Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry
We address the issue of why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two forms and four forms on an equal footing. The doubling of the two-form vector space due to th...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/7962426 |
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| author | Hyun Seok Yang Sangheon Yun |
| author_facet | Hyun Seok Yang Sangheon Yun |
| author_sort | Hyun Seok Yang |
| collection | DOAJ |
| description | We address the issue of why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two forms and four forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles the variety of six-dimensional spin manifolds. We explore how the doubling is related to the mirror symmetry of Calabi-Yau manifolds. Via the gauge theory formulation of six-dimensional Riemannian manifolds, we show that the curvature tensor of a Calabi-Yau manifold satisfies the Hermitian Yang-Mills equations on the Calabi-Yau manifold. Therefore, the mirror symmetry of Calabi-Yau manifolds can be recast as the mirror pair of Hermitian Yang-Mills instantons. We discuss the mirror symmetry from the gauge theory perspective. |
| format | Article |
| id | doaj-art-5ba3d92395684d52a93d90045caac722 |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-5ba3d92395684d52a93d90045caac7222025-02-03T01:21:29ZengWileyAdvances in High Energy Physics1687-73571687-73652017-01-01201710.1155/2017/79624267962426Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror SymmetryHyun Seok Yang0Sangheon Yun1Center for Quantum Spacetime, Sogang University, Seoul 121-741, Republic of KoreaInstitute for the Early Universe, Ewha Womans University, Seoul 120-750, Republic of KoreaWe address the issue of why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two forms and four forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles the variety of six-dimensional spin manifolds. We explore how the doubling is related to the mirror symmetry of Calabi-Yau manifolds. Via the gauge theory formulation of six-dimensional Riemannian manifolds, we show that the curvature tensor of a Calabi-Yau manifold satisfies the Hermitian Yang-Mills equations on the Calabi-Yau manifold. Therefore, the mirror symmetry of Calabi-Yau manifolds can be recast as the mirror pair of Hermitian Yang-Mills instantons. We discuss the mirror symmetry from the gauge theory perspective.http://dx.doi.org/10.1155/2017/7962426 |
| spellingShingle | Hyun Seok Yang Sangheon Yun Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry Advances in High Energy Physics |
| title | Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry |
| title_full | Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry |
| title_fullStr | Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry |
| title_full_unstemmed | Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry |
| title_short | Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry |
| title_sort | calabi yau manifolds hermitian yang mills instantons and mirror symmetry |
| url | http://dx.doi.org/10.1155/2017/7962426 |
| work_keys_str_mv | AT hyunseokyang calabiyaumanifoldshermitianyangmillsinstantonsandmirrorsymmetry AT sangheonyun calabiyaumanifoldshermitianyangmillsinstantonsandmirrorsymmetry |