Calabi-Yau Manifolds and the Standard Model

Details Calabi-Yau Manifolds and the Standard Model Calabi-Yau Manifolds and the Standard Model

2005-11-08

arxiv.org/abs/hep-th/0511086v2

Physics

High Energy Physics

High Energy Physics - Theory

4 pages

Scientific paper

For any subgroup G of O(n), define a "G-manifold" to be an n-dimensional Riemannian manifold whose holonomy group is contained in G. Then a G-manifold where G is the Standard Model gauge group is precisely a Calabi-Yau manifold of 10 real dimensions whose tangent spaces split into orthogonal 4- and 6-dimensional subspaces, each preserved by the complex structure and parallel transport. In particular, the product of Calabi-Yau manifolds of dimensions 4 and 6 gives such a G-manifold. Moreover, any such G-manifold is naturally a spin manifold, and Dirac spinors on this manifold transform in the representation of G corresponding to one generation of Standard Model fermions and their antiparticles.

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