CALABI-YAU MODULI SPACE, MIRROR MANIFOLDS AND SPACETIME TOPOLOGY CHANGE IN STRING THEORY

We analyze the moduli spaces of Calabi-Yau three-folds and their assoc iated conformally invariant nonlinear sigma-models and show that they are described by an unexpectedly rich geometrical structure. Specifica lly, the Kahler sector of the moduli space of such Calabi-Yau conforma l theories admits a decomposition into adjacent domains some of which correspond to the (complexified) Kahler cones of topologically distinc t manifolds. These domains are separated by walls corresponding to sin gular Calabi-Yau spaces in which the spacetime metric has degenerated in certain regions. We show that the union of these domains is isomorp hic to the complex structure moduli space of a single topological Cala bi-Yau space-the mirror. In this way we resolve a puzzle for mirror sy mmetry raised by the apparent asymmetry between the Kahler and complex structure moduli spaces of a Calabi-Yau manifold. Furthermore, using mirror symmetry, we show that we can interpolate in a physically smoot h manner between any two theories represented by distinct points in th e Kahler moduli space, even if such points correspond to topologically distinct spaces. Spacetime topology change in string theory, therefor e, is realized by the most basic operation of deformation by a truly m arginal operator. Finally, this work also yields some important insigh ts on the nature of orbifolds in string theory.