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Jan17-09, 11:08 PM
P: 478
Quote Quote by jdstokes View Post
because this is not true of, e.g., SU(5) or SO(10) grand unified theories. I don't understand what this says about string theory?
Ahh good. I should be more careful with what I say in the following :)

I perhaps should have made a different statement, that all of the things we have observed so far live is representations smaller than the adjoint, but you would have pointed out to me the large higgs representations that are needed in GUTs in general. The statement is correct in the context of the standard model, but is not true in SU(5), where the fermions come in a 5* + 10, or SO(10) where the fermions live in the spinor rep. Of course, very few people believe in SU(5) anymore (the minimal SUSY models are firmly dead by dim 5 and dim 6 proton decay, see Pierce and Murayama,, and evading the constraints with SO(10) gets a bit tight (see "SUSY GUTs under siege" by Dermisek, Mafi, and Raby).

So what DOES this say about strings?

First of all, when you get your hands dirty with string models, you find that it is difficult to get representations larger than the adjoint. In fact, I only know of one way to get large representations (i.e. bigger than adjoints) out of string theory. This is in a paper by Kieth Dienes here: Conversely, I know of TONS of ways to get small representations out of string theory. "Small" here means "smaller than adjoint".

So, the question again comes: what does this say for the SO(10) models that require higgses in the 45 + 120 + 210 + ... representations. I would say that the question isn't "what does this say about strings", but "what does this say about SUSY GUTs"? I don't know what the right answer is, but I have never seen a string model that gets something like the complicated SO(10) models that people build. (The Dienes paper only shows that it is possible, and I know one of his students is working on that.) My feeling is that these models don't have a good stringy embedding. (Please, don't take my word for it---I'd LOVE to see some realistic SO(10) models come out of string theory :) )

Of course, you can even construct models that don't NEED SO(10) or E6---we certainly have never seen SO(10) or E6. You can break E8 (or SO(32))directly to the standard model at the string scale and have a perfectly happy model. Or, you can view the unification of forces as an accident, and imagine that we live on intersecting stacks of 6 branes wrapped around various cycles of various Calabi Yau shapes. Or (...) Getting particle physics from string theory is a robust field, with many approaches. But from what I know, you are more or less limited to the smallest (adjoint or smaller) representations of whatever gauge group you have.

I'm not sure about the gauge group problem, but I read about an idea in Lee Smolin's book about treating particles as braids in the spin-network. Does this idea hold much water?
Have you heard of a successful model? The absolute best attempt that I've seen predicts a fourth generation, which is pretty well eliminated by Z decays and astrophysical constraints. Of course, Nature could be weird like that, but I don't think so.

There was a Connes' non-commutative geometry standard model a few years ago, but that was firmly ruled out earlier this year by CDF, when they killed a higgs at 160 GeV. (Of course, as a good model builder, Connes found a way to fix his model, but this is the same things that people deride string theorists for...) And, of course, there is the Lisi model which has nice cartoons, but probably can't describe Nature.

If getting standard model looking things out of other QG (notice absence of L!!!) approaches were easy (as is the case in string theory), then someone would have done it. This means that it is probably hard, or not possible. "Hard" doesn't mean that it should be eliminated from the spectrum of possibilities, it just makes it more difficult to be optimistic about it being true.

But either way, in my mind this is the main argument for string theory---not only is it a finite theory of quantum gravity, it contains non-Abelian gauge symmetries and chiral matter, and it even contains the right KIND of chiral matter (small reps).