- #1

- 192

- 6

## Main Question or Discussion Point

Ok, I really know nothing about this subject. Yeah, I know the definition, a Kahler manifold with a vanishing first chern class and a su(n) holonomy. I do think it's a cool mathematical concept that you could compact non-compact dimensions and in doing such you can generate the coupling constants in physics for the compact parts, su(3)Xsu(2)Xu(1), but how do you compact a non compact dimension? I can kind of see it like taking and infinitely long piece of string and mapping it onto a circle over and over, but how is this done mathematically, or is the Calabi yau manifold already considered to have six compact dimensions? Now M theory is considered to be in eleven dimensions so wouldn't you need seven compact dimensions not six to leave you with [tex]\mathbb{R}^4[/tex], but the only seven dimensional irreducible Riemann manifolds I see are so(7) and [tex]G_2[/tex]. I don't think [tex]G_2[/tex] is large enough to squeeze the standard model into so that just leaves you with so(7). So to my extremely naive understanding of things it would seem to me that your looking for a 11 dimensional non-compact Einstein manifold whose maximal compact subgroup is so(7).

Something like [tex]dS_4 \otimes so(4)[/tex]

I take it no such thing exists.

Something like [tex]dS_4 \otimes so(4)[/tex]

I take it no such thing exists.