Model building and phenomenological aspects of F-Theory GUTs

Abstract

In recent years, Grand Unified Theories (GUTs) constructed from F-theory have been extensively studied due to the substantial scope for model building and phenomenology which they provide. This thesis will motivate and introduce the basic tools required for model building in the setting of local F-theory. Starting with GUT groups of E6, SO(10) and SU(5), a group theoretic dictionary between the three types of theory is formulated, which provides considerable insight into how to build a realistic model. The spectral cover formalism is then applied to each case, enabling the possible low energy spectra after flux breaking of the GUT group to be found. Using these results an E6 based model is constructed that demonstrates, for the first time, that it is possible to construct a phenomenologically viable model which leads to the MSSM at low energies. In addition to the MSSM model, the E6 starting point is also used to build F-theory models in which the low energy supersymmetric theory contains the particle content of three 27 dimensional representations of the underlying E6 gauge group, with the possibility of a gauged U(1) group surviving down to the TeV scale. The models with TeV scale exotics initially appear to be inconsistent due to a splitting of the gauge couplings at the unification scale which is too large, and incompatible with the formalism. However, in E6 models with flux breaking, there are bulk exotics coming from the 78 dimensional adjoint representation which are always present in the spectrum, and it turns out that a set of these exotics provide a natural way to achieve gauge coupling unification at the one-loop level, even for models with TeV exotics. This motivates a detailed study of bulk exotics, where specific topological formulae determining the multiplicities of bulk states are investigated, and the constraints imposed by these relations applied to the spectra of the models previously studied. In particular, bulk exotics are relevant to the almost miraculous restoration of gauge coupling unification in the case of the models with TeV scale exotics. The consistent local F-theory models with low energy exotics have distinctive characteristics when compared with other, similar models, and so provide potential opportunities to be tested at the LHC.

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