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.

A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation of the gravitational field. This is shown to be true in the case of a perturbation of Minkowski space-time.

Starting from a Yang‐Mills‐Dirac theory defined in ten dimensions we classify the semi‐realistic particle physics models resulting from their Forgacs‐Manton dimensional reduction. The higher‐dimensional gauge group is chosen to be E8. This choice as well as the dimensionality of the space‐time is suggested by the heterotic string theory. Furthermore, we assume that the space‐time on which the theory is defined can be written in the compactified form M4 × B, with M4 the ordinary Minkowski spacetime and B = S/R a 6 ‐ dim homogeneous coset space. We constrain our investigation in those cases where the dimensional reduction leads in four dimensions to phenomenologically interesting and anomaly‐free GUTs such as E6, SO(10) and SU(5). However the four‐dimensional surviving scalars transform in the fundamental of the resulting gauge group are not suitable for the superstrong symmetry breaking of the Standard Model. The main objective of our work is the investigation to which extent the latter can be achieved by employing the Wilson flux breaking mechanism.

Abstract.A possible way to resolve the singularities of general relativity is to assume that the description of space-time using commuting coordinates is not valid above a certain fundamental scale; beyond that scale the space-time has noncommutative structure leading in turn to a resolution of the singularity. We present models which realize this idea within the so-called frame formalism.

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