CalabiYau moduli space, mirror manifolds and spacetime topology change in string theory
Abstract
We analyze the moduli spaces of CalabiYau threefolds and their associated conformally invariant nonlinear σmodels and show that they are described by an unexpectedly rich geometrical structure. Specifically, the Kähler sector of the moduli space of such CalabiYau conformal theories admits a decomposition into adjacent domains some of which correspond to the (complexified) Kähler cones of topologically distinct manifolds. These domains are separated by walls corresponding to singular CalabiYau spaces in which the spacetime metric has degenerated in certain regions. We show that the union of these domains is isomorphic to the complex structure moduli space of a single topological CalabiYau space—the mirror. In this way we resolve a puzzle for mirror symmetry raised by the apparent asymmetry between the Kähler and complex structure moduli spaces of a CalabiYau manifold. Furthermore, using mirror symmetry, we show that we can interpolate in a physically smooth manner between any two theories represented by distinct points in the Kähler moduli space, even if such points correspond to topologically distinct spaces. Spacetime topology change in string theory, therefore, is realized by the most basic operation of deformation by a truly marginal operator. Finally, this work also yields some important insights on the nature of orbifolds in string theory.
 Publication:

Nuclear Physics B
 Pub Date:
 March 1994
 DOI:
 10.1016/05503213(94)903212
 arXiv:
 arXiv:hepth/9309097
 Bibcode:
 1994NuPhB.416..414A
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 74 pages (with 20 figures)