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Chabrol Lilian - One of the best experts on this subject based on the ideXlab platform.

  • Geometry of $\mathbb{R}^{+}\times E_{3(3)}$ exceptional field theory and F-theory
    'Springer Science and Business Media LLC', 2019
    Co-Authors: Chabrol Lilian
    Abstract:

    International audienceWe consider a non trivial solution to the section condition in the context of ℝ$^{+}$ ×E$_{3(3)}$ exceptional field theory and show that allowing fields to depend on the additional stringy coordinates of the extended internal space permits to describe the monodromies of (p, q) 7-branes in the context of F-theory. General expressions of non trivial fluxes with associated linear and quadratic constraints are obtained via a comparison to the embedding tensor of eight dimensional gauged maximal supergravity with gauged trombone symmetry. We write an explicit generalised Christoffel Symbol for E$_{3(3)}$ EFT and show that the equations of motion of F-theory, namely the vanishing of a 4 dimensional Ricci tensor with two of its dimensions fibered, can be obtained from a generalised Ricci tensor and an appropriate type IIB ansatz for the metric

  • Geometry of $\mathbb{R}^{+}\times E_{3(3)}$ Exceptional Field Theory and F-theory
    'Springer Science and Business Media LLC', 2019
    Co-Authors: Chabrol Lilian
    Abstract:

    We consider a non trivial solution to the section condition in the context of $\mathbb{R}^{+}\times E_{3(3)}$ exceptional field theory and show that allowing fields to depend on the additional stringy coordinates of the extended internal space permits to describe the monodromies of (p,q) 7-branes in the context of F-theory. General expressions of non trivial fluxes with associated linear and quadratic constraints are obtained via a comparison to the embedding tensor of eight dimensional gauged maximal supergravity with gauged trombone symmetry. We write an explicit generalised Christoffel Symbol for $E_{3(3)}$ EFT and show that the equations of motion of F-theory, namely the vanishing of a 4 dimensional Ricci tensor with two of its dimensions fibered, can be obtained from a generalised Ricci tensor and an appropriate type IIB ansatz for the metric

Mann R B - One of the best experts on this subject based on the ideXlab platform.

  • Palatini Variational Principle for an Extended Einstein-Hilbert Action
    1997
    Co-Authors: Burton H, Mann R B
    Abstract:

    We consider a Palatini variation on a generalized Einstein-Hilbert action. We find that the Hilbert constraint, that the connection equals the Christoffel Symbol, arises only as a special case of this general action, while for particular values of the coefficients of this generalized action, the connection is completely unconstrained. We discuss the relationship between this situation and that usually encountered in the Palatini formulation

  • Palatini Variational Principle for an Extended Einstein-Hilbert Action
    'American Physical Society (APS)', 1997
    Co-Authors: Burton H, Mann R B
    Abstract:

    We consider a Palatini variation on a generalized Einstein-Hilbert action. We find that the Hilbert constraint, that the connection equals the Christoffel Symbol, arises only as a special case of this general action, while for particular values of the coefficients of this generalized action, the connection is completely unconstrained. We discuss the relationship between this situation and that usually encountered in the Palatini formulation.Comment: 14 pages, LaTe

Vollick, Dan N. - One of the best experts on this subject based on the ideXlab platform.

  • On the Dirac field in the Palatini form of 1/R gravity
    'American Physical Society (APS)', 2004
    Co-Authors: Vollick, Dan N.
    Abstract:

    In recent papers (astro-ph/0306630, gr-qc/0312041) I have argued that the observed cosmological acceleration can be accounted for by the inclusion of a 1/R term in the gravitational action in the Palatini formalism. Subsequently, Flanagan (astro-ph/0308111, gr-qc/0403063) argued that this theory is equivalent to a scalar-tensor theory which produces corrections to the standard model that are ruled out experimentally. In this article I examine the Dirac field coupled to 1/R gravity. The Dirac action contains the connection which was taken to be the Christoffel Symbol, not an independent quantity, in the papers by Flanagan. Since the metric and connection are taken to be independent in the Palatini approach it is natural to allow the connection that appears in the Dirac action to be an independent quantity. This is the approach that is taken in this paper. The resulting theory is very different and much more complicated than the one discussed in Flanagan's papers.Comment: 6 pages, LaTe

  • On the Dirac field in the Palatini form of 1/R gravity
    2004
    Co-Authors: Vollick, Dan N.
    Abstract:

    In recent papers (astro-ph/0306630, gr-qc/0312041) I have argued that the observed cosmological acceleration can be accounted for by the inclusion of a 1/R term in the gravitational action in the Palatini formalism. Subsequently, Flanagan (astro-ph/0308111, gr-qc/0403063) argued that this theory is equivalent to a scalar-tensor theory which produces corrections to the standard model that are ruled out experimentally. In this article I examine the Dirac field coupled to 1/R gravity. The Dirac action contains the connection which was taken to be the Christoffel Symbol, not an independent quantity, in the papers by Flanagan. Since the metric and connection are taken to be independent in the Palatini approach it is natural to allow the connection that appears in the Dirac action to be an independent quantity. This is the approach that is taken in this paper. The resulting theory is very different and much more complicated than the one discussed in Flanagan's papers

Burton H - One of the best experts on this subject based on the ideXlab platform.

  • Palatini Variational Principle for an Extended Einstein-Hilbert Action
    1997
    Co-Authors: Burton H, Mann R B
    Abstract:

    We consider a Palatini variation on a generalized Einstein-Hilbert action. We find that the Hilbert constraint, that the connection equals the Christoffel Symbol, arises only as a special case of this general action, while for particular values of the coefficients of this generalized action, the connection is completely unconstrained. We discuss the relationship between this situation and that usually encountered in the Palatini formulation

  • Palatini Variational Principle for an Extended Einstein-Hilbert Action
    'American Physical Society (APS)', 1997
    Co-Authors: Burton H, Mann R B
    Abstract:

    We consider a Palatini variation on a generalized Einstein-Hilbert action. We find that the Hilbert constraint, that the connection equals the Christoffel Symbol, arises only as a special case of this general action, while for particular values of the coefficients of this generalized action, the connection is completely unconstrained. We discuss the relationship between this situation and that usually encountered in the Palatini formulation.Comment: 14 pages, LaTe

Victor Tapia - One of the best experts on this subject based on the ideXlab platform.

  • a constructive demonstration of the uniqueness of the Christoffel Symbol
    arXiv: Differential Geometry, 2001
    Co-Authors: Victor Tapia
    Abstract:

    In this note we exhibit a constructive demonstration of the uniqueness of the Christoffel Symbol.

  • (g) =
    2001
    Co-Authors: Victor Tapia
    Abstract:

    is usually introduced (Spivak, 1975) as the connection which solves the metricity condition ∇λgµν = 0. (2) On the other hand, whether the Christoffel Symbol is the only connection which can be constructed from a symmetric second–rank tensor gµν remains an open question. In this note we exhibit a constructive demonstration of the uniqueness of the Christoffel Symbol. Let us start by reviewing some simple results of tensor calculus. Let M be an n–dimensional differentiable manifold. Several geometric objects can be introduced over conveniently defined fibered bundles based on M. In order to classify them we adopt a taxonomic approach, cf. (Visconti, 1992): a tensor is an object which transforms like a tensor, etc. The previous definition makes reference to the way in which an object transforms under changes of local coordinates. Let x µ, µ = 1, 2, · · ·, n, and yα, α = 1, 2, · · ·,n, be local coordinates on M. Both sets are related by yα = yα (xµ), and the differential form of this relation is dy α () α ∂y = dx µ. (3) ∂x µ Due to the intrinsic function theorem, this relation tells us that yα are functions of x µ, yα = yα (xµ). In order to express x µ as functions of yα, x µ = x µ(yα), we need to invert eq. (3). This can be achieved if