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Why not a countably infinite landscape?
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PostPosted: Tue Mar 29, 2005 6:12 am    Post subject: Why not a countably infinite landscape? Reply with quote

The landscape reputedly has ten to the one hundred or ten to the five
hundred different members, each with a number of infinitely adjustable
parameters. But supposedly it does not have an infinite number of
members. Yang-Mills theory, on the other hand, has at least a
countably infinite number of discretely different examples, e.g. SU(N)
for every value of N. Why is it that String Theory does not have a
similarly uncountable number of instantiations? For instance, in
chapter 15 of his book, Zwiebach, constructs a representation of a
theory similar to the standard model using three baryonic branes, two
right branes, one left brane and one leptonic brane. Suppose one uses
N baryonic branes instead of three. What makes the model fail?

Or to put it another way, which values of SU(N) can not be embedded in
string theory? Is it still believed that the group must be included in
E8xE8 or SO(32)?

I don't understand either string theory, or the landscape, but this
new stuff has me very confused. Once, there were only a few models.
Now there are a lot, but not an infinite number.

One more example: at a recent conference, Bryan Greene showed his
schematic picture of a three dimensional grid with a sphere at every
intersection. At the same conference, Lenny Susskind, discussing the
KLMT and KKLMTT constructions, (which he called Rube Goldberg
contraptions) showed a picture that looked like a two scoop ice cream
cone, only the "scoops" were tori, rather than spheres. Even
forgetting the cone, which I think is supposed to represent a conifold,
why doesn't replacing Brian Greene's sphere at every intersection
an with N hole torus at every intersection lead to a countably
infinite landscape?

I would be grateful to anyone who can shed some enlightenment on which
simple manifolds are not allowed and why not. TIA.

Jim Graber
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Joined: 09 Apr 2005
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PostPosted: Sat Apr 09, 2005 3:52 pm    Post subject: Re: Why not a countably infinite landscape? Reply with quote

<jgraber@mailaps.org> wrote in message
news:1112015962.209171.226800@f14g2000cwb.googlegroups.com...

Quote:
The landscape reputedly has ten to the one hundred or ten to the five
hundred different members, each with a number of infinitely adjustable
parameters. But supposedly it does not have an infinite number of
members. Yang-Mills theory, on the other hand, has at least a
countably infinite number of discretely different examples, e.g. SU(N)
for every value of N. Why is it that String Theory does not have a
similarly uncountable number of instantiations?


It's because the construction has to be at least the minimum of some
complicated potentials (think of the geometry as fields). For example, an
arbitrary geometry you draw, if consistent at all, could rapidly decay to
infinite flat space. Approximately calculating the potentials and equations
of motions, taking into account of quantum correctons etc, is very difficult
and is what many landscape string theorists work on.
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