M-theory on manifolds of G2 holonomy: the first twenty years
Abstract
In 1981, covariantly constant spinors were introduced into Kaluza-Klein theory as a way of counting the number of supersymmetries surviving compactification. These are related to the holonomy group of the compactifying manifold. The first non-trivial example was provided in 1982 by D=11 supergravity on the squashed S7, whose G2 holonomy yields N=1 in D=4. In 1983, another example was provided by D=11 supergravity on K3, whose SU(2) holonomy yields half the maximum supersymmetry. In 2002, G2 and K3 manifolds continue to feature prominently in the full D=11 M-theory and its dualities. In particular, singular G2 compactifications can yield chiral (N=1,D=4) models with realistic gauge groups. The notion of generalized holonomy is also discussed.
Keywords
Cite
@article{arxiv.hep-th/0201062,
title = {M-theory on manifolds of G2 holonomy: the first twenty years},
author = {M. J. Duff},
journal= {arXiv preprint arXiv:hep-th/0201062},
year = {2011}
}
Comments
Notes added on n, the number of allowed M-theory supersymmetries. Asymmetric orbifold compactifications of Type II strings from D=10 to D=2 permit n=0,1,2,3,4,5,6,8,9,10,12,16,17,18,20,24,32