BRST quantization of a spinning particle, in which the dependent Klein-Gordon equation is imposed independently; this makes $b$ purely algebraic. The failure of $b$ to be a derivation of $m_2$ defines the bracket $b_2$, the seed of the hidden $BV^l_\infty$ structure. Tensoring $K$ with a second copy $\tilde K$ and projecting with $b_-=\tfrac12(b\otimes\tilde 1-1\otimes\tilde b)$ yields the $L_\infty$ algebra of the double copy, with $B_1=m_1\otimes\tilde 1+1\otimes\tilde m_1$ and $B_2=-\tfrac12b_-(m_2\otimes\tilde m_2)$. The N=4 supersymmetry maps $\rho_n(\epsilon)$, chosen to commute with both $m_1$ and $b$, combine under the tensor product into $\Sigma_1=\rho_1\otimes\tilde 1+1\otimes\tilde\rho_1$ and $\Sigma_2=\tfrac12b_-(\rho_2\otimes\tilde m_2+m_2\otimes\tilde\rho_2)$, producing the N=8 action.

What would settle it

Compute the quartic-order $L_\infty$ brackets of the double copy and test the generalized Jacobi identities together with preservation of the $b_-$ constraint; if the identities fail or the fermionic tower produces extra propagating degrees of freedom, the cubic-order result does not extend to the interacting theory. A cohomological check that the infinite Noether-identity tower is acyclic after the projection would directly settle the physical-equivalence assumption.

Watch

Extended reading notes

Core claim

The central discovery is that global supersymmetry can be lifted from the N=4 gauge theory to its kinematic algebra in a way that is compatible with the hidden BV algebra underlying color-kinematics duality. The linear supersymmetry map $\rho_1(\epsilon)$ can be chosen to commute with both the differential $m_1$ and the b operator, and the bilinear map $\rho_2(\epsilon)$ then satisfies the required homotopy compatibility. Consequently, on $K\otimes\tilde K$ with the $b_-$ projection and the section constraint, the relation $[B_1,\Sigma_2]=[\Sigma_1,B_2]$ holds, giving a consistent N=8 supersymmetry action. The free theory reproduces the standard N=8 supergravity spectrum: graviton, eight gravitini, 28 vectors, 56 spin-1/2 fermions, and 70 real scalars, organized in SU(8) representations. The paper claims this establishes, to cubic order, an off-shell local gauge-invariant double copy realization of maximal supergravity.

Load-bearing premise

The construction assumes that adding the dependent Klein-Gordon equation as an independent equation in the fermionic complex does not alter the physical content after the projection that defines the double copy; if that tower of redundant equations contributes spurious states, the resulting theory would not be ordinary N=8 supergravity.

Editorial extensions

If this is right

  • To cubic order, every off-shell local gauge-invariant interaction of N=8 supergravity is encoded in the double-copied $L_\infty$ brackets of N=4 SYM.
  • The doubled supersymmetry parameter $(\epsilon^A,\tilde\epsilon^{\tilde A})$ organizes the gravitini, vectors, spinors, and scalars into SU(8) representations, including the rank-four self-dual 70 of scalars.
  • The free double-copy field equations reduce to the standard N=8 equations: linearized Einstein, Rarita-Schwinger (via the Fang-Fronsdal form), Dirac, Maxwell, and self-duality constraints.
  • The redundant fermionic formulation makes the b operator derivative-free and local, which is what permits a manifestly local double copy without differential constraints on fields.
  • Extending the construction to quartic and higher orders is the stated next step; the paper argues the $BV^l_\infty$ structure maps should determine those brackets.

Reading between the lines

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

  • Editorial inference: If the all-order extension succeeds, the double copy would provide a constructive, off-shell proof of color-kinematics duality for the maximally supersymmetric pair, potentially giving a new handle on the UV-finiteness question of N=8 supergravity.
  • Editorial inference: The non-Lagrangian character of the present formulation, especially the Ramond-Ramond sector with field strengths as elementary, mirrors known obstacles in type II string field theory; a Sen-type action may be adaptable to this double-copy setting.
  • Editorial inference: The same machinery may apply to other supersymmetric gauge theories, such as N=1 SYM in D=10, where double copy should produce type II supergravity in a doubled formulation; the paper lists this as future work.
  • Editorial inference: A cohomological analysis of the fermionic complex would decide whether the infinite tower of Noether identities truly decouples; until that is done, the physical-equivalence step remains the main open assumption.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper develops an off-shell double copy of N=4 super Yang-Mills theory in four dimensions with the aim of realizing N=8 supergravity at the level of homotopy algebras. The authors construct a kinematic algebra for N=4 SYM, including a redundant fermionic complex in which the dependent Klein-Gordon equation is added as an independent equation, and show that the corresponding b operator becomes an algebraic degree shift. They then combine two copies of this kinematic algebra to obtain an L-infinity algebra on a level-matched subspace and propose a double-copy prescription for global supersymmetry via maps rho_n(epsilon) and Sigma_n(epsilon). Explicit free-field equations are derived and matched to the linearized spectrum of N=8 supergravity, with the fields reorganized into SU(8) multiplets. The stated claim is that the construction realizes off-shell, local, gauge-invariant N=8 supergravity to cubic order in fields.

Significance. If fully established, this work would be a major step toward a first-principles off-shell double copy of maximal supergravity, arguably the central open problem in the homotopy-algebraic double-copy program. The paper contains several genuinely useful and convincing ingredients: the explicit free-theory analysis in Sections 3.3 and 4, the worldline derivation of the redundant fermionic complex in Appendix B, and the representation-theoretic repackaging of the spectrum into SU(8) multiplets. The free-field identification with N=8 supergravity is presented in detail and is persuasive. However, the advertised cubic-order result is not actually demonstrated: the bilinear supersymmetry map rho_2 is never given explicitly, the closure of the N=8 supersymmetry algebra is not checked, and no comparison of cubic vertices with standard N=8 supergravity is provided. The paper is therefore better described as establishing the free theory and proposing a plausible cubic extension, with the decisive nonlinear verification still missing.

major comments (4)
  1. [§3.2, Eqs. (3.8c), (3.18)] The bilinear supersymmetry map rho_2(epsilon) is never given explicitly. After the shift (2.54), the paper assumes the relation rm1,rho_2(epsilon)s = rrho_1(epsilon),m2s, but no formula, existence proof, or component check for rho_2 is supplied. Since Sigma_2 is defined through rho_2 in equation (3.18), the derivation of (3.15) is conditional on an unproven assumption. The central cubic-order claim therefore lacks its key input; please provide an explicit rho_2 (or a constructive proof of existence) and verify (3.8c) in components.
  2. [§3.2 and §4] The covariance condition rB1,Sigma_2s = rSigma_1,B2s is weaker than the statement that the double copy carries an action of the N=8 supersymmetry algebra. The authors themselves note in Section 3.2 that the presence of eight supercharges does not imply that the N=8 supersymmetry algebra is obeyed, but Section 4 then verifies only the linearized field equations and the SU(8) multiplet structure. No computation of the graded commutator of two Sigma_1(epsilon) maps, no closure check up to B1-exact terms, and no comparison of the cubic couplings with the standard N=8 supergravity vertices is presented. The claim that N=8 supergravity is realized to cubic order therefore remains unverified at the most decisive point.
  3. [§2.2, Eqs. (2.23)-(2.25); Appendix B] The redundant fermionic complex, in which the dependent Klein-Gordon equation is added as an independent equation and an infinite tower of trivial Noether identities is generated, is assumed not to change the physical content of the double copy after the b- projection (3.2). The worldline BRST construction in Appendix B shows that the complex arises naturally, but it does not prove that the extra cohomology is trivial in the interacting theory. Because the b operator enters the double-copy bracket B2 in (3.4b), a spurious contribution in the fermionic complex could in principle alter the cubic interactions. Please provide a cohomological argument, or at least an explicit demonstration that the added degrees of freedom decouple at cubic order.
  4. [§4.3] The reorganization of the free fields into SU(8) representations in equations (4.35)-(4.47) does not by itself establish the claimed enhancement of the R-symmetry from SU(4)×SU(4) to SU(8). To prove the enhancement one must show that the field equations and supersymmetry transformations are invariant under the full SU(8), not merely that the fields can be labeled by SU(8) indices. Since the free equations in Section 3.3 are written with manifest SU(4)×SU(4) indices and no SU(8)-covariant form is given, the dynamical R-symmetry enhancement remains an assumption rather than a demonstrated result.
minor comments (4)
  1. [Abstract and §5] The abstract advertises 'off-shell, local and gauge invariant N=8 supergravity', while Section 5 states that the construction is 'manifestly non-Lagrangian'. This tension should be clarified, perhaps by explicitly defining 'off-shell' as working with gauge-covariant field equations rather than an action.
  2. [§2.4, Eq. (2.54)] The shift operator H_1(epsilon) used to redefine rho_1 and rho_2 is never displayed. Giving its explicit action would make the shift (2.54) concrete and would help the reader verify the claimed properties of the shifted rho_1.
  3. [§3.3] The notation for the Ramond-Ramond bispinors, such as F_A~B and F^A_~B, is dense and easy to confuse. A short table listing the spinor index types and chirality assignments before equation (3.25) would improve readability.
  4. [§4.2, Eqs. (4.17)-(4.22)] The derivation that the Fang-Fronsdal type equation (4.22) is equivalent to the Rarita-Schwinger equation is terse. A short remark explaining why the step 'sigma-trace of the spin 3/2 equation' yields the vanishing of sigma^{mu nu} Psi_{mu nu} would make the logic easier to follow.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the construction is self-contained from N=4 SYM kinematic data, and the N=8 supergravity identification is checked against external standard results rather than assumed.

full rationale

The paper's derivation chain is non-circular. The double-copy bracket B2 = -(1/2)b^-(m2⊗m2~) and the supersymmetry map Σ2 = (1/2)b^-(ρ2⊗m2~ + m2⊗ρ~2) are constructed from the C8 kinematic algebra of N=4 SYM, not from the target N=8 theory. The identification with N=8 supergravity is then tested against external benchmarks: the Cremmer-Julia/de Wit-Nicolai spectrum, the Fang-Fronsdal/Rarita-Schwinger form of the gravitino equations, the Bargmann-Wigner equations for the R-R bispinors, and the SU(8) multiplet assignment. These are independent checks, not inputs. The paper itself explicitly disclaims that having eight supercharges automatically gives the N=8 algebra: 'This, per se, does not imply that the N=8 supersymmetry algebra is obeyed' (Section 3.2), and then verifies only what it verifies. The acknowledged self-citations ([22,25], and related technical results) supply prior general double-copy machinery for Yang-Mills theory; those results are prior published, their assumptions do not include N=8 supergravity, and they are used as lemmas rather than as substitutes for the N=8 identification. The skeptical concerns—no explicit ρ2 after the exact shift (2.54), no explicit cubic-order closure check of the supersymmetry algebra, and no cohomological proof that the redundant fermionic complex is physically equivalent—are gaps in verification or rigor, not cases where the output reduces by definition to the input. There are no fitted parameters, no predictions forced by construction, and no target-renamed inputs. Therefore the circularity score is 0.

Assumptions & free parameters 0 free parameters · 6 assumptions · 1 invented entities

The construction has no fitted parameters. It rests on the standard L8/C8/BV^l_8 framework (largely developed in the authors' prior work), on the new redundant fermionic complex introduced here, and on the asserted existence of the rho2 map; the latter is the least supported element.

assumptions (6)
  • domain assumption Every perturbative semi-classical field theory can be encoded in an L8 algebra whose brackets encode vertices and equations of motion.
    Invoked in Section 2.2 to justify the homotopy algebra formulation; standard in the field, cited [38-41].
  • domain assumption For adjoint-valued fields the L8 algebra factorizes as X = K x g with a kinematic C8 algebra K.
    Used in Section 2.3 (eq. 2.28) to color-strip the theory; standard within the double copy program.
  • domain assumption The b operator exists with b^2=0 and bB1+B1b=l, and the kinematic algebra carries the BV^l_8 structure of Reiterer and the authors' prior work.
    Central to the double copy prescription (Section 2.2-2.3); relies on [22,25,47].
  • ad hoc to paper Adding the dependent Klein-Gordon equation as an independent equation (redundant fermionic complex) does not change the physical content and yields the same double copy spectrum after the b- projection.
    Section 2.2 (eqs. 2.23-2.25); this is a new modeling choice specific to this paper, flagged as abandoning an action principle.
  • domain assumption The section constraint (strong constraint) of double field theory can be imposed consistently and allows identification of the doubled coordinates with physical spacetime.
    Used in Section 3.1 and 4.1; standard in DFT [52].
  • ad hoc to paper There exists a bilinear rho2(epsilon) satisfying (3.8c) after the shift (2.54), such that the double copy Sigma2 in (3.18) satisfies (3.15).
    The paper states this consistency requirement but does not display rho2 explicitly; the cubic-order SUSY covariance depends on it.
invented entities (1)
  • Redundant fermionic complex (dependent Klein-Gordon doublet and infinite tower of Noether identities)
    purpose: Make the b operator a pure degree shift on fermions, enabling a local algebraic double copy with unconstrained fields.
    Section 2.2 (eqs. 2.23-2.25) and Appendix B. It is a reformulation of the Dirac equation with an additional dependent equation; no external falsifiable prediction is provided, and its consistency is argued internally via the worldline BRST construction.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Double Copy of Maximal Supersymmetry in $D=4$." pith.science (2026). https://pith.science/paper/JJFJBI5F

@misc{pith2026250102058,
  author       = {Pith},
  title        = {Pith review of: The Double Copy of Maximal Supersymmetry in $D=4$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JJFJBI5F}},
  note         = {Machine review of arXiv:2501.02058}
}
abstract

We realize off-shell, local and gauge invariant $N=8$ supergravity in $D=4$, to cubic order in fields, as the double copy of $N=4$ super Yang-Mills theory (SYM). Employing the homotopy algebra approach, we show that, thanks to a redundant formulation for the fermionic fields, the kinematic algebra $K$ of $N=4$ SYM is compatible with an action of the global supersymmetry algebra. The double copy space is then a subspace of $K\otimes{\widetilde K}$ that inherits an $L_{\infty}$ algebra on which the two copies of the $N=4$ action combine into an action of the $N=8$ supersymmetry algebra, with a corresponding enhancement of the $R$-symmetry group to $SU(8)$.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Off-shell double copy theories in BV

    hep-th 2025-06 conditional novelty 6.0 of 10

    A BV-formalism construction gives off-shell double-copy actions for Chern-Simons, BF, and 2D Yang-Mills theories, with Kodaira-Spencer and Kähler gravity as natural examples.

Reference graph

Works this paper leans on

70 extracted references · 22 canonical work pages · cited by 1 Pith paper

  1. [1]

    Supersymmetric Yang -Mills Theories,

    L. Brink, J. H. Schwarz, and J. Scherk, “Supersymmetric Yang -Mills Theories,” Nucl. Phys. B 121 (1977) 77–92

    work page 1977

  2. [2]

    The SO(8) Supergravity,

    E. Cremmer and B. Julia, “The SO(8) Supergravity,” Nucl. Phys. B 159 (1979) 141–212

    work page 1979

  3. [3]

    N=8 Supergravity,

    B. de Wit and H. Nicolai, “N=8 Supergravity,” Nucl. Phys. B 208 (1982) 323

    work page 1982

  4. [4]

    Maximally Supersymmetric Yang-Mills Theory. The Story of N = 4 Yang-Mills Theory

    L. Brink, “Maximally Supersymmetric Yang–Mills Theory: The Story of N = 4 Yang–Mills Theory,” Int. J. Mod. Phys. A 31 no. 01, (2016) 1630002, arXiv:1511.02971 [hep-th]

    work page Pith review arXiv 2016

  5. [5]

    N=8 Supergravity, and beyond

    H. Nicolai, “N=8 Supergravity, and beyond,” 9, 2024. arXiv:2409.18656 [hep-th]

    work page Pith review arXiv 2024

  6. [6]

    IS THE END IN SIGHT FOR THEORETICAL PHYSICS? ,

    S. W. Hawking, “IS THE END IN SIGHT FOR THEORETICAL PHYSICS? ,” Phys. Bull. 32 (1981) 15–17

    work page 1981

  7. [7]

    New Relations f or Gauge-Theory Amplitudes,

    Z. Bern, J. J. M. Carrasco, and H. Johansson, “New Relations f or Gauge-Theory Amplitudes,” Phys. Rev. D 78 (2008) 085011, arXiv:0805.3993 [hep-ph]

    arXiv 2008

  8. [8]

    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, arXiv:1004.0476 [hep-th]

    arXiv 2010

Show all 70 references
  1. [9]

    Five-Point Amplitudes in N= 4 Super-Yang-Mills Theory and N=8 Supergravity,

    J. J. M. Carrasco and H. Johansson, “Five-Point Amplitudes in N= 4 Super-Yang-Mills Theory and N=8 Supergravity,” Phys. Rev. D 85 (2012) 025006, arXiv:1106.4711 [hep-th]

    2012 arXiv

  2. [10]

    N ą= 4 Supergravity Amplitudes from Gauge Theory at One Loop,

    Z. Bern, C. Boucher-Veronneau, and H. Johansson, “N ą= 4 Supergravity Amplitudes from Gauge Theory at One Loop,” Phys. Rev. D 84 (2011) 105035, arXiv:1107.1935 [hep-th] . 38

    2011 arXiv

  3. [11]

    The duality between color and kinematics and its applications,

    Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. R oiban, “The duality between color and kinematics and its applications,” J. Phys. A 57 no. 33, (2024) 333002, arXiv:1909.01358 [hep-th]

    2024 arXiv

  4. [12]

    The SAGEX review on scattering amplitudes Chapter 2: An invitation to color-kin ematics duality and the double copy,

    Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. R oiban, “The SAGEX review on scattering amplitudes Chapter 2: An invitation to color-kin ematics duality and the double copy,” J. Phys. A 55 no. 44, (2022) 443003, arXiv:2203.13013 [hep-th]

    2022 arXiv

  5. [13]

    Snowm ass White Paper: the Double Copy and its Applications,

    T. Adamo, J. J. M. Carrasco, M. Carrillo-Gonz´ alez, M. Chiodar oli, H. Elvang, H. Johansson, D. O’Connell, R. Roiban, and O. Schlotterer, “Snowm ass White Paper: the Double Copy and its Applications,” in Snowmass 2021 . 4, 2022. arXiv:2204.06547 [hep-th]

    2021 arXiv

  6. [14]

    Gravity as the Square of Gauge Theory,

    Z. Bern, T. Dennen, Y.-t. Huang, and M. Kiermaier, “Gravity as the Square of Gauge Theory,” Phys. Rev. D 82 (2010) 065003, arXiv:1004.0693 [hep-th]

    2010 arXiv

  7. [15]

    The Momentum Kernel of Gauge and Gravity Theories,

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, T. Sondergaard, an d P. Vanhove, “The Momentum Kernel of Gauge and Gravity Theories,” JHEP 01 (2011) 001, arXiv:1010.3933 [hep-th]

    2011 arXiv

  8. [16]

    Explicit BCJ N umerators from Pure Spinors,

    C. R. Mafra, O. Schlotterer, and S. Stieberger, “Explicit BCJ N umerators from Pure Spinors,” JHEP 07 (2011) 092, arXiv:1104.5224 [hep-th]

    2011 arXiv

  9. [17]

    A Relation Between Tr ee Amplitudes of Closed and Open Strings,

    H. Kawai, D. C. Lewellen, and S. H. H. Tye, “A Relation Between Tr ee Amplitudes of Closed and Open Strings,” Nucl. Phys. B 269 (1986) 1–23

    1986

  10. [18]

    Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory a nd Gravity Amplitudes,

    Z. Bern, J. J. M. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, “Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory a nd Gravity Amplitudes,” Phys. Rev. D 85 (2012) 105014, arXiv:1201.5366 [hep-th]

    2012 arXiv

  11. [19]

    Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes ,

    Z. Bern, J. J. Carrasco, W.-M. Chen, H. Johansson, and R. Ro iban, “Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes ,” Phys. Rev. Lett. 118 no. 18, (2017) 181602, arXiv:1701.02519 [hep-th]

    2017 arXiv

  12. [20]

    Five-loop four-point integrand of N “ 8 supergravity as a generalized double copy,

    Z. Bern, J. J. M. Carrasco, W.-M. Chen, H. Johansson, R. Roib an, and M. Zeng, “Five-loop four-point integrand of N “ 8 supergravity as a generalized double copy,” Phys. Rev. D 96 no. 12, (2017) 126012, arXiv:1708.06807 [hep-th]

    2017 arXiv

  13. [21]

    Double Copy from Homotopy Algebras,

    L. Borsten, H. Kim, B. Jurˇ co, T. Macrelli, C. Saemann, and M. W olf, “Double Copy from Homotopy Algebras,” Fortsch. Phys. 69 no. 8-9, (2021) 2100075, arXiv:2102.11390 [hep-th]

    2021 arXiv

  14. [22]

    The gauge structu re of double field theory follows from Yang-Mills theory,

    R. Bonezzi, F. Diaz-Jaramillo, and O. Hohm, “The gauge structu re of double field theory follows from Yang-Mills theory,” Phys. Rev. D 106 no. 2, (2022) 026004, arXiv:2203.07397 [hep-th] . 39

    2022 arXiv

  15. [23]

    Kinematic Lie Algebras From Twistor Spaces,

    L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wo lf, “Kinematic Lie Algebras From Twistor Spaces,” arXiv:2211.13261 [hep-th]

    arXiv

  16. [24]

    Colour-kinematics duality, double copy, and homotopy algebras,

    L. Borsten, H. Kim, B. Jurco, T. Macrelli, C. Saemann, and M. Wo lf, “Colour-kinematics duality, double copy, and homotopy algebras,” PoS ICHEP2022 (11, 2022) 426, arXiv:2211.16405 [hep-th]

    2022 arXiv

  17. [25]

    Gauge invariant double copy of Yang-Mills theory: The quartic theory,

    R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, “Gauge invariant double copy of Yang-Mills theory: The quartic theory,” Phys. Rev. D 107 no. 12, (2023) 126015, arXiv:2212.04513 [hep-th]

    2023 arXiv

  18. [26]

    Weakly constrained double field theory as the double copy of Yang-Mills theory,

    R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, “Weakly constrained double field theory as the double copy of Yang-Mills theory,” Phys. Rev. D 109 no. 6, (2024) 066020, arXiv:2309.03289 [hep-th]

    2024 arXiv

  19. [27]

    Gauge independent kinematic algebra of self-dual Yang-Mills theory,

    R. Bonezzi, F. Diaz-Jaramillo, and S. Nagy, “Gauge independent kinematic algebra of self-dual Yang-Mills theory,” Phys. Rev. D 108 no. 6, (2023) 065007, arXiv:2306.08558 [hep-th]

    2023 arXiv

  20. [28]

    Double Copy from Tensor Products of Metric BV ■ -algebras,

    L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wo lf, “Double Copy from Tensor Products of Metric BV ■ -algebras,” arXiv:2307.02563 [hep-th]

    arXiv

  21. [29]

    Double-copying self-dual Yang-Mills theory to self-dual gravity o n twistor space,

    L. Borsten, B. Jurco, H. Kim, T. Macrelli, C. Saemann, and M. Wo lf, “Double-copying self-dual Yang-Mills theory to self-dual gravity o n twistor space,” JHEP 11 (2023) 172, arXiv:2307.10383 [hep-th]

    2023 arXiv

  22. [30]

    Double copy of 3D Ch ern-Simons theory and 6D Kodaira-Spencer gravity,

    R. Bonezzi, F. Diaz-Jaramillo, and O. Hohm, “Double copy of 3D Ch ern-Simons theory and 6D Kodaira-Spencer gravity,” Phys. Rev. D 110 no. 4, (2024) 045024, arXiv:2404.16830 [hep-th]

    2024 arXiv

  23. [31]

    The BV double of a Courant algebroid,

    A. M. Zeitlin, “The BV double of a Courant algebroid,” arXiv:2410.20510 [math.QA]

    arXiv

  24. [32]

    Gravity as Gauge Theory Squared: A Ghost Story,

    A. Anastasiou, L. Borsten, M. J. Duff, S. Nagy, and M. Zoccali, “Gravity as Gauge Theory Squared: A Ghost Story,” Phys. Rev. Lett. 121 no. 21, (2018) 211601, arXiv:1807.02486 [hep-th]

    2018 arXiv

  25. [33]

    The pure BRST Einstein-Hilbert Lagra ngian from the double-copy to cubic order,

    L. Borsten and S. Nagy, “The pure BRST Einstein-Hilbert Lagra ngian from the double-copy to cubic order,” JHEP 07 (2020) 093, arXiv:2004.14945 [hep-th]

    2020 arXiv

  26. [34]

    Becchi-Rouet-Stora-Tyutin-Lagrangian Double Copy of Yang-M ills Theory,

    L. Borsten, B. Jurˇ co, H. Kim, T. Macrelli, C. Saemann, and M. W olf, “Becchi-Rouet-Stora-Tyutin-Lagrangian Double Copy of Yang-M ills Theory,” Phys. Rev. Lett. 126 no. 19, (2021) 191601, arXiv:2007.13803 [hep-th]

    2021 arXiv

  27. [35]

    On the Lagrangian formulation of t he double copy to cubic order,

    P. Ferrero and D. Francia, “On the Lagrangian formulation of t he double copy to cubic order,” JHEP 02 (2021) 213, arXiv:2012.00713 [hep-th] . 40

    2021 arXiv

  28. [36]

    Double field theory as the double copy of Yang-Mills theory,

    F. Diaz-Jaramillo, O. Hohm, and J. Plefka, “Double field theory as the double copy of Yang-Mills theory,” Phys. Rev. D 105 no. 4, (2022) 045012, arXiv:2109.01153 [hep-th]

    2022 arXiv

  29. [37]

    BRST symme try and the convolutional double copy,

    M. Godazgar, C. N. Pope, A. Saha, and H. Zhang, “BRST symme try and the convolutional double copy,” JHEP 11 (2022) 038, arXiv:2208.06903 [hep-th]

    2022 arXiv

  30. [38]

    Closed string field theory: Quantum action and th e B-V master equation,

    B. Zwiebach, “Closed string field theory: Quantum action and th e B-V master equation,” Nucl. Phys. B 390 (1993) 33–152, arXiv:hep-th/9206084

    1993 arXiv

  31. [39]

    Introduction to SH Lie algebras for p hysicists,

    T. Lada and J. Stasheff, “Introduction to SH Lie algebras for p hysicists,” Int. J. Theor. Phys. 32 (1993) 1087–1104, arXiv:hep-th/9209099

    1993 arXiv

  32. [40]

    L8 Algebras and Field Theory,

    O. Hohm and B. Zwiebach, “ L8 Algebras and Field Theory,” Fortsch. Phys. 65 no. 3-4, (2017) 1700014, arXiv:1701.08824 [hep-th]

    2017 arXiv

  33. [41]

    L8-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism,

    B. Jurˇ co, L. Raspollini, C. S¨ amann, and M. Wolf, “L8-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism,” Fortsch. Phys. 67 no. 7, (2019) 1900025, arXiv:1809.09899 [hep-th]

    2019 arXiv

  34. [42]

    Homotopy Lie Superalgebra in Yang-Mills Theory,

    A. M. Zeitlin, “Homotopy Lie Superalgebra in Yang-Mills Theory,” JHEP 09 (2007) 068, arXiv:0708.1773 [hep-th]

    2007 arXiv

  35. [43]

    Conformal Field Theory and Algebraic Structure o f Gauge Theory,

    A. M. Zeitlin, “Conformal Field Theory and Algebraic Structure o f Gauge Theory,” JHEP 03 (2010) 056, arXiv:0812.1840 [hep-th]

    2010 arXiv

  36. [44]

    New perspectives on the BRST algebraic structure of string theory,

    B. H. Lian and G. J. Zuckerman, “New perspectives on the BRST algebraic structure of string theory,” Commun. Math. Phys. 154 (1993) 613–646, arXiv:hep-th/9211072

    1993 arXiv

  37. [45]

    Quasiclassical Lian-Zuckerman Homotopy Algebra s, Courant Algebroids and Gauge Theory,

    A. M. Zeitlin, “Quasiclassical Lian-Zuckerman Homotopy Algebra s, Courant Algebroids and Gauge Theory,” Commun. Math. Phys. 303 (2011) 331–359, arXiv:0910.3652 [math.QA]

    2011 arXiv

  38. [46]

    Beltrami-Courant differentials and G8-algebras,

    A. M. Zeitlin, “Beltrami-Courant differentials and G8-algebras,” Adv. Theor. Math. Phys. 19 (2015) 1249–1275, arXiv:1404.3069 [math.QA]

    2015 arXiv

  39. [47]

    A homotopy BV algebra for Yang-Mills and color-kin ematics,

    M. Reiterer, “A homotopy BV algebra for Yang-Mills and color-kin ematics,” arXiv:1912.03110 [math-ph]

    1912 arXiv

  40. [48]

    10D super-Yang-Mills scattering amplitudes from its pure spinor action,

    M. Ben-Shahar and M. Guillen, “10D super-Yang-Mills scattering amplitudes from its pure spinor action,” JHEP 12 (2021) 014, arXiv:2108.11708 [hep-th]

    2021 arXiv

  41. [49]

    Off-Shell Color-Kinematics Duality for Chern-Simons,

    M. Ben-Shahar and H. Johansson, “Off-Shell Color-Kinematics Duality for Chern-Simons,” arXiv:2112.11452 [hep-th]

    arXiv

  42. [50]

    Off-shell color-k inematics duality from codifferentials,

    M. Ben-Shahar, F. Bonechi, and M. Zabzine, “Off-shell color-k inematics duality from codifferentials,” arXiv:2409.11484 [hep-th] . 41

    arXiv

  43. [51]

    Superspace duality in low-energy superstrings,

    W. Siegel, “Superspace duality in low-energy superstrings,” Phys. Rev. D 48 (1993) 2826–2837, arXiv:hep-th/9305073

    1993 arXiv

  44. [52]

    Double Field Theory,

    C. Hull and B. Zwiebach, “Double Field Theory,” JHEP 09 (2009) 099, arXiv:0904.4664 [hep-th]

    2009 arXiv

  45. [53]

    Background independent ac tion for double field theory,

    O. Hohm, C. Hull, and B. Zwiebach, “Background independent ac tion for double field theory,” JHEP 07 (2010) 016, arXiv:1003.5027 [hep-th]

    2010 arXiv

  46. [54]

    Gravit y = Yang-Mills,

    R. Bonezzi, C. Chiaffrino, F. Diaz-Jaramillo, and O. Hohm, “Gravit y = Yang-Mills,” 6, 2023. arXiv:2306.14788 [hep-th]

    2023 arXiv

  47. [55]

    Superg ravity as Generalised Geometry I: Type II Theories,

    A. Coimbra, C. Strickland-Constable, and D. Waldram, “Superg ravity as Generalised Geometry I: Type II Theories,” JHEP 11 (2011) 091, arXiv:1107.1733 [hep-th]

    2011 arXiv

  48. [56]

    N=1 Supersymmetric Double Field Theor y,

    O. Hohm and S. K. Kwak, “N=1 Supersymmetric Double Field Theor y,” JHEP 03 (2012) 080, arXiv:1111.7293 [hep-th]

    2012 arXiv

  49. [57]

    Supersymmetric Double Field T heory: Stringy Reformulation of Supergravity,

    I. Jeon, K. Lee, and J.-H. Park, “Supersymmetric Double Field T heory: Stringy Reformulation of Supergravity,” Phys. Rev. D 85 (2012) 081501, arXiv:1112.0069 [hep-th] . [Erratum: Phys.Rev.D 86, 089903 (2012)]

    2012 arXiv

  50. [58]

    Massless Fields with Half Integral Spin ,

    J. Fang and C. Fronsdal, “Massless Fields with Half Integral Spin ,” Phys. Rev. D 18 (1978) 3630

    1978

  51. [59]

    An Introduction t o free higher-spin fields,

    N. Bouatta, G. Compere, and A. Sagnotti, “An Introduction t o free higher-spin fields,” in 1st Solvay Workshop on Higher Spin Gauge Theories , pp. 79–99. 9, 2004. arXiv:hep-th/0409068

    2004 arXiv

  52. [60]

    Hidden Constants: Th e Theta Parameter of QCD and the Cosmological Constant of N=8 Supergra vity,

    A. Aurilia, H. Nicolai, and P. K. Townsend, “Hidden Constants: Th e Theta Parameter of QCD and the Cosmological Constant of N=8 Supergra vity,” Nucl. Phys. B 176 (1980) 509–522

    1980

  53. [61]

    Vertex operators for the kinematic algebra of Yang-Mills theory,

    R. Bonezzi, C. Chiaffrino, and O. Hohm, “Vertex operators for the kinematic algebra of Yang-Mills theory,” arXiv:2408.17341 [hep-th]

    arXiv

  54. [62]

    Globa l symmetries of Yang-Mills squared in various dimensions,

    A. Anastasiou, L. Borsten, M. J. Hughes, and S. Nagy, “Globa l symmetries of Yang-Mills squared in various dimensions,” JHEP 01 (2016) 148, arXiv:1502.05359 [hep-th]

    2016 arXiv

  55. [63]

    Unification of Type II St rings and T-duality,

    O. Hohm, S. K. Kwak, and B. Zwiebach, “Unification of Type II St rings and T-duality,” Phys. Rev. Lett. 107 (2011) 171603, arXiv:1106.5452 [hep-th]

    2011 arXiv

  56. [64]

    Double Field Theory of Ty pe II Strings,

    O. Hohm, S. K. Kwak, and B. Zwiebach, “Double Field Theory of Ty pe II Strings,” JHEP 09 (2011) 013, arXiv:1107.0008 [hep-th] . 42

    2011 arXiv

  57. [65]

    Covariant Action for Type IIB Supergravity,

    A. Sen, “Covariant Action for Type IIB Supergravity,” JHEP 07 (2016) 017, arXiv:1511.08220 [hep-th]

    2016 arXiv

  58. [66]

    Costello and O

    K. Costello and O. Gwilliam, Factorization Algebras in Quantum Field Theory . Cambridge University Press, 12, 2016

    2016

  59. [67]

    Costello and O

    K. Costello and O. Gwilliam, Factorization Algebras in Quantum Field Theory . New Mathematical Monographs (41). Cambridge University Press, 9, 2021

    2021

  60. [68]

    Particle Spin Dynamics as the Gr assmann Variant of Classical Mechanics,

    F. A. Berezin and M. S. Marinov, “Particle Spin Dynamics as the Gr assmann Variant of Classical Mechanics,” Annals Phys. 104 (1977) 336

    1977

  61. [69]

    L ocal Supersymmetry for Spinning Particles,

    L. Brink, S. Deser, B. Zumino, P. Di Vecchia, and P. S. Howe, “L ocal Supersymmetry for Spinning Particles,” Phys. Lett. B 64 (1976) 435. [Erratum: Phys.Lett.B 68, 488 (1977)]

    1976

  62. [70]

    Supersymmetrie s and the Pseudoclassical Relativistic electron,

    A. Barducci, R. Casalbuoni, and L. Lusanna, “Supersymmetrie s and the Pseudoclassical Relativistic electron,” Nuovo Cim. A 35 (1976) 377. 43

    1976

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.