A review of geometry of $G_2$ holonomy 7-folds

Question

It is know that in order to have ${\cal N}=1$ 4D compactification of M-theory or 11D SUGRA, one has to take the internal space to be a manifold of $G_2$ holonomy. Moreover, such manifolds are considered as possible target spaces of Topological M-theory.

Could anybody recommend a review of geometry and topology of 7-folds of $G_2$ holonomy? I am a physicist, so the reviews written by physicist or at least for physicists are most welcome.

Answer 1

This here is good;

• Spiro Karigiannis, $G_2$-Conifolds: A survey, 2014 (pdf)

Comments

Thanks, but the discussion there is very sketchy. Do you know of any more detailed introductions?

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There are detailed discussions in the mathematical literature.But the "reviews written by physicist or at least for physicists" that you ask for are all at least this sketchy.