Superspace without torsion and the composite fundamental fermions

Abstract

(N=2)-superspace without torsion is described, which is equivalent to an 8-space with a discrete internal subspace. A number and a character of ties determine now an internal symmetry group, while in the supersymmetrical models this one is determined by an extension degree N. Such a model can be constructed for no less than 4 generations of the two-component fundamental fermions. Analogues of the Higgs fields appear in the model naturally after transition to the Grassmannian extra coordinates. The connection between discrete and continues internal symmetries of the model is discussed. If one considers gravity as embedding the curved 4-space into a 12-dimensional flat space, a U(1)-symmetry appears transformations of which should be connected with the ones of SU(2)-group. If super-strong interacting gravitons are constituents of the composite fermions, all this may open us another way to unify the known interactions. The main feature of this new approach may be the external see of gravitons underlying an internal structure of particles; the lack of any divergencies would be due the Planckian spectrum of external gravitons.