Consistency problems of hypergravity

Aragone, C.; Deser, S.

doi:10.1016/0370-2693(79)90808-6

Cited by 278 publications

(390 citation statements)

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“…Therefore, the construction of the consistent lagrangian theory of conformal higher spin fields (achieved in this paper) is an important step towards solution of the higher spin interaction problem [5] (see Sec. (2.2) below for a little bit more detailed reference to the higher spin problem).…”

Section: Conclusion 119 1 Introduction and Statement Of The Resultsmentioning

confidence: 99%

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Conformal higher spin theory

2003

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We construct gauge theory of interacting symmetric traceless tensors of all ranks s = 0, 1, 2, 3, ... which generalizes Weyl-invariant dilaton gravity to the higher spin case, in any dimension d > 2. The action is given by the trace of the projector to the subspace with positive eigenvalues of an arbitrary hermitian differential operatorĤ, and the symmetric tensors emerge after expansion of the latter in power series in derivatives. After decomposition in perturbative series around conformally flat pointĤ = 2 with Euclidean metric, the action functional describes conformal higher spin theory. Namely, the linear in fluctuation term cancels, while the one quadratic in fluctuation breaks up as a sum of conformal higher spin theories, the latter being free gauge theories of symmetric traceless tensors of rank s with with the algebra of observables of the quantized point particle. Each global symmetry produces a Noether current constructed out of ψ according to general formula we present in the paper. In the caseĤ = 2 the algebra of observables is an extension of the conformal algebra decomposed w.r.t. its adjoint action as a direct sum of finite-dimensional representations characterized by traceless rectangular two-row Young tableaux. This infinite-dimensional algebra coincides, in d = 3, 4, 6 with conformal higher spin algebras constructed before in terms of even spinor oscillators, which origin is due to twistor reformulation of the dynamics of the massless particle. The construction of the paper may be a starting point for diverse conjectures. First, we discuss the extension of the geometry "quantized point particle + conformal higher spin fields in d dimensions" to the one "tensionless d − 1 brane + higher spin massless fields in d + 1 dimensions", where the phase of ψ appear to describe transverse motion of the brane inside d + 1-bulk. This picture arises in the semiclassical approximation to the quantized particle dynamics, the latter approximation provides d-dimensional generalization of W -geometry elaborated on by Hull in d = 1, 2 case. Next, we propose a candidate on the role of Higgs-like higher spin compensator able to spontaneously break higher spin symmetries. At last, we make the conjecture that, in even dimensions d, the action of conformal higher spin theory equals the logarithmically divergent term of the action of massless higher spin fields on AdS d+1 evaluated on the solutions of Dirichlet-like problem, where conformal higher spin fields are boundary values of massless higher spin fields on AdS d+1 , the latter conjecture conforms with recent proposal (for d = 4) by Tseytlin and provides information on the full higher spin action in AdS d+1 .

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Section: Conclusion 119 1 Introduction and Statement Of The Resultsmentioning

confidence: 99%

“…5 The action (112) is covariant w.r.t. infinite-dimensional Lie algebra G which has the structure of a semidirect product of all canonical transformations with parameters ǫ(x, p)…”

Section: Classical Geometrymentioning

confidence: 99%

Conformal higher spin theory

2003

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“…As mentioned in Introduction one reason for this is that the full spectrum of fields in the appropriate higher spin supermultiplet also contains spin 0, 1/2 and 1 massless fields not included in the consideration of this paper. Our modest goal here is to show that, similarly to the 4d case [16], the problem with (cubic) higher-spingravitational interactions in the flat background [30,31] can be avoided in AdS 5 .…”

Section: General Propertiesmentioning

confidence: 99%

supersymmetric theory of higher spin gauge fields in AdS5 at the cubic level

2003

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“…Severe restrictions arise from powerful no-go theorems [1][2][3][4][5], which prohibit, in Minkowski space, minimal coupling to gravity, when the particle's spin s ≥ 5 2 , as well as to electromagnetism (EM), when s ≥ 3 2 . However, these particles may still interact through gravitational and EM multipoles.…”

Section: Jhep08(2012)093 1 Introductionmentioning

confidence: 99%

“…We do not consider mixed-symmetry fields, and restrict our attention to totally symmetric Dirac fermions ψ µ 1 ...µn , of spin s = n+ 1 2 . For these fields, we employ the powerful machinery of BRST-BV cohomological methods [20,21] to construct systematically consistent interaction vertices, 2 with the underlying assumptions of locality, Poincaré invariance and conservation of parity, and without relying on other methods. The would-be off-shell 1 − s − s cubic vertices will complement their bosonic counterparts constructed in [9].…”

Section: Jhep08(2012)093 1 Introductionmentioning

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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Consistency problems of hypergravity

Cited by 278 publications

References 6 publications

Conformal higher spin theory

Conformal higher spin theory

supersymmetric theory of higher spin gauge fields in AdS5 at the cubic level

Higher-spin fermionic gauge fields and their electromagnetic coupling

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