Supersymmetric F-Theory Gut Models



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F-theory is a twelve-dimensional geometric version of string theory and is believed to be a natural framework for GUT model building. The aim of this dissertation is to study how gauge theories realized by F-theory can accommodate GUT models. In this dissertation, we focus on local and semi-local GUT model building in F-theory. For local GUT models, we build SU(5) GUTs by using abelian U(1) fluxes via the SU(6) gauge group. Doing so, we obtain non-minimal spectra of the MSSM with doublet-triplet splitting by switching on abelian U(1)2 fluxes. We also classify all supersymmetric U(1)2 fluxes by requiring an exotic-free bulk spectrum. For semi-local GUT models, we start with an E8 singularity and obtain lower rank gauge groups by unfolding the singularity governed by spectral covers. In this framework, the spectra can be calculated by the intersection numbers of spectral covers and matter curves. In particular, we use SU(4) spectral covers and abelian U(1)X fluxes to build flipped SU(5) models. We show that three-generation spectra of flipped SU(5) models can be achieved by turning on suitable fluxes. To construct E6 GUTs, we consider SU(3) spectral covers breaking E8 down to E6. Also three-generation extended MSSM can be obtained by using non-abelian SU(2) ? U(1)2 fluxes.