[en] An analysis of the origin of the D = 26 critical dimension for (bosonic) Liouville's field theory (LFT) is presented. It is proved that D= 26 is associated to octonions which are also connected with the zero modes of LFT. As a by-product it is devised an algorithm which can be applied to any field theory of gravitation type (e.g. supergravities) to obtain predictions on its space-time content and/or its symmetry-breaking pattern

[en] The coupled Yang-Mills supergravity theory in ten dimensions leads naturally to spacetimes of the form t x M³ x M⁶, where M⁶ is a compact homogeneous space with a non-integrable almost complex structure. (author)

[en] By using the de Rham-Yano-Bochner lemma on harmonic tensor fields in a compact orientable manifold, it is shown that the extra dimensions in eleven-dimensional simple supergravity will be Ricci-flat if they are compact

[en] The masses before spontaneous symmetry breaking are studied for a theory of supergravity using a multiconnected superior space. It is found that the lowest nonvanishing masses must be much higher than Planck's

[en] Two new alternative representations are presented for the action of an arbitrary number N of HKX transformations on an arbitrary Weyl solution. The resulting new class of Ernst potentials depends on 2N real parameters. Applications of the derived representations are shown. (author)

[en] The reduction of N=1 supergravity from ten-dimensional space is implemented in such a way that in four-dimensional space--time only the fields belonging to the gravitational multiplet of extended N=4 supergravity are preserved. In the reduction process the Cremmer--Scherk--Ferrara action for N=4 supergravity is derived. In the framework of the technique used it turns out to be possible to construct the interaction of N=4 supergravity with an Abelian and with a Yang--Mills N=4 matter multiplet

[en] The stability of the isometry group against quantum fluctuations is studied. In the case of M⁴xS³, the effective potential is calculated for the conformally coupled scalar fields including the squashed parameter. The results at one-loop level show that a round sphere is unstable against the deformation. This induces the symmetry breaking SO(4)→SU(2)xU(1). (author)

[en] I study a model of a compactified Kaluza-Klein theory as an SU(2) gauge theory on a flat n-dimensional Minkowski space Mⁿ in a direct product with a two sphere S². The gauge and ghost gaussian functional integrals (one loop effective potentials) are explicitly calculated. To this order, SU(2) does indeed breakdown dynamically to U(1) on Mⁿ x S² as Hosotani previously conjectured. On Mⁿ, there is an infinite tower of massive gauge bosons with m² proportional to m_planck² with a massless photon and two tachyons. A renormalization scheme for Mⁿ x S² for all odd n and for n = 2 is presented. The n = 2 result reproduces the standard four dimensional beta function for a fixed spatial background. In addition, the perturbation theory on M² is developed. In particular, induced tree level fermion-gauge field and one loop fermion-higgs Yukawa couplings are computed. The latter calculation generates a mass hierarchy for the massless fermions on M²

[en] Some aspects of supergravity theories, obtained as point field limit of superstrings are discussed. Positive semidefinite potentials in extended sueprgravities obtained from dimensional reduction of D = 10 theories are considered. The supersymmetric completion of Chern-Simons terms and of higher curvature invariants is also analyzed

[en] It is demonstrated that a geometric interpretation of Kaehler transformations in superspace allows to construct the full action for matter and Yang-Mills fields coupled to supergravity in a concise way, both in terms of superfields and component fields