N=1 Finite Unified Theories - Predictions and Dualities

N = 1, all-loop Finite Unified Theories (FUTs) are very interesting not only since they realize an old theoretical dream, but also due the remarkable predictive power of particular models as well as for providing candidates that might shed light in non-perturbative Physics. Here we discuss (a) the recent developments concerning the soft supersymmetry breaking (SSB) sector of these theories and the resulting predictions in very interesting realistic models, and (b) the results of a recent search for duals of N=1, all-loop FUTs.Comment: Latex, 8 pages; talk given at ``31st Internat. Symp. Ahrenshoop Theory of Elementary Particles'' Buckow, Sept. 2-6, 9

Soft Supersymmetry Breaking from Coset Space Dimensional Reduction

The Coset Space Dimensional Reduction scheme is briefly reviewed. Then a ten-dimensional supersymmetric $E_8$ gauge theory is reduced over symmetric and non-symmetric six-dimensional coset spaces. In general a four-dimensional non-supersymmetric gauge theory is obtained in case the used coset space is symmetric, while a softly broken supersymmetric gauge theory is obtained if the used coset space is non-symmetric. In the process of exhibiting the above properties we also present two attractive models, worth exploiting further, which lead to interesting GUTs with three families in four dimensions.Comment: 16 pages, Contribution to SUSY01 Dubna Russia, CORFU2001 Corfu Greece, SQS01 Karpacz Poland and I Summer School in Modern Mathematical Physics Sokobanja Yugoslavi

μ\mu-term due to the non-universal supersymmetry breaking and the Higgs mass

We propose a solution to the $\mu$-problem due to the non-universal soft supersymmetry breaking in a class of supersymmetric extensions of the SM with an extra U(1) and the NMSSM. Our scenario resembles an earlier one which has been proposed as a solution to the $\mu$-problem in the framework of similar models but it has rather different features from that. Theoretically crucial points in the present scenario are the realization of the required non-universal soft supersymmetry breaking parameters and the concern to avoid the vacuum instability due to tadpoles. We discuss them in some detail. In particular, on the non-universal soft supersymmetry breaking we discuss the superstring and the field theory with reduction of couplings possibilities. We also study the weak scale radiative symmetry breaking in the considered models and estimate the upper mass bound of the lightest neutral Higgs scalar. The latter tends to be smaller in the present scenario as compared to the previous one.Comment: LaTeX, 28 pages, 2 eps-figures included into the text, minor chang

Dimensional Reduction of ten-dimensional Supersymmetric Gauge Theories in the N=1, D=4 Superfield Formalism

A ten-dimensional supersymmetric gauge theory is written in terms of N=1, D=4 superfields. The theory is dimensionally reduced over six-dimensional coset spaces. We find that the resulting four-dimensional theory is either a softly broken N=1 supersymmetric gauge theory or a non-supersymmetric gauge theory depending on whether the coset spaces used in the reduction are non-symmetric or symmetric. In both cases examples susceptible to yield realistic models are presented.Comment: 24 page

Strongly-interacting fermions from a higher-dimensional unified gauge theory

The method of coset-space dimensional reduction is employed in order to proceed from a gauged E_8 * E_8' unified theory defined in 10 dimensions to 4 dimensions. The resulting theory comprises the Standard Model along with a strongly-interacting fermion sector which breaks the electroweak symmetry dynamically at the right scale.Comment: 12 LaTeX pages, version to be published in Physics Letters

Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions

Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle physics models in the context of higher-dimensional gauge theories with non-commutative extra dimensions. These ideas have been developed in two complementary ways, namely (i) starting with a higher-dimensional gauge theory and dimensionally reducing it to four dimensions over fuzzy internal spaces and (ii) starting with a four-dimensional, renormalizable gauge theory and dynamically generating fuzzy extra dimensions. We describe the above approaches and moreover we discuss the inclusion of fermions and the construction of realistic chiral theories in this context