Mirror symmetry and elliptic Calabi-Yau manifolds

Abstract 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 threef...

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Main Authors: Yu-Chien Huang, Washington Taylor
Format: Article
Language:English
Published: SpringerOpen 2019-04-01
Series:Journal of High Energy Physics
Subjects:
Online Access:http://link.springer.com/article/10.1007/JHEP04(2019)083
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author Yu-Chien Huang
Washington Taylor
author_facet Yu-Chien Huang
Washington Taylor
author_sort Yu-Chien Huang
collection DOAJ
description Abstract 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 ˜ $$ \tilde{B} $$ that is related through toric geometry to the line bundle −6K 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.
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spelling doaj.art-4b9cd79e1a5148e8a0a2e3647a7949ec2022-12-22T00:13:37ZengSpringerOpenJournal of High Energy Physics1029-84792019-04-012019413110.1007/JHEP04(2019)083Mirror symmetry and elliptic Calabi-Yau manifoldsYu-Chien Huang0Washington Taylor1Center for Theoretical Physics, Department of Physics, Massachusetts Institute of TechnologyCenter for Theoretical Physics, Department of Physics, Massachusetts Institute of TechnologyAbstract 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 ˜ $$ \tilde{B} $$ that is related through toric geometry to the line bundle −6K 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.http://link.springer.com/article/10.1007/JHEP04(2019)083Differential and Algebraic GeometryF-TheoryString DualitySuperstring Vacua
spellingShingle Yu-Chien Huang
Washington Taylor
Mirror symmetry and elliptic Calabi-Yau manifolds
Journal of High Energy Physics
Differential and Algebraic Geometry
F-Theory
String Duality
Superstring Vacua
title Mirror symmetry and elliptic Calabi-Yau manifolds
title_full Mirror symmetry and elliptic Calabi-Yau manifolds
title_fullStr Mirror symmetry and elliptic Calabi-Yau manifolds
title_full_unstemmed Mirror symmetry and elliptic Calabi-Yau manifolds
title_short Mirror symmetry and elliptic Calabi-Yau manifolds
title_sort mirror symmetry and elliptic calabi yau manifolds
topic Differential and Algebraic Geometry
F-Theory
String Duality
Superstring Vacua
url http://link.springer.com/article/10.1007/JHEP04(2019)083
work_keys_str_mv AT yuchienhuang mirrorsymmetryandellipticcalabiyaumanifolds
AT washingtontaylor mirrorsymmetryandellipticcalabiyaumanifolds