F-theory and Grand Unified Theories

F-theory and Grand Unified Theories String theory remains the main contender for achieving a consistent quantum theory of gravitation, which will reconcile gravitation with the Standard Model. In order to do so, string theory must be able to reproduce our low energy description of particle physics when compactified to 4 non-compact dimensions. In this review we introduce the 12-dimensional F-theory as a framework for a non-perturbative description of compactifications of Type IIB string theory with [p, q] 7-branes, and a varying axion-dilaton. We review the main motivations for introducing F-theory, which includes a geometric interpretation of the Type IIB SL(2,Z) symmetry as the modular group of a torus (elliptic curve), and the monodromy and backreaction of 7-branes. With a focus on compactifications of F-theory on K3 surfaces the geometry of elliptic fibrations is introduced along with the emergence of gauge groups, and a duality to Type IIB on orientifolds. General methods for generating matter and Yukawa couplings with 7-branes wrapping a del Pezzo surface in the internal space is then presented. These features are shown to appear at loci of singularities with increasing co-dimension. Finally, the developed tools of model building are used to provide an overview of the phenomenological properties of a local F-theory model with an SU(5) supersymmetric Grand Unified Theory. The description includes discussions of the local brane construction, GUT breaking by hyperflux, SUSY breaking, proton decay, flavour physics and neutrino physics. In the light of this, F-theory is a promising framework for embedding the Standard Model in string theory.