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This is a conceptual question. One popular criticism against String Theory is its high number of solutions, around $ 10^{500} $.

  • Is it true that each solution is corresponding to a specific possible universe?

  • If yes, can we identify and pick a single solution that is corresponding to our universe?

  • If yes, can we use this solution to make testable/falsifiable prediction in our universe?

Please also point out what is possibly wrong in my fact and thinking process.

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Is it true that each solution corresponds to a specific possible universe?

This is looking it backwards. One looks at all these vacua for solutions that fit our current cosmological observations, which is a single one out of this huge number.

If yes, can we identify and pick a single solution that corresponds to our universe?

Researchers are trying but have not been able to do so. Look at this talk, page 23:

To summarize the status of the string landscape as a “top-down” concept which leads to candidate vacua, EFT,(effective field theory) and predictions,

Classification and calculational techniques are moderately well developed but by no means a mature subject.

In addition people have suggested other relevant classes of 4d vacua (e.g.nonsupersymmetric), and in studying cosmology one may need to understand vacua with other numbers of large dimensions. So this is definitely a work in progress.

On the other hand, the string landscape is mathematically well-defined structure, someday even rigorously so, and eventually, we will understand it

The link is informative, read from the beginning.

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  • $\begingroup$ The talk is informative. But the situation seems pretty bad. It seems people still have no clue how to match the solutions (vacua) to our specific universe, supposed multiverse exist and ours is one of them. It is even not sure that one of the solutions matches our specific universe. Imho, it is too ambitious at the moment, a specialized/narrowed-down version of the theory is essentially needed, then we can remove some restriction and generalize it later. $\endgroup$
    – THN
    Commented Jun 17, 2018 at 6:29
  • $\begingroup$ In other words, supposed String Theory is the final theory, we need some useful intermediate theories before getting to that, like Newtonian Mechanics, General Relativity, Quantum Mechanics, Standard Model... $\endgroup$
    – THN
    Commented Jun 17, 2018 at 6:39
  • $\begingroup$ we have the effective gravitational field theory used in the Big Bang model. and it is not "supposed String Theory is the final theory, " but "supposed a String Theory is the final theory," . As you cannot say a "lagrangian theory is the final particle theory" but "the standard model lagrangian is the particle theory" . String theories (note plural) have quantization of gravity, have representations to fit the standard model of particle physics, and have supersymmetry so that the infinities are canceled in calculations . In a sense it is a theory that fits theoretical particle models $\endgroup$
    – anna v
    Commented Jun 17, 2018 at 6:47
  • $\begingroup$ to become phenomenology a single one has to be found that could give new predictions and thus be validated. $\endgroup$
    – anna v
    Commented Jun 17, 2018 at 6:49
  • $\begingroup$ "supposed String Theory is the final theory", here I refer to some people's multiverse interpretation, that all solutions are valid and corresponding to different universes, so each solution is supposed to be the final theory for a specific universe (not sure if this interpretation is correct though). What I suggested is, maybe solving String Theory directly is infeasible. To make useful predictions and to advance technology (new computer, new engine...), we may need some intermediate theories instead. $\endgroup$
    – THN
    Commented Jun 17, 2018 at 7:53

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