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It is said that string theory is a unification of particle physics and gravitation.

Is there a reasonably simple explanation for how the standard model arises as a limit of string theory?
How does string theory account for the observed particle spectrum and the three generations?

Edit (March 23, 2012):
In the mean time, I read the paper arXiv:1101.2457 suggested in the answer by John Rennie.
My impression from reading this paper is that string theory currently does not predict any particular particle content, and that (p.13) to get close to a derivation of the standard model one must assume that string theory reduces at low energies to a SUSY GUT.
If this is correct, wouldn't this mean that part of what is to be predicted is instead assumed?
Thus one would have to wait for a specific prediction of the resulting parameters in order to see whether or not string theory indeed describes particle physics.

Some particular observations/quotes substantiating the above:
(15) looks like input from the standard model
The masses of the superparticles after (27) are apparently freely chosen to yield the subsequent prediction. This sort of arguments only shows that some SUSY GUT (and hence perhaps string theory) is compatible with the standard model, but has no predictive value.
p.39: ''The authors impose an intermediate SO(10) SUSY GUT.''
p.58: ''As discussed earlier in Section 4.1, random searches in the string landscape suggest that the Standard Model is very rare. This may also suggest that string theory cannot make predictions for low energy physics.''
p.59: ''Perhaps string theory can be predictive, IF we understood the rules for choosing the correct position in the string landscape.''

So my followup question is:
Is the above impression correct, or do I lack information available elsewhere?

Edit (March 25, 2012):
Ron Maimon's answer clarified to some extent what can be expected from string theory, but leaves details open that in my opinion are needed to justify his narrative. Upon his request, I posted the new questions separately as More questions on string theory and the standard model

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Usually people make a vacuum which is supersymmetric, and embed the SUSY standard model in string theory, then try to break SUSY. String theory is a big theory, and includes any consistent gravity background--- trying to get the standard model out is like asking "How does the ratio of Jupiter/Saturn orbit come from Newton's mechanics". Most of the standard model is an accident that can dynamically change. –  Ron Maimon Mar 23 '12 at 17:16
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It can't be that, as this would mean that string theory is a metatheory without predicting power. In Newton's mechanics, you prescribe 100 constants, and get out an infinite of predictions. in string theory, you need to prescribe the standard model to get an infinity of predictions. But then string theory is not needed at all, as the standard model itself predicts the rest! –  Arnold Neumaier Mar 23 '12 at 17:27
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A Theory of Everything of course is needed since the Standard Model does not incorporate gravity and there is no unification of known forces. Once a specific projection that embeds the standard model is identified there will certainly be predictive power in the interactions of gravity with the other forces. –  anna v Mar 24 '12 at 4:57
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@ArnoldNeumaier: You should ask your new stuff as a new question, linking to this one. It is not good to make everyone change the answers after they have been upvoted, because the upvoters might not like the changes. –  Ron Maimon Mar 25 '12 at 19:59
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I exactly agree with Ron, I upvoted the original version of the question but I dont like the edits too much ... In addition, I think a question should not be used as a "discussion thread" ... –  Dilaton Mar 25 '12 at 20:07

2 Answers 2

up vote 11 down vote accepted

String theory includes every self-consistent conceivable quantum gravity situation, including 11 dimensional M-theory vacuum, and various compactifications with SUSY (and zero cosmological constant), and so on. It can't pick out the standard model uniquely, or uniquely predict the parameters of the standard model, anymore than Newtonian mechanics can predict the ratio of the orbit of Jupiter to that of Saturn. This doesn't make string theory a bad theory. Newtonian mechanics is still incredibly predictive for the solar system.

String theory is maximally predictive, it predicts as much as can be predicted, and no more. This should be enough to make severe testable predictions, even for experiments strictly at low energies--- because the theory has no adjustable parameters. Unless we are extremely unfortunate, and a bazillion standard model vacua exist, with the right dark-matter and cosmological constant, we should be able to discriminate between all the possibilities by just going through them conceptually until we find the right one, or rule them all out.

What "no adjustable parameters" means is that if you want to get the standard model out, you need to make a consistent geometrical or string-geometrical ansatz for how the universe looks at small distances, and then you get the standard model for certain geometries. If we could do extremely high energy experiments, like make Planckian black holes, we could explore this geometry directly, and then string theory would predict relations between the geometry and low-energy particle physics.

We can't explore the geometry directly, but we are lucky in that these geometries at short distances are not infinitely rich. They are tightly constrained, so you don't have infinite freedom. You can't stuff too much structure without making the size of the small dimensions wrong, you can't put arbitrary stuff, you are limited by constraints of forcing the low-energy stuff to be connected to high energy stuff.

Most phenomenological string work since the 1990s does not take any of these constraints into account, because they aren't present if you go to large extra dimensions.

You don't have infinitely many different vacua which are qualitatively like our universe, you only have a finite (very large) number, on the order of the number of sentences that fit on a napkin.

You can go through all the vacua, and find the one that fits our universe, or fail to find it. The vacua which are like our universe are not supersymmetric, and will not have any continuously adjustible parameters. You might say "it is hopeless to search through these possibilities", but consider that the number of possible solar systems is greater, and we only have data that is available from Earth.

There is no more way of predicting which compactification will come out of the big-bang than of predicting how a plate will smash (although you possibly can make statistics). But there are some constraints on how a plate smashes--- you can't get more pieces than the plate had originally: if you have a big piece, you have to have fewer small piece elsewhere. This procedure is most tightly constrained by the assumption of low-energy supersymmetry, which requires analytic manifolds of a type studied by mathematicians, the Calabi-Yaus, and so observation of low-energy SUSY would be a tremendous clue for the geometry.

Of course, the real world might not be supersymmetric until the quntum gravity scale, it might have a SUSY breaking which makes a non-SUSY low-energy spectrum. We know such vacua exist, but they generally have a big cosmological constant. But the example of SO(16) SO(16) heterotic strings shows that there are simple examples where you get a non-SUSY low energy vacuum without work.

If your intuition is from field theory, you think that you can just make up whatever you want. This is just not so in string theory. You can't make up anything without geoemtry, and you only have so much geometry to go around. The theory should be able to, from the qualitative structure of the standard model, plus the SUSY, plus say 2-decimal place data on 20 parameters (that's enough to discrimnate between 10^40 possibilities which are qualitatively identical to the SM), it should predict the rest of the decimal places with absolutely no adjustible anything. Further, finding the right vacuum will predict as much as can be predicted about every experiment you can perform.

This is the best we can do. The idea that we can predict the standard model uniquely was only suggested in string propaganda from the 1980s, which nobody in the field really took seriously, which claimed that the string vacuum will be unique and identical to ours. This was the 1980s fib that string theorists pushed, because they could tell people "We will predict the SM parameters". This is mostly true, but not by predicting them from scratch, but from the clues they give us to the microscopic geometry (which is certainly enough when the extra dimensions are small).

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+1; I actually find your answer to be a very useful explanation of the string theory agenda. The Einstein dream comes true - ultimate geometrization. And I also like your solar system analogy: we're stuck with a specific SM the same way we're stuck with Mother Earth. My non-string theorist's take home message is that SS is a dead end albeit an extremely elegant one. –  Slaviks Mar 23 '12 at 18:30
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@Slaviks:What? How can you possibly read that into the above? This is a deranged reaction. The strings are obviously correct, Einstein's dream has come true. the theory works and is certainly the unique correct theory. Finding our vacuum might be the only way to determine what the dark matter really is, and how it interacts, how exactly inflation happened, or what the monopole spectrum is. On a more practical level, the theory will say what comes out of black holes (even astrophysical ones). Strings are a dead end like Newtonian mechanics is a dead end. I wish we had more such dead ends. –  Ron Maimon Mar 23 '12 at 19:19
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@NickKidman: The question of uniqueness is subtle for a theory that describes the whole universe. It can be argued (and Banks does argue) that each asymptotically inequivalent string vacuum is a different theory. Thats terminology debate. Most of the different vacua are explcitly linked at high energies by varying certain scalar field values, and this is the M-theory web of dualities between all the SUSY string vacua in 10d and 11d. These dualities showed that the different string theories constructed in the 1980s are different vacuum states of one theory, but this is not a physical process. –  Ron Maimon Mar 23 '12 at 23:45
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If we had a full deSitter compatible string theory, we should be able to link all the string vacua together by physical processes going through the deSitter spaces. The deSitter vacuum can decay to a true vacuum, and which one it chooses is quantum mechanically indefinite. If you pump up a scalar field to make a patch of the universe into an inflating small deSitter state, and you wait for the universe to relax, you should be able to make any other string vacuum. This is not technically true today, because we don't have deSitter strings. But 10d strings are linked by VEVs and moduli. –  Ron Maimon Mar 23 '12 at 23:49
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@NickKidman: We see gravity. The entropy/area law plus unitarity means that quantum gravity obeys the holographic principle, and string theory is the only holographic theory. I don't know if you buy the last statement, but for me the dimension changing miracles in AdS/CFT are fully persuasive. Everything else is established physics. So maybe there is a different consistent 3+1d quantum gravity, like loops, but then it should reproduce AdS/CFT, and something like strings, near extremal black holes, and from experience, this means that it should be linked to string theory by changing background. –  Ron Maimon Mar 23 '12 at 23:57

There have been many reviews over the years. Speaking as a strictly amateur string theorist http://arxiv.org/abs/1101.2457 seems a reasonably good, and recent, review of the current state of the art.

In response to Arnold: bear in mind this is the blind leading the blind, since I'm only an interested spectator.

From the early days of superstring theory two links to the standard model have been apparent. Firstly string theory could yield a gauge theory as a low energy limit, and secondly it could account for the three generations because the number of generations was connected to the topology of the Calabi-Yau manifold used for compactification.

The gauge theory as a low energy limit has never been contentious, but it's long been appreciated that it was hard to get exactly the standard model along with all it's symmetry groups. Early attempts produced extra symmetry groups that would have experimentally observable consequences. It was also assumed that N=1 supersymmetry would be retained until low energy because it was required to tame the Higgs mass, so you weren't looking for a Standard Model directly. You'd be looking for something like the MSSM, and then symmetry break this to produce the Standard Model. This is the area Raby is concentrating on. I can't comment further without going a long way beyond what I'm sure of.

It's always seemed to me far more interesting that you could account for the number of generations. After all, even the SU(5) and SO(10) GUTs don't predict the number of generations, and it seemed somehow elegant that such a fundamental property was simply related to topology. Having said that, this was based on compactification on a Calabi-Yau manifold, and that in turn is necessary to preserve N=1 supersymmetry. If supersymmetry isn't found at the LHC people will start to wonder if a Calabi-Yau manifold is needed at all. And of course the brane world approaches don't compactify.

Anyhow, your impressions seem valid to me. The issue of how predictive string theory can be is a longstanding and troublesome one. Hence Susskind's conversion to anthropic reasoning (which may be absolutely correct - no-one knows).

If a real string theorist comes along please be gentle with me - the above is hopefully more rigorous than the average popular science article, but it comes with no guarantees.

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I read the paper, and augmented my question accordingly. Could you please address my points in your answer? –  Arnold Neumaier Mar 23 '12 at 17:01

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