Heterotic-Heterotic String Duality and Multiple K3 Fibrations
Paul S. Aspinwall, Mark Gross
TL;DR
This work investigates how Calabi–Yau threefolds with multiple K3 fibrations realize dualities between heterotic strings that are perturbatively inequivalent. By employing a double fibration geometry, the authors show that exchanging the two K3 fibrations maps between dual heterotic theories, with the heterotic dilaton encoded as the base size on the Type IIA side and four-dimensional duality requiring $h^{1,1}=3$, $h^{2,1}=243$; the construction recovers the Duff–Minasian–Witten six-dimensional example and supports the KV:N=2 conjectures. They demonstrate how gauge groups reorganize under duality via extremal transitions, e.g., perturbative $E_7\times E_7$ on one side becoming nonperturbative on the other, and produce a dual CY $X'$ with $(h^{1,1},h^{2,1})=(17,61)$ and gauge content including $U(1)^{4+14}$. The paper also presents an extreme case with an infinite family of K3 fibrations linked by a duality group $O(1,17;\mathbb{Z})$, illustrating that infinite fibrations yield infinitely many dual heterotic strings reduced to finitely many equivalence classes by dualities, and showing the duality's power to mix perturbative and nonperturbative sectors.
Abstract
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 four dimensions. We study cases where a Calabi-Yau manifold can have more than one such fibration leading to equivalences between perturbatively inequivalent heterotic strings. This allows an analysis of an example in six dimensions due to Duff, Minasian and Witten and enables us to 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 Calabi-Yau manifold which admits an infinite number of K3 fibrations leading to infinite set of equivalent heterotic strings.