String Compactifications from the Worldsheet and Target Space Point of View

Abstract

This thesis presents research on compactifications of type II superstring theories, combining worldsheet and target space approaches. This is achieved by using supersymmetric gauge theory techniques together with geometrical methods. After reviewing relevant physical and mathematical concepts we turn to a study of correlation functions in two-dimensional gauged linear sigma models and demonstrate how these encode the target space geometry to a large extent. We present an elementary algorithm to determine the Picard--Fuchs differential operators, governing the moduli space geometries, from the defining gauge theory spectrum directly. Next, we employ the Givental I-function to propose explicit formulas for the holomorphic solutions annihilated by these differential operators for models with general non-Abelian gauge groups and a large class of matter spectra. These formulas provide an alternative, efficient way of deriving the Picard--Fuchs operators for non-Abelian gauge theories, where other approaches quickly become computationally unfeasible. Lastly, we consider Calabi--Yau fourfolds that arise as target spaces of non-Abelian gauged linear sigma models. We demonstrate that their quantum cohomology ring is not necessarily generated by products of marginal deformations alone and discuss implications of this property.