# Calabi-Yau space and M theory

## Main Question or Discussion Point

Hello,

Physicists have formulated a "Calabi-Yau space", to show the supplementary dimensions in the string theory. But this space have six dimensions, and the M theory, the presentest string theory, have seven supplementary dimensions...

So, what is this Calabi-Yau space in the string theory today ? Is she still using ?

The hermit

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I'll take a quick shot at this, altho I am by no means best qualified. C-Y manifolds are very small highly folded spaces which are thought to fill all of space, and are supposed to explain the missing energy in some particle reactions.

String theorists come in all sorts, and I am sure C-Y manifolds are still being explored, but Marcus is probably best able to report on the current status in the literature.

The M-theory si belived to be some strong coupling limit of some of the best known string theorys. In particular it first appeared as an strong coupling limit of type II A. The spectrum of D0-branes of type IIA seemed to behae as if theoy would be Kaluza-Klein modes of another theory. But KK modes inidcate an aditional dimension so that theory was in an upper dimension, i.e. it was a theory in 11 dimensions. The aditional dimension should be compactified in a circle of a certain radius. The radius of that circle was related to the coupling of the type II A theory by a relation typically of the form $$R=\lambda^{2/3}$$.

This implies that the size of the aditional dimension would be diferent that the size of the rest of the aditional dimensions of type II A theory wich would be tipically of planck size.

Later it was realized that M-theory would also be an strong coupling limit of heterotic E(8)xE(8) string theory. That limit is known as "heterotic M-theory". One realization of this scenarios is the Horava-Witten model. Ther the 11th dimension is "orbifolded" to $$S^1/Z(2)$$. That orbifold can be viewed as asegment with the extrems being distinguised points because they are invariant under the action of Z(2).

Well, with this preliminars I can give ou the answer. The orbifolded 11th dimension together with the other 10 dimensions acts as a bulk space.The extremse of the orbifold are 10 dimensinal hyperplanes. Each o this hyperplanes has associated an E(8)xE(8) matter hypermultiplet. One is the "visible" sector and the other is the "hidden" sector. I guess that this could sound to many of you. Yes, it is very similar to the Randall-Sundrum brane cosmologies. All what remains to do is to compactify the hyperplanes. They are compactified to Calaby-Yaus, or whatever, to a planckian size.

This is grosso modo one possible way to deal with the 11 dimensions of M-theory.

Demystifier