Lubos Motl

Subject: Re: Penrose "nukes" string theory on the road to reality.

bcc

On May 2, 2006, at 2:49 PM, Lubos Motl wrote:

Incidentally, Calabi-Yau manifolds are of course Ricci-flat - this is one of their defining feature.

R_{mn} = 0

Yes, Penrose says that.

This also implies that the Riemann tensor

G_{mn} = 0

Well in 3 + 1

Guv + /\(Dark Energy)guv = 0 and you can relate this to O(4,1) DeSitter Space.

1//\ is the Horizon area Holograph "Screen" with (1/4/\Lp*^2) BITS in 3 + 1.

What happens in 9 + 1? Is there a larger dimensional "De Sitter space"? Hey, is that M-theory? I mean the meaning of the 10th space dimension? Something like O(10,1)?

The fact that complex Kahler manifolds with a vanishing first Chern class admit a Ricci-flat metric was conjectured by Calabi in 1957 and proved by 1977 which is why we call these manifolds Calabi-Yau manifolds.

Penrose says you need more than that, something like Killing field isometries to reduce the redundant functional freedom. An Iranian student of Bohm's in 1971 was really into Kahler manifolds - ahead of his time.

Inclusion of zero-point energy is obtained by standard perturbative techniques in string theory, and one can prove that at every order, a stable solution exists.

Penrose's statements that Calabi-Yaus spontaneously want to collapse to a singularity or anything like that are silly.

Best
Lubos

OK, I cannot argue with you - at least not yet. ;-
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