NONPERTURBATIVE SUPERPOTENTIALS IN STRING THEORY

The non-perturbative superpotential can be effectively calculated in M -theory compactification to three dimensions on a Calabi-Yau four-fold X. For certain X, the superpotential is identically zero, while for o ther X, a non-perturbative superpotential is generated. Using F-theory , these results carry over to certain Type IIB and heterotic string co mpactifications to four dimensions with N = 1 supersymmetry. In the he terotic string case, the non-perturbative superpotential can be interp reted as coming from space-time and world-sheet instantons; in many si mple cases contributions come only from finitely many values of the in stanton numbers.