Instanton effects and the landscape of string theory

In this dissertation we study non-perturbative effects in four-dimensional N = 1 compactifications of superstring theory and F-theory, primarily focusing on the importance of instanton corrections to the superpotential.;We utilize dualities and limits of F-theory to elucidate the physics of M5-instantons. We study the Pfaffian prefactor via heterotic duality and demonstrate its dependence on seven-brane structure and points of enhanced symmetry. Utilizing anomaly inflow and string junctions, we shed light on the localization and representation theoretic structure of instanton zero modes upon movement in moduli space. We perform a geometric uplift of an instanton in a type IIb GUT to an instanton in F-theory and identify a class of geometries which allow for the determinantion of all uncharged instanton corrections. Utilizing Seiberg-Witten theory, we explain the quantum splitting of certain seven-brane stacks.;Motivated by the systematic study of instantons, we study the computability structure of the string theory landscape. We cast the study of fairly generic physical properties into the language of computability theory and show that this amounts to solving systems of diophantine equations. Utilizing the negative solution to Hilbert's 10th problem, we argue that in such systematic studies there may be no algorithm by which one can determine all physical effects. This argument holds for any suitably large class of physical theories, including the landscape.;We study a large class of semi-realistic N = 1 quiver gauge theories which can arise in string compactifications. We present many MSSM quivers where the presence of anomalous U (1) symmetries and instanton corrections can account for observed phenomenological hierarchies, including the Yukawa couplings of the MSSM. We propose a new mechanism for obtaining small neutrino masses via an instanton-induced Weinberg operator and systematically study singlet-extended standard models.;We discuss constraints on chiral matter in these quivers which are necessary for string consistency but are not known field theoretic constraints. Many field theoretically well-behaved quivers violate these constraints, including nearly all MSSM quivers. The constraints are violated in a way suggestive of the preferred structure of exotics beyond the standard model. We systematically demonstrate that some exotic representations are highly favored over others.