Διαστατική ελάττωση υπερσυμμετρικών θεωριών βαθμίδας

Abstract

Main objective of the present dissertation is the determination of all the possible low energy models which emerge in four dimensions by the dimensional reduction of a gauge theory over multiple connected coset spaces. The higher dimensional gauge theory is chosen to be the one that the Heterotic string theory suggests: (i) it is defined in ten dimensions, (ii) it is based on the E8 ? E8 symmetry group and (iii) it is N = 1 globally supersymmetric. The search of all four-dimensional gauge theories resulting from the aforementioned dimensional reduction, is restricted only to models which are potentially interesting from a phenomenological point of view. This requirement constrain these models to come from one of the known Grand Unified Theories (GUTs) in an intermediate stage of the spontaneous symmetry breaking. Main result of my study is that extensions of the Standard Model (SM) which are based on the Pati-Salam group structure can be obtained in four dimensions. A second direction of research which is discussed in this dissertation is based on the following conclusions of a previous research work: (i) It is possible to obtain fourdimensional theories with a non-abelian gauge symmetry by the dimensional reduction of a higher dimensional U(1) noncommutative theory and (ii) the particle physics models resulting from this particular dimensional reduction are renormalizable. The objective of the present dissertation in this direction is the study of the last remark. Starting with the most general renormalizable gauge theory with scalar fields (consistent with the dimensional reduction over a fuzzy sphere) which can be defined in four dimensions, it turns out that fuzzy extra dimensions emerge dynamically. This is supported by the calculation of the spectrum of vector and scalar bosons. In this way, the renormalizability of the four-dimensional low energy models resulting from the dimensional reduction over fuzzy coset spaces is verified. Finally, it is extremely interesting to assume noncommutative characteristics not only for the internal space of a higher dimensional theory, but also for the four-dimensional Minkowski space, M4, providing that these appear only in an elementary length scale which is assumed to be the Planck length. In this framework, the approach of linearized noncommutative gravity was examined and the connection of the algebra describing the noncommutative space with its geometry was studied. It turned out that the linear perturbation which describes the noncommutativity of the algebra contributes to the Ricci curvature tensor in a non-trivial way. This conclusion suggests a possible fundamental connection between the noncommutative geometry and the theory of gravity, which have to be investigated further.