Effective gauge theories from fuzzy extra dimensions

Ünal, Gönül
In this thesis, we investigate the formulation and various aspects of gauge theories with fuzzy extra dimensions. In SU (N ) gauge theories coupled to a suitable number of adjoint scalar fields, we determine a family of fuzzy vacuum configurations dynamically emerging after the spontaneously symmetry breaking of the gauge symmetry. The emergent models are conjectured to be effective U (n) (n < N ) gauge theories with fuzzy extra dimensions. Making use of the equivariant parametrization technique and focusing on the simplest member of the family of fuzzy vacua, we obtain all the SU (2) × SU (2)-equivariant gauge fields in a U (4) model which characterize its low energy degrees of freedom. Low energy effective action of a U (3) gauge theory on R 2 × S F 2 is also determined and its vortex type solutions are investigated in detail. In this thesis, we also formulate the quantum Hall effect (QHE) on the complex Grassmannians Gr 2 (C N ). We use the group theoretical techniques to solve the Landau problem and provide the energy spectrum and eigenstates of charged particles on this space under the influence of Abelian and non-Abelian background magnetic monopoles.