Heterotic-Heterotic String Duality and Multiple K3 Fibrations

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.

13 pages, LaTeX

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Cited by in corpus (24)

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• Introduction to Seiberg-Witten Theory and its Stringy Origin
• Instanton sums and five-dimensional gauge theories
• Fibrations in CICY Threefolds
• Point-like Instantons and the Spin(32)/Z2 Heterotic String
• Non-Perturbative Properties of Heterotic String Vacua Compactified on $K3\times T^2$
• Toric K3-Fibred Calabi-Yau Manifolds with del Pezzo Divisors for String Compactifications
• New Higgs Transitions between Dual N=2 String Models
• Holomorphic Couplings in String Theory
• Phases, Flops and F-theory: SU(5) Gauge Theories
• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
• Duality in String Theory
• F-Theory on Quotients of Elliptic Calabi-Yau Threefolds
• Comments on A,B,C Chains of Heterotic and Type II Vacua
• String Vacua with N=2 Supersymmetry in Four Dimensions
• Calabi-Yau Varieties and Pencils of K3 Surfaces
• Benchmarks on the brane
• Thirty years of Erice on the brane
• M-theory on G_2 manifolds and the method of (p,q) brane webs
• Dualities between K3 fibered Calabi-Yau three-folds