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

Understand

We address the issue 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.