# Calabi-Yau manifolds and compactification of extra dimensions in M-theory

I just finished learning M(atrix) theory and the basics of the compactification of extra dimensions.

The extra 6 dimensions of superstring theory can be compactified on 3 Calabi-Yau manifolds (because 6 real dimensions means 3 complex dimensions).

However, when it comes to M-theory, one cannot compactify on 3.5 Calabi-Yau manifolds, so after compactifying 6 dimensions, where does the extra 1 dimension go? Is it just compactified on a circle, or something like that?

• For clarity, there are CY's of complex dimension two, three, etc., not just one. May 26, 2013 at 14:16
• Keyword in this context: $G_2$-manifolds. May 26, 2013 at 16:00
• See on the nLab at ncatlab.org/nlab/show/M-theory+on+G2-manifolds Sep 2, 2013 at 13:16