Abstract
We study aspects of Heterotic/F-theory duality for compactifications with Abelian discrete gauge symmetries. We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group {mathbb{Z}}_n . Such models are obtained by studying first a specific toric set-up whose associated Heterotic vector bundle has structure group {mathbb{Z}}_n . By employing a conjectured Heterotic/F-theory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compactifications to six dimensions. We provide explicit constructions of mirror-pairs for symmetric examples with {mathbb{Z}}_2 and {mathbb{Z}}_3 , in six dimensions. The Heterotic models with symmetric discrete symmetries are related in field theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stückelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of fibrations with torsional sections and those with multi-sections.
Highlights
Introduction and summary of resultsRecent years have witnessed important advances in F-theory compactifications [1,2,3]
As the main focus of this work is the investigation of discrete symmetries, we review their appearance on the F-theory side as well as on the Heterotic side in this subsection
In this note we have presented core steps in the understanding of discrete symmetries within the Heterotic/F-theory duality
Summary
Recent years have witnessed important advances in F-theory compactifications [1,2,3]. By employing the conjectured F-theory/Heterotic mirror-symmetry we construct dual toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order n, for compactifications in six dimensions. We construct and analyse the mirror dual pairs for the case of symmetric Z2 and Z3 symmetry These constructions provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of fibrations with torsional sections and those with multi-sections. The basic statement of Heterotic/F-theory duality is that the Heterotic E8 ˆ E8 String compactified on a torus, which we denote by Z1, is equivalent to F-theory compactified on an elliptically fibered K3 surface X2
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