Saturday, May 13, 2017

How does string theory reduce to the standard model?


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



Answer



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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