Warped Strings: Self-dual Flux and Contemporary Compactifications

String theory is a leading candidate for the quantum theory of gravitation and is the only serious unified theory of all the forces of physics. Additionally, string theory seems to be mathematically unique, and it is possible that all the parameters of physics could be determined by the dynamics of string theory. However, there are two intertwined problems. First is that string theory requires ten dimensions for mathematical consistency, so six must be compact or otherwise decoupled from the physics we observe. Also, there exist many different ground states of string theory, so it is difficult to make predictions that are generic to string theory. Therefore, it is crucial to gain a broad understanding of all the string theory vacua, particularly those compactified to four dimensions. In recent years, our understanding of string theory compactifications has expanded greatly to include many new classes of solutions. In this dissertation, I discuss type IIB string compactifications in which the three-form field strengths satisfy a self-duality condition on the internal manifold. I begin with an overview of the models, giving preliminary formulae and several points of view from which they can be understood. Then I will describe windows into the small radius behavior of the compactifications, which is more complicated than compactifications without fluxes, which are more well-known. I will describe details of the flux-generated potential and nonperturbative corrections to it. These nonperturbative corrections allow a discussion of the cosmological constant and possible mechanisms for the universe to decay from one energy state to another. I conclude with comments on related topics and interesting directions for future study. As this document is a dissertation, I will indicate my own contributions to the subject. However, for the purpose of completeness and in hopes of helping the readers, I will include a fairly comprehensive review of related literature. The early part of the dissertation is much more a literature review because there are many results upon which my contributions have been founded.