String theory flux vacua with different flux quanta seemingly form a discrete set, but they can often be continuously connected by applying monodromies of the Calabi-Yau geometry. Such continuously connected vacua are interesting from the point of view of cosmology, and for constructing domain walls, for example. An intriguing question is which vacua can be continuously connected in this way, and which cannot. I discuss the example of the mirror quintic, and show that there is an extra trick which connects even more vacua. Using toric geometry and geometric transitions, the mirror quintic can be deformed into a manifold of Hodge numbers (86,2). One can apply the larger mondromy group of the latter manifold, and then go back through the geometric transition to find new connections between the vacua of the mirror quintic.

IHES