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Fermionic Spencer Cohomologies of D=11 Supergravity

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Pith's one-line read The D=11 Poincaré superalgebra has exactly one new fermionic Spencer cohomology class, isomorphic to a spinor.

desk verdict A serious extension of Spencer cohomology for the D=11 Poincaré superalgebra, with one load-bearing computational step that still needs to be made reproducible. read the letter →

arxiv 2411.16869 v2 pith:FCRKA7SC submitted 2024-11-25 hep-th math-phmath.MPmath.RT

C.A. Cremonini , P.A. Grassi , R. Noris , L. Ravera , A. Santi This is my paper · ORCID
classification hep-thmath-phmath.MPmath.RT MSC 17B5617B70 PACS 04.65.+e
keywords SpencercohomologyD=11supergravityPoincarésuperalgebrafiltereddeformationsHilbert-PoincaréseriesMolien-WeylformulaKillingsuperalgebrasno-gotheorem
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 sets out to determine the Spencer cohomology of the $D=11$ Poincaré superalgebra in form number 2 and positive grading, and then to use that cohomology to control filtered deformations along odd directions. It finds one genuinely new fermionic class, $H^{1,2}(m,p) \cong S$, alongside the known bosonic class $H^{2,2}(m,p) \cong \Lambda^4 V$, with $H^{3,2}$ and $H^{4,2}$ vanishing. It then proposes a definition of filtered deformations with odd first-order directions and proves a no-go theorem: a maximally supersymmetric filtered subdeformation whose odd direction is generic (timelike) and nilpotent is isomorphic to a first-order odd deformation, so the underlying Lorentzian manifold is flat. A sympathetic reader would care because this closes the first-order deformation problem along generic fermionic directions and leaves the lightlike case as the only possible source of non-flat odd supergeometries.

What carries the argument

The argument runs through the Spencer complex $C^\bullet(m,\mathfrak{p})$ — the Chevalley-Eilenberg cochains of the supertranslation ideal $m=\mathfrak{p}_{-1}\oplus\mathfrak{p}_{-2}$ with values in $\mathfrak{p}$, graded by spinor and vector form number. The Molien-Weyl integral formula, implemented over the compact Cartan torus of $\mathrm{Spin}(11)$ with the Weyl weight function and plethystic exponentials, produces Hilbert-Poincaré $U$-series and Euler characteristics that predict the cohomology; the Cartan-Tanaka prolongation viewpoint then organizes the cocycle equations. A normalization procedure removes coboundaries and reduces $H^{1,2}$ to a system of Clifford-algebra equations, while the deformation analysis uses the Jacobi identities for filtered deformations over an exterior algebra $\Lambda^\bullet W$, with nilpotency of the first-order direction as a cohomological condition. The load-bearing objects are the cocycle $\varepsilon_\varphi+\epsilon_\varphi=\partial(Z\otimes\varphi)$ and the grading element $Z$.

What would settle it

Find a nonzero solution $(\varepsilon,\epsilon)$ of the normalized cocycle system in Corollary 4.1, for example by solving the explicit equations (4.20)-(4.22) with a different symbolic computation or a different explicit gamma-matrix realization; any nonzero solution would enlarge $H^{1,2}(m,\mathfrak{p})$ beyond $S$ and overturn Theorem 1.1, while re-deriving the same vanishing by hand would confirm it.

Watch

Extended reading notes

Core claim

The paper's central claim is that the Spencer cohomology of the $D=11$ Poincaré superalgebra $\mathfrak{p}$ in form number 2 is completely determined: $H^{1,2}(m,p) \cong S$, $H^{2,2}(m,p) \cong \Lambda^4 V$, and $H^{3,2}=H^{4,2}=0$, with all higher positive gradings vanishing by degree reasons. The new fermionic class $H^{1,2}$ is odd, irreducible, and represented by $\varepsilon_\varphi+\epsilon_\varphi=\partial(Z\otimes\varphi)$, the Spencer coboundary of the grading element paired with a spinor. The paper further claims that any maximally supersymmetric filtered subdeformation of $\mathfrak{p}$ whose first-order odd direction is generic (timelike) and nilpotent is isomorphic to a first-order odd filtered subdeformation, and consequently the underlying Lorentzian manifold is flat. This is presented as a no-go theorem for non-flat highly supersymmetric backgrounds along generic fermionic directions.

Load-bearing premise

Everything in Theorem 1.1 concerning the new group $H^{1,2}$ rests on the assertion that the Clifford-algebra system (4.20)-(4.22) has only the zero solution, which the paper verifies in a computer-algebra notebook rather than by a self-contained proof.

Editorial extensions

If this is right

  • The new class $H^{1,2}(m,\mathfrak{p}) \cong S$ provides the first fermionic first-order deformation direction of the $D=11$ Poincaré superalgebra, in addition to the known bosonic $\Lambda^4 V$ class.
  • Because $H^{3,2}=H^{4,2}=0$, the first-order odd deformation problem along generic spinor directions has no higher Spencer obstructions at those degrees.
  • The no-go theorem implies that a maximally supersymmetric filtered subdeformation with generic nilpotent odd first-order direction is isomorphic to a first-order odd deformation, forcing the underlying Lorentzian manifold to be flat.
  • The Euler-characteristic data in the Hilbert-Poincaré series indicate non-trivial Spencer cohomology at higher form numbers, which the paper identifies as candidates for higher cocycles deforming $\mathfrak{p}$ into strongly homotopy Lie algebras.

Reading between the lines

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

  • A consequence left implicit is that the vanishing proof of normalized cocycles is the load-bearing step; an independent, hand-checkable proof of the Clifford system (4.20)-(4.22) would remove the only computational black box in Theorem 1.1.
  • The no-go theorem deliberately excludes lightlike spinors, so the lightlike orbit of the projectivized spinor representation is the natural place to search for non-flat maximally supersymmetric odd deformations.
  • Because the $H^{1,2}$ class disappears when $\mathfrak{p}$ is extended to the conformal superalgebra $\mathfrak{p}\oplus\mathbb{R}Z$, the same machinery in a conformal setting would likely trivialize the extra spinorial 1-form, suggesting that this spinor is an artifact of the Poincaré rather than the conformal frame.
  • Running the same Molien-Weyl and Spencer analysis in lower dimensions, for instance $N=1$ in $D=4$, would give a tractable test of whether the no-go pattern persists outside eleven dimensions.
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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

2 major / 4 minor

Summary. The paper computes Spencer cohomology groups of the D=11 Poincaré superalgebra, concentrating on fermionic groups of Z-grading 1 and 3 at form number 2, and uses the result H^{1,2}(m,p) ≅ S to study maximally supersymmetric filtered subdeformations along generic odd directions. The main results are Theorem 1.1 (classification of H^{d,2} for all positive d), Theorem 1.2 (collapsed Hilbert-Poincaré series computed by Molien-Weyl techniques), and Theorem 5.1 (a no-go theorem for maximally supersymmetric filtered subdeformations of p with generic nilpotent odd infinitesimal deformation).

Significance. If the results are correct, the paper completes the classification of H^{d,2}(m,p), identifies a novel fermionic Spencer class isomorphic to S, and provides a rigorous framework for odd filtered deformations of the D=11 Poincaré superalgebra. The Molien-Weyl computation of Hilbert-Poincaré series for different isotypic components is a useful technical contribution, as is the explicit use of Cartan-Tanaka prolongation and injectivity results from earlier work. The paper is also transparent about where its argument relies on computer assistance. The main caveat is that the key vanishing step behind H^{1,2} ≅ S is not proved in the manuscript itself; this is load-bearing for Theorem 1.1(1) and for the subsequent deformation no-go theorem.

major comments (2)
  1. [§4.2.2 below Eq. (4.22)] The central vanishing result is not established in the text. After reducing the normalized cocycle conditions to the linear system (4.20)-(4.22), the authors state that they 'haven't been able to find a sufficiently clear and complete proof' and refer to an accompanying Mathematica supplement, which is not reproduced in the paper. This vanishing is exactly what converts the inclusion H^{1,2} ⊃ S from Proposition 4.2 into the isomorphism H^{1,2} ≅ S in Theorem 1.1(1). The Euler characteristic information in Theorem 1.2 only controls alternating sums over form number and is compatible with the existence of additional cocycles, so it cannot certify the vanishing. I recommend either supplying a complete hand-checkable derivation of ε = ϵ = 0 from (4.20)-(4.22) or, at minimum, making the supplement fully self-contained and independently verifiable (documented code, explicit Clifford-algebra realization, and all outputs that imply the vanishing).
  2. [§5.4] The no-go theorem inherits the computational gap in Theorem 4.1. Corollary 5.1 parametrizes the infinitesimal deformation as ε + ϵ = ∂(Z ⊗ ϕ) + ∂X_S using H^{1,2}(m,h) ≅ H^{1,2}(m,p) and Theorem 4.1; if additional cocycles existed in H^{1,2}(m,p), the parametrization would be incomplete and the reduction to the nilpotent first-order form (5.48) would not follow. The paper should state explicitly that the validity of Theorem 5.1 is conditional on a complete proof of Theorem 4.1, and the revision should address this dependence when the missing computation is supplied.
minor comments (4)
  1. [§3.2] The invariant form ω^(4)_2 is used in equations (3.8)-(3.9) before its definition is given immediately after (3.9); please move the definition before its first use.
  2. [Proposition 4.2] The statement 'H^{1,2}(m,p) ⊃ S^* ∼= S as an so(V)-submodule' is ambiguous; it should say that H^{1,2}(m,p) contains a submodule isomorphic to S, rather than using the subset symbol with an isomorphism.
  3. [§3.3, Lemma 3.1] Lemma 3.1 and the resulting Table 2 rely on a Mathematica notebook that is referenced but not included in the text. Since these computations are not used in the proof of the main classification, this is not a blocking issue, but including the notebook as an ancillary file or listing the intermediate series explicitly would improve reproducibility.
  4. [§4.2.2] The sentence 'we haven't been able to find a sufficiently clear and complete proof that avoids discussing too many subcases' is honest but effectively concedes that Theorem 4.1 is not proven in the paper; the revision should either remove this concession by supplying the proof or clearly mark Theorem 4.1 as a computational claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: H^{1,2}(m,p)≅S is derived from the cocycle system (4.20)-(4.22), with self-citations used only as independent published theorems and the Hilbert-Poincaré series as a consistency check.

full rationale

The derivation is self-contained with respect to the claimed circularity patterns. Theorem 4.1, which supplies the vanishing of normalized cocycles and hence H^{1,2}(m,p)≅S, is obtained by reducing the cocycle condition to the linear system (4.20)-(4.22) and solving it, with the help of an explicit Clifford-algebra computation in the Mathematica supplement, rather than by assuming the cohomology group. The Hilbert-Poincaré series in Theorem 1.2 is used only as an Euler-characteristic consistency check; the paper explicitly says at §4.2.2 that the Euler characteristic is coherent with but does not prove the vanishing, so the classification is not an input to the proof. The prior results [3], [5] and [33] (with shared authorship by A. Santi) are invoked as published theorems for the even-degree Spencer cohomology, the H^{2,2} description, and the injectivity of the Spencer differential/first prolongation; these are parameter-free external results that do not assume H^{1,2}=S, so the citations constitute independent evidence rather than a self-citation chain. The one caveat is a verification gap, not circularity: in §4.2.2 below Eq. (4.22) the authors write "we haven't been able to find a sufficiently clear and complete proof" and defer the solution of (4.20)-(4.22) to an unreproduced Mathematica supplement; a bug there would enlarge H^{1,2} and propagate to Theorems 1.1 and 5.1. This is a correctness risk, not a reduction of the result to its own input, and does not raise the circularity score.

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

The central claims rest on standard facts about the D=11 spinor representation, the triviality of the first Cartan-Tanaka prolongation (published in [33]), the Fierz decomposition, the classical Molien-Weyl formula, and two assumptions specific to the no-go theorem: compact (timelike) stabilizer and nilpotent first-order deformation. No parameters are fitted to data.

assumptions (6)
  • standard math The Dirac current κ : S⊗S → V is the unique (up to scaling) so(V)-equivariant symmetric map
    Invoked in the definition of the Poincaré superalgebra bracket in §1.1 (Eq. (1.1)) based on the irreducibility of the Majorana spinor representation S of Spin(1,10).
  • standard math First Cartan-Tanaka prolongation of p and of p⊕RZ is trivial
    Used in §4.2 to establish injectivity of the Spencer operator on C^{1,1}; cited from Altomani-Santi [33].
  • standard math The Fierz decomposition ⊙^2 S ≅ Λ^1 V ⊕ Λ^2 V ⊕ Λ^5 V holds for D=11 Majorana spinors
    Used in §4.2 to normalize cocycles and in Proposition 4.3; standard Clifford algebra identity.
  • domain assumption The action of Spin(V) on P(S) has a unique open (timelike) orbit with compact stabilizer
    The no-go theorem Theorem 5.1 restricts to the timelike (generic) orbit; used in §5.4 to decompose Λ^4 V and to reduce h0.
  • ad hoc to paper The first-order infinitesimal deformation is nilpotent (Definition 5.2)
    This is a technical cohomological assumption introduced by the authors; it is not generic but satisfied in many natural cases. The no-go theorem is conditional on it.
  • standard math Classical Molien-Weyl formula and Weyl integration formula for compact Lie groups
    The starting point of §2, used to compute Hilbert-Poincaré series; standard invariant theory.

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Cite this review

Pith. "Pith review of Fermionic Spencer Cohomologies of D=11 Supergravity." pith.science (2026). https://pith.science/paper/FCRKA7SC

@misc{pith2026241116869,
  author       = {Pith},
  title        = {Pith review of: Fermionic Spencer Cohomologies of D=11 Supergravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FCRKA7SC}},
  note         = {Machine review of arXiv:2411.16869}
}
abstract

We combine the theory of Cartan-Tanaka prolongations with the Molien-Weyl integral formula and Hilbert-Poincar\'e series to compute the Spencer cohomology groups of the $D=11$ Poincar\'e superalgebra $\mathfrak p$, relevant for superspace formulations of $11$-dimensional supergravity in terms of nonholonomic superstructures. This includes novel fermionic Spencer groups, providing with new cohomology classes of $\mathbb Z$-grading $1$ and form number $2$. Using the Hilbert-Poincar\'e series and the Euler characteristic, we also explore Spencer cohomology contributions in higher form numbers. We then propose a new general definition of filtered deformations of graded Lie superalgebras along first-order fermionic directions and investigate such deformations of $\mathfrak p$ that are maximally supersymmetric. In particular, we establish a no-go type theorem for maximally supersymmetric filtered subdeformations of $\mathfrak p$ along timelike (i.e., generic) first-order fermionic directions.

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Cited by 1 Pith paper

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Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages · cited by 1 Pith paper

  1. [1]

    de Medeiros, J

    P. de Medeiros, J. Figueroa-O’Farrill and A. Santi,Killing superalgebras for Lorentzian four-manifolds, JHEP06, 106 (2016)

    work page 2016

  2. [2]

    de Medeiros, J

    P. de Medeiros, J. Figueroa-O’Farrill and A. Santi,Killing superalgebras for Lorentzian six-manifolds, J. Geom. Phys.132, 13-44 (2018)

    work page 2018

  3. [3]

    Figueroa-O’Farrill and A

    J. Figueroa-O’Farrill and A. Santi,Spencer cohomology and 11-dimensional supergravity, Commun. Math. Phys.349, 627–660 (2017)

    work page 2017

  4. [4]

    Figueroa-O’Farrill and A

    J. Figueroa-O’Farrill and A. Santi,Eleven-dimensional supergravity from filtered subdeforma- tions of the Poincaré superalgebra, J. Phys. A49, 295204 (2016)

    work page 2016

  5. [5]

    Figueroa-O’Farrill and A

    J. Figueroa-O’Farrill and A. Santi,On the algebraic structure of Killing superalgebras, Adv. Theor. Math. Phys.21, 1115-1160 (2017)

    work page 2017

  6. [6]

    Geometry, Lie Theory and Applications

    A. Santi,Remarks on highly supersymmetric backgrounds of 11-dimensional supergravity, Proceedings of the Abel Symposium 2019 “Geometry, Lie Theory and Applications”, Springer series “Abel Symposia”, 253–277 (2022)

    work page 2022

  7. [7]

    Santi and A

    A. Santi and A. Spiro,Super-Poincare algebras, space-times and supergravities (I), Adv. Theor. Math. Phys.16, 1411-1441 (2012). 37

    work page 2012

  8. [8]

    Santi and A

    A. Santi and A. Spiro,Super-Poincare algebras, space-times and supergravities (II), J. Math. Phys.53, 032505 (2012)

    work page 2012

Show all 46 references
  1. [9]

    Beckett, J

    A. Beckett, J. Figueroa-O’Farrill,Killing superalgebras for lorentzian five-manifolds, JHEP7 (2021)

    2021

  2. [10]

    Figueroa-O’Farrill, G

    J. Figueroa-O’Farrill, G. Franchetti,Kaluza-Klein reductions of maximally supersymmetric five-dimensional Lorentzian spacetimes, Classical Quantum Gravity39, 40 pp (2022)

    2022

  3. [11]

    S. J. Cheng and V. G. Kac,Generalized Spencer cohomology and filtered deformations of Z-graded Lie superalgebras, Adv. Theor. Math. Phys.2, 1141-1182 (1998)

    1998

  4. [12]

    Chevalley and S

    C. Chevalley and S. Eilenberg,Cohomology Theory of Lie Groups and Lie Algebras, Trans. Amer. Math. Soc.63, 85-124 (1948)

    1948

  5. [13]

    Nahm,Supersymmetries and their representations, Nucl

    W. Nahm,Supersymmetries and their representations, Nucl. Phys.B135, 149–166 (1978)

    1978

  6. [14]

    Cremmer, B

    E. Cremmer, B. Julia and J. Scherk,Supergravity Theory in Eleven-Dimensions, Phys. Lett. B76, 409-412 (1978)

    1978

  7. [15]

    Kruglikov, A

    B. Kruglikov, A. Santi, D. TheSymmetries of supergeometries related to nonholonomic superdistributions, Transform. Groups29(2024), 179–229

    2024

  8. [16]

    van Nieuwenhuizen,Unitarity of supergravity andZ2 or Z2×Z 2 or Z2×Z 2×Z 2 gradings of gauge and ghost fields, J

    P. van Nieuwenhuizen,Unitarity of supergravity andZ2 or Z2×Z 2 or Z2×Z 2×Z 2 gradings of gauge and ghost fields, J. Math. Phys.21, 2562–2566 (1980)

    1980

  9. [17]

    Derksen and G

    H. Derksen and G. KemperComputational Invariant Theory, New York: Springer (2002)

    2002

  10. [18]

    Procesi,Lie groups: An approach through invariants and representations, Universitext

    C. Procesi,Lie groups: An approach through invariants and representations, Universitext. New York, NY: Springer. (2007)

    2007

  11. [19]

    C. A. Cremonini, P. A. Grassi, R. Noris, L. Ravera,Supergravities and Branes from Hilbert- Poincaré Series, JHEP12, 088 (2023)

    2023

  12. [20]

    Sullivan,Infinitesimal computations in topology, Publications Mathématiques de l’IHES 47, 269-331 (1977)

    D. Sullivan,Infinitesimal computations in topology, Publications Mathématiques de l’IHES 47, 269-331 (1977)

    1977

  13. [21]

    Castellani, R

    L. Castellani, R. D’Auria and P. Frè,Supergravity and superstrings: A Geometric perspective, Vol. 1-3, Published in Singapore: World Scientific, 1991

    1991

  14. [22]

    Castellani and A

    L. Castellani and A. Perotto,Free differential algebras: Their use in field theory and dual formulation, Lett. Math. Phys.38, 321 (1996)

    1996

  15. [23]

    Castellani, P

    L. Castellani, P. Frè, F. Giani, K. Pilch and P. van Nieuwenhuizen,Beyondd = 11Supergravity and Cartan Integrable Systems, Phys. Rev. D26, 1481 (1982)

    1982

  16. [24]

    D’Auria, P

    R. D’Auria, P. Frè and T. Regge,Graded Lie Algebra Cohomology and Supergravity, Riv. Nuovo Cim.3N12, 1 (1980)

    1980

  17. [25]

    D’Auria and P

    R. D’Auria and P. Frè,Geometric Supergravity in d = 11 and Its Hidden Supergroup, Nucl. Phys. B201(1982), 101-140 [erratum: Nucl. Phys. B206(1982), 496]

    1982

  18. [26]

    Fialowski,An example of formal deformations of Lie algebras, in Deformation Theory of Algebras and Structures and Applications, Kluwer 1988, 375–401

    A. Fialowski,An example of formal deformations of Lie algebras, in Deformation Theory of Algebras and Structures and Applications, Kluwer 1988, 375–401. 38

    1988

  19. [27]

    Pouliot,Molien function for duality, JHEP01, 021 (1999)

    P. Pouliot,Molien function for duality, JHEP01, 021 (1999)

    1999

  20. [28]

    Weyl,Classical Groups: their Invariants and Representations, Princeton University Press (1997)

    H. Weyl,Classical Groups: their Invariants and Representations, Princeton University Press (1997)

    1997

  21. [29]

    B. Feng, A. Hanany and Y. H. He,Counting gauge invariants: The Plethystic program, JHEP 03, 090 (2007)

    2007

  22. [30]

    Hanany, N

    A. Hanany, N. Mekareeya and G. Torri,The Hilbert Series of Adjoint SQCD, Nucl. Phys. B 825, 52-97 (2010)

    2010

  23. [31]

    Binegar,Cohomology and deformations of Lie superalgebras, Lett

    B. Binegar,Cohomology and deformations of Lie superalgebras, Lett. Math. Phys.12(1986), no. 4, 301–308

    1986

  24. [32]

    D. A. Leites,Cohomology of Lie superalgebras, Funkcional. Anal. i Prilozen.9(1975), no. 4, 75–76

    1975

  25. [33]

    Altomani and A

    A. Altomani and A. Santi,Classification of maximal transitive prolongations of super-Poincaré algebras, Adv. Math.265, 60–96 (2014)

    2014

  26. [34]

    A. S. Galaev,Irreducible complex skew-Berger algebras, Differential Geom. Appl.27, 743–754, 2009

    2009

  27. [35]

    Andrianopoli, R

    L. Andrianopoli, R. D’Auria and L. Ravera,Hidden Gauge Structure of Supersymmetric Free Differential Algebras, JHEP1608, 095 (2016)

    2016

  28. [36]

    Andrianopoli, R

    L. Andrianopoli, R. D’Auria and L. Ravera,More on the Hidden Symmetries of 11D Super- gravity, Phys. Lett. B772, 578 (2017)

    2017

  29. [37]

    Ravera,On the Hidden Symmetries ofD = 11Supergravity, Springer Proc

    L. Ravera,On the Hidden Symmetries ofD = 11Supergravity, Springer Proc. Math. Stat. 396(2022), 211-222

    2022

  30. [38]

    Ravera,Hidden role of Maxwell superalgebras in the free differential algebras of D = 4 and D = 11 supergravity, Eur

    L. Ravera,Hidden role of Maxwell superalgebras in the free differential algebras of D = 4 and D = 11 supergravity, Eur. Phys. J. C78, 211 (2018)

    2018

  31. [39]

    Candiello, K

    A. Candiello, K. Lechner,Duality in supergravity theories, Nuclear Physics B412, 479–501 (1994)

    1994

  32. [40]

    P. S. Howe,Weyl superspace, Phys. Lett. B415, 149–155 (1997)

    1997

  33. [41]

    Samtleben,Lectures on Gauged Supergravity and Flux Compactifications, Class

    H. Samtleben,Lectures on Gauged Supergravity and Flux Compactifications, Class. Quant. Grav.25(2008), 214002

    2008

  34. [42]

    Trigiante,Gauged Supergravities, Phys

    M. Trigiante,Gauged Supergravities, Phys. Rept.680(2017), 1-175

    2017

  35. [43]

    de Wit and H

    B. de Wit and H. Samtleben,Gauged maximal supergravities and hierarchies of nonAbelian vector-tensor systems, Fortsch. Phys.53(2005), 442-449

    2005

  36. [44]

    de Wit, H

    B. de Wit, H. Samtleben and M. Trigiante,Magnetic charges in local field theory, JHEP09 (2005), 016

    2005

  37. [45]

    de Wit, H

    B. de Wit, H. Samtleben and M. Trigiante,The Maximal D=4 supergravities, JHEP06 (2007), 049

    2007

  38. [46]

    de Wit, H

    B. de Wit, H. Nicolai and H. Samtleben,Gauged Supergravities, Tensor Hierarchies, and M-Theory, JHEP02(2008), 044. 39

    2008

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