Connections To Physics
These manifolds are important in string theory. They break the original supersymmetry to 1/8 of the original amount. For example, M-theory compactified on a manifold leads to a realistic four-dimensional (11-7=4) theory with N=1 supersymmetry. The resulting low energy effective supergravity contains a single supergravity supermultiplet, a number of chiral supermultiplets equal to the third Betti number of the manifold and a number of U(1) vector supermultiplets equal to the second Betti number.
See also: Calabi-Yau manifold, Spin(7) manifold
Read more about this topic: G2 Manifold
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