Mirror symmetry and elliptic Calabi-Yau manifolds

A bstract We find that for many Calabi-Yau threefolds with elliptic or genus one fibrations mirror symmetry factorizes between the fiber and the base of the fibration. In the simplest examples, the generic CY elliptic fibration over any toric base surface B that supports an elliptic Calabi-Yau three...

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Bibliographic Details
Published in:The journal of high energy physics 2019-04, Vol.2019 (4), p.1-31, Article 83
Main Authors: Huang, Yu-Chien, Taylor, Washington
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Differential and Algebraic Geometry
Electrical equipment
Elementary Particles
F-Theory
High energy physics
High Energy Physics - Theory
Manifolds (mathematics)
Mathematics - Algebraic Geometry
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Duality
String Theory
Superstring Vacua
Symmetry
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Summary:A bstract We find that for many Calabi-Yau threefolds with elliptic or genus one fibrations mirror symmetry factorizes between the fiber and the base of the fibration. In the simplest examples, the generic CY elliptic fibration over any toric base surface B that supports an elliptic Calabi-Yau threefold has a mirror that is an elliptic fibration over a dual toric base surface B ˜ that is related through toric geometry to the line bundle −6 K B . The Kreuzer-Skarke database includes all these examples and gives a wide range of other more complicated constructions where mirror symmetry also factorizes. Since recent evidence suggests that most Calabi-Yau threefolds are elliptic or genus one fibered, this points to a new way of understanding mirror symmetry that may apply to a large fraction of smooth Calabi-Yau threefolds. The factorization structure identified here can also apply for CalabiYau manifolds of higher dimension.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP04(2019)083