Some exact results on the superpotential from Calabi-Yau compactifications

We prove that certain superpotential couplings in compactified string theories are given exactly by the values calculated at sigma-model tree level. In particular, the 27³ coupling in (2,2) compactifications is a coupling of this sort. We explicitly check our results by examining the couplings in an exactly soluble model proposed by Gepner as a particular point in the moduli space of (2,2) compactifications on Y_{4; 5}. We thus determine the exact values of the normalized 27³ couplings for any value of the radius of Y_{4; 5}.