No self-interaction for two-column massless fields

Bekaert, Xavier; Boulanger, Nicolas; Cnockaert, Sandrine

doi:10.1063/1.1823032

Cited by 117 publications

(228 citation statements)

References 38 publications

Supporting

Mentioning

220

Contrasting

Unclassified

Order By: Relevance

“…Interactions would amount to second quantization of these spinning particle models. Needless to say, this is an ambitious program, see [39] for a review of interacting higher spin theories.…”

Section: Discussionmentioning

confidence: 99%

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Hallowell

Waldron

2007

Commun. Math. Phys.

View full text Add to dashboard Cite

We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p + 2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are tensors or spinor-tensors on the curved background while conserved charges correspond to the various differential geometry operators acting on these. The Hamiltonian generalizes Lichnerowicz's wave/Laplace operator. It is central, and the models are supersymmetric whenever the background is a symmetric space, although there is an osp(2p|Q) superalgebra for any curved background. The lowest purely bosonic example (2p, Q) = (2, 0) corresponds to a deformed Jacobi group and describes Lichnerowicz's original algebra of constant curvature, differential geometric operators acting on symmetric tensors. The case (2p, Q) = (0, 1) is simply the N = 1 superparticle whose supercharge amounts to the Dirac operator acting on spinors. The (2p, Q) = (0, 2) model is the N = 2 supersymmetric quantum mechanics corresponding to differential forms. (This latter pair of models are supersymmetric on any Riemannian background.) When Q is odd, the models apply to spinor-tensors. The (2p, Q) = (2, 1) model is distinguished by admitting a central Lichnerowicz-Dirac operator when the background is constant curvature. The new supersymmetric models are novel in that the Hamiltonian is not just a square of super charges, but rather a sum of commutators of supercharges and commutators of bosonic charges. These models and superalgebras are a very useful tool for any study involving high rank tensors and spinors on manifolds.

show abstract

Section: Discussionmentioning

confidence: 99%

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Hallowell

Waldron

2007

Commun. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…, 8, that in three dimensions are dual to the Kaluza-Klein vectors A µ m . As the latter originate from components of the D " 11 metric, this amounts to including in the theory components of a 'dual graviton' [23][24][25][26] at the full non-linear level, something that is considered impossible on the grounds of the no-go theorems in [27,28]. In EFT this problem is resolved due to the presence of the extra E 8p8q gauge symmetry from (1.3).…”

Section: Introductionmentioning

confidence: 99%

“…Next we consider the non-covariant variation of the covariantized Einstein-Hilbert term, which is given by [20] 28) where the second term comes from the non-covariant transformation (3.24) of the vector field A µ M via (3.27). The non-covariant variation of the Chern-Simons term follows from (3.9) and yields 29) up to total derivatives.…”

Section: The Actionmentioning

confidence: 99%

Exceptional field theory. III.E8(8)

2014

View full text Add to dashboard Cite

We develop exceptional field theory for E 8p8q , defined on a (3+248)-dimensional generalized spacetime with extended coordinates in the adjoint representation of E 8p8q . The fields transform under E 8p8q generalized diffeomorphisms and are subject to covariant section constraints. The bosonic fields include an 'internal' dreibein and an E 8p8q -valued 'zweihundertachtundvierzigbein' (248-bein). Crucially, the theory also features gauge vectors for the E 8p8q E-bracket governing the generalized diffeomorphism algebra and covariantly constrained gauge vectors for a separate but constrained E 8p8q gauge symmetry. The complete bosonic theory, with a novel Chern-Simons term for the gauge vectors, is uniquely determined by gauge invariance under internal and external generalized diffeomorphisms. The theory consistently comprises components of the dual graviton encoded in the 248-bein. Upon picking particular solutions of the constraints the theory reduces to D " 11 or type IIB supergravity, for which the dual graviton becomes pure gauge. This resolves the dual graviton problem, as we discuss in detail.

show abstract

“…Thus, when dualizing B 2 into B 6 , O(D, D) covariance requires that we also dualize the graviton into a 'dual graviton'. While at the linearized level there is a straightforward procedure to dualize the graviton [1,2], leading to a field living in the mixed-Young tableau representation (D − 3, 1), 1 there are strong no-go theorems implying that at the non-linear level some new ingredients are needed [3,4].…”

Section: Jhep06(2016)026mentioning

confidence: 99%

“…A first attempt to introduce a 4-index antisymmetric tensor into the DFT action (together with sources) was performed in [28] in the formulation of [28][29][30][31]. Moreover, in [32] it was argued that the duality relation between the embedding tensor θ M N P of lower dimensional supergravity and a (D − 1)-potential D (D−1),M N P can be uplifted to higher dimensions by introducing mixed-symmetry dual potentials (in particular, relating the so-called Q-and R-fluxes to (8,2) and (9, 3) mixedsymmetry tensor fields, respectively) and that these mixed-symmetry potentials can be encoded in an antisymmetric 4…”

Section: Jhep06(2016)026mentioning

confidence: 99%

Dual double field theory

Bergshoeff

Hohm

Penas

et al. 2016

J. High Energ. Phys.

View full text Add to dashboard Cite

We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D, D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D, D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for "exotic" dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.

show abstract

No self-interaction for two-column massless fields

Cited by 117 publications

References 38 publications

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Exceptional field theory. III.E8(8)

Dual double field theory

Contact Info

Product

Resources

About