G2 manifold
From Wikipedia, the free encyclopedia
- The correct title of this article is G2 manifold. It features superscript or subscript characters that are substituted or omitted because of technical limitations.
A G2 manifold, also known as a Joyce manifold, is a seven-dimensional Riemannian manifold with holonomy group G2. The group G2 is one of 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. The name is for Dominic Joyce.
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 G2 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 G2 manifold and a number of U(1) vector supermultiplets equal to the second Betti number.
See also: Calabi-Yau manifold, Spin(7) manifold
[edit] References
- Dominic D. Joyce Compact Manifolds with Special Holonomy (Oxford Mathematical Monographs) ISBN 0-19-850601-5
 |
This geometry-related article is a stub. You can help Wikipedia by expanding it. |
