Do some vacua in superstring theory reproduce the SM?

[nrqed]

A quick question: are there known solutions to superstring theory that reproduce all the properties of the standard model at low energy? I mean: three families, gauge groups, pattern of symmetry breaking, correct quantum number assignments, etc.

It may be that the question is not precise enough, in which case please let me know.

Thanks!

 

[mitchell porter]

There would be innumerable vacua which give the supersymmetric standard model. Then what matters are the scale of supersymmetry breaking, and the specific values of the masses and couplings. But those quantities depend on the expectation values of the moduli, and those are presently incalculable. So what one has in string phenomenology, are vacua where e.g. one argues that the yukawa matrices have the right qualitative properties.

Nonsupersymmetric string phenomenology (e.g. Keith Dienes) has not yet produced a standard-model vacuum, to my knowledge.

 

[nrqed]

There would be innumerable vacua which give the supersymmetric standard model. Then what matters are the scale of supersymmetry breaking, and the specific values of the masses and couplings. But those quantities depend on the expectation values of the moduli, and those are presently incalculable. So what one has in string phenomenology, are vacua where e.g. one argues that the yukawa matrices have the right qualitative properties.

Nonsupersymmetric string phenomenology (e.g. Keith Dienes) has not yet produced a standard-model vacuum, to my knowledge.

Thank you! So in principle the standard model could be recovered, given the right SUSY breaking pattern and expectation values.

It is interesting that you mention Keith, when we were graduate students our desks were only a few meters apart... I should contact him to say hi.

 

[Haelfix]

I would say that is not known at the moment, and is frequently handwaved.

Generically quite a few stringy compactifications can get the massless spectrum correctly. So they'll output a three generation model with eg a SU(5) or SO(10) GUT (with small representations), some sort of GUT breaking scheme and a MSSM like spectrum. So in the models where that sort of thing is possible, its typically not possible to calculate the Yukawas without a Herculean effort. Other stringy models can get the Yukawas (or at least the hierarchy between Yukawas) but then that will typically make other things incalculable. Always this trade off.

Of course to be realistic, you aren't done yet. The various moduli of that specific model will need to be stabilized, the exact masses will need to be calculated (and there are a finite amount of values they can take which may or may not correspond to reality), SUSY will need to be broken and various cosmological problems will have to be addressed (for instance its quite pointless to get the SM if you don't have an inflaton and/or appropriate DM candidate as well). The field of string pheno I would say is in a bit of limbo at the moment, as it awaits experimental guidance. A lot of bottom up model builders are moving away from building simple MSSM or SM like constructions and instead looking at far more complicated models with large decoupled matter sectors, relatively esoteric cosmological mechanisms and so forth.

 

[phyzguy]

A quick question: are there known solutions to superstring theory that reproduce all the properties of the standard model at low energy? I mean: three families, gauge groups, pattern of symmetry breaking, correct quantum number assignments, etc.

I think this is an excellent question, and one that I have asked myself frequently. Why are we concerned that there might be 10^500 possible string vacuua if we don't know if there is even one that represents our universe?

 

[Haelfix]

To make a very bad analogy, if you have a finite set of legos, and you have a city that exists and you don't know what it's made off. A natural hypothesis might be that its made of legos.

Why would you think that? Well you know that *all* of the various structures you see can in principle be made out of compositions of legos, also you know that the city can't be made out of brick/wood/steel/most things you can check. Now the problem is this set of legos of course has a very large number of permutations and combinations (many times more than 10^500) so its difficult to know whether the exact city is reproducible given the set you have in front of you. Often you get something very close to the city, but a few legos are out of place. On the plus side you get a lot of indirect evidence that you are on the right track, b/c various numbers tend to just work (maybe the tensile strength numbers of various structures tend to come out right) so people keep working on it. In any event, it is indeed a natural program to pursue given the nonexistence of any known alternative structure and the many successes in getting partial results that didn't have to work out.

Incidentally, the famous example of the 10^500 flux vacua of type II compactifications is interesting. It turns out that none of them actually possesses an electron (and so are all ruled out on physical ground). Of course since that time, more of them have been found that do (in fact many times larger than that set), but it is a cautionary lesson about the dangers of handwaving and jumping on premature research.

This set of lectures is pretty up to date in the state of the art, and is suitable for grad students:
https://arxiv.org/abs/1804.08792

 

[atyy]

Maybe I need to buy Legos.

 

[ohwilleke]

To make a very bad analogy, if you have a finite set of legos, and you have a city that exists and you don't know what it's made off. A natural hypothesis might be that its made of legos.

Why would you think that? Well you know that *all* of the various structures you see can in principle be made out of compositions of legos, also you know that the city can't be made out of brick/wood/steel/most things you can check.

It is really much worse than that analogy.

We know that the lion's share of the legos (vacua) in the pile are the kind with the bumps on the top, but from our observation, all of the various structures we see in the city involve "female legos" with the bumps pointed inward rather than outward and we haven't even seen any legos like that in the pile yet. The pile of legos is a big stack, and we can't see all of the legos, so it's certainly possible that there are female legos in the pile, but we haven't seen any of those kinds of legos yet.

Indeed, we haven't even ever seen a stand alone lego either. We've seen clumps of legos that might be made out of individual legos (i.e. strings), but we haven't been able to come up with a parts list that has the full specifications for how the legos combine into the clumps we see and have have several competing parts list sheets circulating around.

And, the only way that this city can hold together work is there are six completely undetected dimensions of space that exist solely to make the rubber bands holding some of the structures together (i.e. gravity) much weaker than we would naively expect them to be.

Moreover, the parts of the pile of legos that have been studied most closely have features that may not be present at all in the real structures, because we didn't have as good of a view of the real structures when we started looking at the lego pile (e.g. supersymmetry, Marjorana neutrinos, baryon number and lepton number violation, proton decay, and dark matter).

 

[Islam Hassan]

This is a very instructive thread. Please, how can one devise a similar, very good —or very bad— analogy to illustrate AdS/CFT?