Particle Physics from Singular Geometries

Abstract

We study string compactifications on spaces that are either partial or fully singular and analyze the symmetries in the effective theories that they generically give rise to. In the heterotic case we consider orbifolds and their fully singular Landau-Ginzburg phase. Using mirror symmetry we deform back to the orbifold and smooth spaces while keeping track of all enhanced Landau-Ginzburg symmetries and their breakdown. In this way we provide a new tool to calculate R-and non R-symmetries for geometries where the usual methods are hard to apply. We also consider the Z₂ × Z₄</nobr> orbifold and its properties for phenomenological applications in detail. Analyzing the symmetries of the theory and the effects of Wilson lines provides a generic pattern for the locations of MSSM matter in the orbifold space in order to exhibit phenomenological necessary properties. In the F-theory framework the singularities appear not in the physical compactification but as singularities of elliptic fibrations. We analyze the special of additional sections and multi-sections of the elliptic fibrations that give rise to gauged U(1) and discrete gauge symmetries. We are establishing a link between various fiber realizations and the resulting symmetries and their breakdown in the effective theories. By doing so we reveal new geometries and their properties that yield U(1) symmetries with novel features as well as discrete symmetries. By engineering additional SU(5) singularities in addition to two U(1) symmetries we consider F-theory GUT models relevant for phenomenology. The gauge group is broken down to the standard model with matter parity and the spectrum matches that of the MSSM.