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It was known that string theory was hard to test. However, I'm wondering how would the string theory do with the existing theories.

For example, could the low energy effective field theory of the string theory reconstruct the hydrogen atom(self consistent)?

I heard that the super symmetry was required to make the string theory self consistent. In the case of the hydrogen atom("string wave" $X_\text{particle}(\tau,\sigma)$), there's proton and electron (two fermions) and hydrogon atom itself and photon (two bosons), though this correspondence was not elementary, the "toy super symmetry" was satisfied if one assume there's only those four "particle string" in the model.

Could there be some "toy model" of the string theory that describe the electron orbit, and with some relativistic correction like that of the quantum mechanics?

Some related posts:

  1. String behavior in electron orbitals?
  2. How are string vibration modes related to particle identity?

What's the hydrogen atom in the string theory?

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    $\begingroup$ Related: physics.stackexchange.com/q/70836/2451 , physics.stackexchange.com/q/114763/2451 , physics.stackexchange.com/q/293947/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Jul 15, 2022 at 4:25
  • $\begingroup$ @Qmechanic so, the description of the dynamics of the hydrogen atom in the string theory wasn't constructed? $\endgroup$ Commented Jul 15, 2022 at 5:16
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    $\begingroup$ The hydrogen atom isn't even described by QFT, let alone string theory. We start from non-relativistic QM, define the atom that way, then use QFT to compute the relativistic corrections. Presumably you could use string theory to computer further corrections, though these would be ridiculously small. $\endgroup$ Commented Jul 15, 2022 at 5:23
  • $\begingroup$ @JohnRennie That was helpful, I thought of something like that but still. 1. Relativistic theory still contain the information of the non relativistic theory(the low energy approximation). 2. Assuming the most common saying that QFT was a big set, with special procedure such as the QED, and sting was another version of QFT. 3. In the toy model, the string has some non perturbative objects such as the D brane at fixed location. Why can't a D brane be wraped into a sphere in the target space and to claim it's an (approximated)particle say proton and start from there.(with the flat background). $\endgroup$ Commented Jul 15, 2022 at 15:10

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