Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry

Yang, Hyun Seok  (Center for Quantum Spacetime, Sogang University, Seoul 121-741, Republic of Korea) ; Yun, Sangheon (Institute for the Early Universe, Ewha Womans University, Seoul 120-750, Republic of Korea)

09 November 2017

Abstract: 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.

Published in: Advances in High Energy Physics 2017 (2017) 7962426
Published by: Hindawi
DOI: 10.1155/2017/7962426
arXiv: 1107.2095
License: CC-BY-3.0

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