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G2 manifold
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G2 manifold

A G2 manifold, also known as a Joyce manifold, is a seven-dimensional Riemannian manifold with holonomy group G2. The group is one the five exceptional simple Lie groups. It can be described as the automorphism group of the octonions, or equivalently, as a proper subgroup of SO(7) that preserves a spinor in the eight-dimensional spinor representation. G2 manifolds are Ricci-flat.

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.

See also: Calabi-Yau manifold, Spin(7) manifold

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