PERIODS FOR CALABI-YAU AND LANDAU-GINZBURG VACUA

The complete structure of the moduli space of Calabi-Yau manifolds and the associated Landau-Ginzburg theories, and hence also of the corres ponding low-energy effective theory that results from (2, 2) superstri ng compactification, may be determined in terms of certain holomorphic functions called periods. These periods are shown to be readily calcu lable for a great many such models. We illustrate this by computing th e periods explicitly for a number of classes of Calabi-Yau manifolds. We also point out that it is possible to read off from the periods cer tain important information relating to the mirror manifolds.