We discuss the mathematical properties of six-dimensional non-Kähler manifolds which occur in the context of N = 1 supersymmetric heterotic and type IIA string compactifications with non-vanishing background H-field. The intrinsic torsion of the associated SU(3) structures falls into five different classes. For heterotic compactifications we present an explicit dictionary between the supersymmetry conditions and these five torsion classes. We show that the non-Ricci flat Iwasawa manifold solves the supersymmetry conditions with non-zero H-field, so that it is a consistent heterotic supersymmetric groundstate.

We present phenomenologically viable SU(5) unified models which are finite to all orders before the spontaneous symmetry breaking. In the case of two models with three families the top quark mass is predicted to be 178.8 GeV.MPI-Ph/92-70

We present a renormalizable 4-dimensional SU(N ) gauge theory with a suitable multiplet of scalar fields, which dynamically develops extra dimensions in the form of a fuzzy sphere S 2 N . We explicitly find the tower of massive KaluzaKlein modes consistent with an interpretation as gauge theory on M 4 × S 2 , the scalars being interpreted as gauge fields on S 2 . The gauge group is broken dynamically, and the low-energy content of the model is determined. Depending on the parameters of the model the low-energy gauge group can be SU(n), or broken further to SU(n 1 ) × SU(n 2 ) × U(1), with mass scale determined by the size of the extra dimension.

No abstract

No abstract