Dear Richard,

You wrote: "the "picture" of the Compact Manifolds as a periodic structure of 6d particles in 3D space." I agree that a crude reading of 10d string theory is consistent with this picture. This picture is built for use in quantum field theories where "particles" are excitations of the "field" that are localized at a fixed point in space-time. To do calculations involving GR this picture simply does not work.


On 10/26/2012 7:01 PM, Richard Ruquist wrote:
On Fri, Oct 26, 2012 at 6:36 PM, Richard Ruquist <yann...@gmail.com> wrote:
The requested excerpt from
http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory:

"Calabi-Yau manifolds in string theory
Superstring theory is a unified theory for all the forces of nature
including quantum gravity. In superstring theory, the fundamental
building block is an extended object, namely a string, whose
vibrations would give rise to the particles encountered in nature. The
constraints for the consistency of such a theory are extremely
stringent. They require in particular that the theory takes place in a
10-dimensional space-time. To make contact with our 4-dimensional
world, it is expected that the 10-dimensional space-time of string
theory is locally the product M4×X of a 4-dimensional Minkowski space
M3,1 with a 6-dimensional space X . The 6-dimensional space X would be
tiny, which would explain why it has not been detected so far at the
existing experimental energy levels. Each choice of the internal space
X leads to a different effective theory on the 4-dimensional Minkowski
space M3,1 , which should be the theory describing our world."

The 6d space is tiny indeed, said by Yau in his book "The Shape of
Inner Space" to be 1000 Planck lengths in diameter. The rest of that
reference apparently describes a number of possible realizatons of the
6d space that is way beyond my comprehension. So now I am reading
http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's
book,
to get a more definitive answer to our questions.
Richard.
>From http://universe-review.ca/R15-26-CalabiYau.htm
"Compactification - Since all of us experience only 3 spatial and 1
temporal dimensions, the 10 and 26 extra-dimensions have to be hidden
under some schemes. One of the two alternatives is to roll them up
into very small size not observable even under a very powerful
microscope. The other one is to consider our existence on a 3 brane
floating in the bulk of ten spatial dimensions. The first alternative
is called compactification. It is more complicated than merely
shrinking the size (of the dimensions). Even in the very simple case
of a (4+1) toy model, compactification to a small circle of radius R
produces particle in the 3-D space with mass = n/R, where n is an
integer. It manifests itself as a scalar particle (spin 0) obeying the
Klein-Gordon equation. Compactification of the 16 extra-dimensions for
the bosonic string, produces the gluon and electroweak gauge fields.
Compactification of the remaining 6 extra-dimensions breaks the
Heterotic string symmetry down  to the point where the hadrons and
leptons of more conventional theories are recovered. Viewed from a
distance, the symmetry-broken Heterotic strings look just like
familiar point particles - but without the infinities and anomalies of
the particle approach. In order to maintain conformal invariance
(i.e., the world sheet should remain unchanged by relabeling), these 6
extra-dimensions have to curl up in a particular way - a more
promising one is the Calabi-Yau manifold (see more in
"Compactification") as shown in Figure 12, where each point stands for
a 3-D space.
Figure 12 Calabi-Yau Space "

The keys words are " produces particle in the 3-D space with mass".
The picture of the compact manifolds, somewhat like a crystalline
structure, did not copy over.

More: "Calabi-Yau Manifold - As mentioned in the section of
"Calabi-Yau Manifold for Dummies", all the above-mentioned
requirements are satisfied by the Calabi-Yau manifold as if it is
"made to order" for the occasion. By the way, it also correctly
reproduce the three generations for the fermions, and is itself a
solution of the 6-D field equation in General Relativity (producing
the gravitino)."

The word embedding appears in this reference: "Another way to compute
g is through "embedding" the Calabi-Yau manifold in a higher
dimensional background space. But so far no one has been able to work
out the coupling constant g or mass for any fermion. Anyway, this is
one example of the attempts to derive fundamental constants in the 3+1
large dimensions from the 6 dimensional compactified space."

Bottomline, I am not satisfied with what I am able to extract from
these references anything to satisfy your criticisms, or even my
concerns. I am afraid that I have been influenced by the "picture" of
the Compact Manifolds as a periodic structure of 6d particles in 3D
space.
Richard



On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King <stephe...@charter.net> wrote:
On 10/26/2012 4:31 PM, Richard Ruquist wrote:
Yes

http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory
Hi Richard,

     Could you cut and paste the specific description that answers Brent's
question?


On Fri, Oct 26, 2012 at 3:01 PM, meekerdb <meeke...@verizon.net> wrote:
On 10/26/2012 5:08 AM, Richard Ruquist wrote:
No Roger,

In string theory dimensions are conserved but can undergo extreme
modification such as in compactification where formerly orthogonal
dimensions become embedded in 3D space in spite of what Brent thinks.

Do you have a reference that describes this 'embedding'?

Brent

--
Onward!

Stephen


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