# Calabi-Yau Manifolds and the Standard Model

@article{Baez2005CalabiYauMA, title={Calabi-Yau Manifolds and the Standard Model}, author={J. Baez}, journal={arXiv: High Energy Physics - Theory}, year={2005} }

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… Expand

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