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

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

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

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

WKB Approximation in Noncommutative Gravity

We consider the quasi-commutative approximation to a noncommutative geometry defined as a generalization of the moving frame formalism. The relation which exists between noncommutativity and geometry is used to study the properties of the high-frequency waves on the flat background.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Orbifolds, fuzzy spheres and chiral fermions

Starting with a N=4 supersymmetric Yang-Mills theory in four dimensions with gauge group SU(3N) we perform an orbifold projection leading to a N=1 supersymmetric SU(N)^3 Yang-Mills theory with matter supermultiplets in bifundamental representations of the gauge group, which is chiral and anomaly free. Subsequently, we search for vacua of the projected theory which can be interpreted as spontaneously generated twisted fuzzy spheres. We show that by adding the appropriate soft supersymmetry breaking terms we can indeed reveal such vacua. Three cases are studied, where the gauge group is spontaneously broken further to the low-energy gauge groups SU(4)xSU(2)xSU(2), SU(4)^3 and SU(3)^3. Such models behave in intermediate scales as higher-dimensional theories with a finite Kaluza-Klein tower, while their low-energy physics is governed by the corresponding zero-modes and exhibit chirality in the fermionic sector. The most interesting case from the phenomenological point of view turns out to be the SU(3)^3 unified theory, which has several interesting features such as (i) it can be promoted to a finite theory, (ii) it breaks further spontaneously first to the MSSM and then to SU(3)xU(1)_{em} due to its own scalar sector, i.e. without the need of additional superfields and (iii) the corresponding vacua lead to spontaneously generated fuzzy spheres.Comment: 24 pages, minor changes, references added, matching with the published versio

The Top-Bottom Hierarchy from Gauge-Yukawa Unification

The idea of Gauge-Yukawa Unification (GYU) based on the principle of reduction of couplings is elucidated. We show how the observed top-bottom mass hierarchy can be explained in terms of supersymmetric GYU by considering an example of the minimal supersymmetric GUT.Comment: 13 pages, LaTeX and epsf package, Postscript figures. To be published in the proceedings of the Yukawa International Seminar '9