Consistent deformations of dual formulations of linearized gravity: A no-go result

Vrije Universiteit Brussel, Bruxelles, Brussels Capital, Belgium
Physical Review D (Impact Factor: 4.64). 10/2002; 67(4). DOI: 10.1103/PhysRevD.67.044010
Source: arXiv


The consistent, local, smooth deformations of the dual formulation of linearized gravity involving a tensor field in the exotic representation of the Lorentz group with Young symmetry type (D-3,1) (one column of length D-3 and one column of length 1) are systematically investigated. The rigidity of the Abelian gauge algebra is first established. We next prove a no-go theorem for interactions involving at most two derivatives of the fields. Comment: Reference added. Version to appear in Phys. Rev. D

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Available from: Nicolas Boulanger, Dec 04, 2012
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    • "The new field C µν m;npqrs indeed has the representation that is expected from the dualization of 10D gravity [34] [35] (although this dualization can not be fully understood at the non-linear level in 10D [36]). The systematics of the vector and tensor fields can be improved upon converting to dual representations by extracting the anti-symmetric tensors˚e ε mnpqr and/or ε αβ . "
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    ABSTRACT: IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional `dual graviton'. The invariant E6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions for the USp(8) covariant fermion fields. Implications are discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.
    Preview · Article · Dec 2014 · Journal of High Energy Physics
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    • ", 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). "
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    ABSTRACT: We develop exceptional field theory for E$_{8(8)}$, defined on a (3+248)-dimensional generalized spacetime with extended coordinates in the adjoint representation of E$_{8(8)}$. The fields transform under E$_{8(8)}$ generalized diffeomorphisms and are subject to covariant section constraints. The bosonic fields include an `internal' dreibein and an E$_{8(8)}$-valued `zweihundertachtundvierzigbein' (248-bein). Crucially, the theory also features gauge vectors for the E$_{8(8)}$ E-bracket governing the generalized diffeomorphism algebra and covariantly constrained gauge vectors for a separate but constrained E$_{8(8)}$ 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.
    Preview · Article · Jun 2014 · Physical Review D
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    • "If no vertices are compatible with any deformation of gauge symmetry, this is considered as a no-go theorem for a consistent interaction. Various no-go results are known for gravitational interactions in various models, see [2], [3], [4], [5], and references therein. "
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    ABSTRACT: It is usually assumed that any consistent interaction either deforms or retains the gauge symmetries of the corresponding free theory. We propose a simple model where an obvious irreducible gauge symmetry does not survive an interaction, while the interaction is consistent as it preserves the number of physical degrees of freedom. The model turns out admitting a less obvious reducible set of gauge generators which is compatible with the interaction and smooth in coupling constant. Possible application to gravity models is discussed.
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