Tensor Gauge Fields in Arbitrary Representations of GL(D, $${\mathbb{R})}$$ : II. Quadratic Actions

Bekaert, Xavier; Boulanger, Nicolas

doi:10.1007/s00220-006-0187-x

Cited by 99 publications

(160 citation statements)

References 69 publications

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“…In this way we can express any EA or any eom in terms of R (s) and traces (in the second set of indices) thereof. Further formulations of eoms that are local and include mixed symmetry cases can be found in [58,59]. Since above we have referred to [4,5], we feel that, to end this section, it is opportune for us to clarify the context in which our results are derived and point out the differences with the spirit of [4,5,39,40].…”

Section: Jhep01(2018)080mentioning

confidence: 99%

One-loop effective actions and higher spins. Part II

Bonora¹,

Cvitan²,

Prester³

et al. 2018

J. High Energ. Phys.

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In this paper we continue and improve the analysis of the effective actions obtained by integrating out a scalar and a fermion field coupled to external symmetric sources, started in the previous paper. The first subject we study is the geometrization of the results obtained there, that is we express them in terms of covariant Jacobi tensors. The second subject concerns the treatment of tadpoles and seagull terms in order to implement off-shell covariance in the initial model. The last and by far largest part of the paper is a repository of results concerning all two point correlators (including mixed ones) of symmetric currents of any spin up to 5 and in any dimensions between 3 and 6. In the massless case we also provide formulas for any spin in any dimension.

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Section: Jhep01(2018)080mentioning

confidence: 99%

One-loop effective actions and higher spins. Part II

Bonora¹,

Cvitan²,

Prester³

et al. 2018

J. High Energ. Phys.

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“…There are now q distinct exterior derivatives and codifferentials. Algebras of this type have been studied by Hull and Medeiros in the context of "exotic" higher spin gauge theories [19] and a mathematical analysis was given in [20,21].…”

Section: Divergence DIVmentioning

confidence: 99%

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Hallowell

Waldron

2007

Commun. Math. Phys.

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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.

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“…In fact, as noticed in [58], evidence for non-locality shows up already at the quartic level. The geometric formulation of free massless higher spins also hints towards the same, as they generically yield non-local EoMs [59,60] if higher-derivative terms are not considered [61,62].…”

Section: Jhep08(2012)093mentioning

confidence: 89%

“…(A.24) and (A.26), the two highest curls of the Fronsdal tensor boil down to objects we have already enlisted in subsection B.1, and therefore need not be considered separately. These equations are generalizations of the Damour-Deser relations [81] (see also [61,62]). For spin 5 2 , in particular, they make it sufficient to consider only symmetrized derivatives of the Fronsdal tensor.…”

Section: Jhep08(2012)093mentioning

confidence: 99%

Higher-spin fermionic gauge fields and their electromagnetic coupling

Henneaux

Gómez

Rahman

2012

J. High Energ. Phys.

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Abstract:We study the electromagnetic coupling of massless higher-spin fermions in flat space. Under the assumptions of locality and Poincaré invariance, we employ the BRST-BV cohomological methods to construct consistent parity-preserving off-shell cubic 1 − s − s vertices. Consistency and non-triviality of the deformations not only rule out minimal coupling, but also restrict the possible number of derivatives. Our findings are in complete agreement with, but derived in a manner independent from, the light-cone-formulation results of Metsaev and the string-theory-inspired results of Sagnotti-Taronna. We prove that any gauge-algebra-preserving vertex cannot deform the gauge transformations. We also show that in a local theory, without additional dynamical higher-spin gauge fields, the non-abelian vertices are eliminated by the lack of consistent second-order deformations.

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Tensor Gauge Fields in Arbitrary Representations of GL(D, $${\mathbb{R})}$$ : II. Quadratic Actions

Cited by 99 publications

References 69 publications

One-loop effective actions and higher spins. Part II

One-loop effective actions and higher spins. Part II

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Higher-spin fermionic gauge fields and their electromagnetic coupling

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