HETEROTIC-HETEROTIC STRING DUALITY AND MULTIPLE K3 FIBRATIONS

A type IIA string compactified on a Calabi-Yau manifold which admits a K3 fibration is believed to be equivalent to a heterotic string in fo ur dimensions. We study cases where a Calabi-Yau manifold can have mor e than one such fibration leading to equivalences between perturbative ly inequivalent heterotic strings. This allows an analysis of an examp le in six dimensions due to Duff, Minasian and Witten and enables us t o go some way to prove a conjecture by Kachru and Vafa. The interplay between gauge groups which arise perturbatively and nonperturbatively is seen clearly in this example. As an extreme case we discuss a Calab i-Yau manifold which admits an infinite number of K3 fibrations leadin g to infinite set of equivalent heterotic strings.