Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry
Joint Authors
Source
Advances in High Energy Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-27, 27 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-11-09
Country of Publication
Egypt
No. of Pages
27
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Yang, Hyun Seok& Yun, Sangheon. 2017. Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry. Advances in High Energy Physics،Vol. 2017, no. 2017, pp.1-27.
https://search.emarefa.net/detail/BIM-1122212
Modern Language Association (MLA)
Yang, Hyun Seok& Yun, Sangheon. Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry. Advances in High Energy Physics No. 2017 (2017), pp.1-27.
https://search.emarefa.net/detail/BIM-1122212
American Medical Association (AMA)
Yang, Hyun Seok& Yun, Sangheon. Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry. Advances in High Energy Physics. 2017. Vol. 2017, no. 2017, pp.1-27.
https://search.emarefa.net/detail/BIM-1122212
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1122212