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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Format: | Article |
Language: | English |
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SpringerOpen
2019-04-01
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Series: | Journal of High Energy Physics |
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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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institution | Directory Open Access Journal |
issn | 1029-8479 |
language | English |
last_indexed | 2024-12-12T20:06:03Z |
publishDate | 2019-04-01 |
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series | Journal of High Energy Physics |
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 |