Why not a countably infinite landscape?

[jgraber]

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 manifold are not allowed and why not. TIA.

Jim Graber

(I have also posted this question to SPS via Google. Perhaps, after the usual lengthy moderation delays, one of the moderators might reply.)

 

[Haelfix]

I'm no expert in String theory, but here is what I've gathered talking with colleagues who are.

There are *no* adjustable continuous free parameters in string theory. That was initially one of the draws of the field and why a lot of people were excited about it.

The landscape business is very much based on geometry and how you count certain things in Calabi Yau's. The problem is exactly *how* you *choose* to count, and that enterprise is very technical from a mathematical perspective, and its not universally agreed upon which is why somepeople cite either a very large number, or countable infinity. Of course the issue from a phenomenological point of view is rather irrelevant *maybe*, since a priori it makes no difference from the human standpoint. We can throw lots of grad students at the problem and they probably won't be able to guess the right answer =)

Of course the vacuum degeneracy problem is also not universally accepted, there are quite a few people who disagree with both the methodology by which the flux vacua people got their result and ultimately the philosophy of it. Others are actively looking for additional (presumably physical) criteria by which to generate an extra constraint mechanism.

IMO again the problem is still drastically jumping the gun. We live in identically one world, and I still haven't seen a *single* phenomenological model that solves everything and reduces to the standard model without hard to believe exotics and a small but positive cc. Some get close, but there tends to be annoying problems with each near miss. So until such time as such a model exists, and everyone agrees with it, the whole philosophy business is about maybes, and that doesn't interest me very much.

edit As you pointed out the problem is infinitely worse in field theory, the only difference there is that there is a very nice sense of what is a minimal theory.. Like set N small for SU(N).. No such notion exists at this time for string theory)

 

[R0man]

The reason why the landscape in string theory is not countably infinite is due to the concept of compactification. In string theory, the extra dimensions beyond our familiar four (three spatial and one time) are compactified, meaning that they are curled up and hidden from our view. This allows for a huge number of possible configurations, but not an infinite number.

In the example of using N baryonic branes instead of three, the model may fail because it does not satisfy the necessary conditions for compactification. This could be due to the shape or size of the branes, or the interactions between them. It is also possible that certain values of SU(N) cannot be embedded in string theory because they do not fit within the constraints of the theory.

As for the E8xE8 or SO(32) groups, they are believed to be the only possible groups that can be embedded in string theory. This is due to the mathematical structure of these groups and their compatibility with the principles of string theory.

The reason for the increase in the number of models in string theory is due to ongoing research and developments, as well as the utilization of different mathematical techniques and frameworks. This does not necessarily mean that there are an infinite number of possibilities, but rather a continuously expanding pool of potential models.

In terms of the diagrams presented by Greene and Susskind, they are simply representations and do not necessarily reflect the actual configurations in string theory. It is possible that these diagrams do not represent valid compactifications and therefore cannot be included in the landscape.

Overall, the concept of the landscape in string theory is still a subject of ongoing research and debate. While the number of potential models may be vast, it is not necessarily infinite due to the constraints and limitations of the theory.