Deformations of solvable Calabi-Yau compactifications

We study the potential for the moduli fields which deform the radii and the complex structure of the Calabi-Yau manifolds on which string propagates. We have found that nonzero potentials for the moduli fields exist in solvable models. We show further that nonperturbative effects due to instantons generate the type of the potentials we have found. The vacuum degeneracies of string theory corresponding to complex structure deformations are lifted due to nonperturbative effects on the world sheet