Heterotic-Heterotic String Duality and Multiple K3 Fibrations

TL;DR

This paper explores how Calabi-Yau manifolds with multiple K3 fibrations lead to dualities between different heterotic string theories, revealing complex gauge interactions and an infinite set of equivalent theories.

Contribution

It demonstrates the existence of Calabi-Yau manifolds with multiple K3 fibrations, establishing dualities between perturbatively inequivalent heterotic strings and analyzing their gauge interactions.

Findings

Multiple K3 fibrations lead to dual heterotic strings.

An example with infinite K3 fibrations shows infinite dualities.

The interplay of perturbative and nonperturbative gauge groups is clarified.

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.