Exactly Solved String Models.

In this dissertation we explore the applications of exactly solved models in contemporary string theory. We use the properties of these models to derive a remarkable duality symmetry in the moduli space of Calabi-Yau compactifications, which generalizes the known symmetries of toroidal compactifications. We describe some of the implications of this duality, which include in principle the possibility of an exact calculation of the metric and couplings on moduli space. Focusing on a specific Calabi-Yau compactification which leads to a three generation model, we study possible symmetry breaking patterns using the exact solution of the model at a point in its moduli space. We calculate the massless spectra of the resulting models, and find some phenomenologically promising deviations from previously studied examples. Finally, we show that the string equations describing minimal conformal models coupled to two dimensional gravity may be derived from an action principle. The main advantage of this formulation is the compact and coherent form in which the action embodies the mathematical structure of the KdV flows.