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Brian Greene writes in The Elegant Universe:

This takes us to the third consequence of the enormous value of the string tension. Strings can execute an infinite number of different vibrational patterns. For instance, in Figure 6.2 we showed the beginnings of a never-ending sequence of possibilities characterized by an ever greater number of peaks and troughs. Doesn't this mean that there would have to be a corresponding never-ending sequence of elementary particles, seemingly in conflict with the experimental situation summarized in Tables 1.1 and 1.2? The answer is yes: If string theory is right, each of the infinitely many resonant patterns of string vibration should correspond to an elementary particle. An essential point, however, is that the high string tension that all but a few of these vibrational patterns will correspond to extremely heavy particles (the few being the lowest-energy vibrations that have near-perfect cancellations with quantum string jitters). And again, the term "heavy" here means many times heavier than the Planck mass. As our most powerful particle accelerators can reach energies only on the order of a thousand times the proton mass, less than a millionth of a billionth of the Planck energy, we are very far from being able to search in the laboratory for any of these new particles predicted by string theory. There are more indirect approaches by which we could search for them, though. For instance, the energies involved at the birth of the universe would have been high enough to produce these particles copiously. In general one would not expect them to survive to the present day, as such super-heavy particles are usually unstable, relinquishing their enormous mass by decaying into a cascade of ever lighter particles, ending with the familiar, relatively light particles in the world around us. However, it is possible that such a super-heavy vibrational string state — a relic from the big bang — did survive to the present. Finding such particles, as we discuss more fully in Chapter 9, would be a monumental discovery, to say the least.

It's true? Or has something changed in theory since then?

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That paragraph is still a good high level description of the state of (perturbative) string theory.

However there are additional elements which complicate the story, which I think Brian Greene probably didn't want to get into. In particular:

  • The way the extra dimensions are compactified affects the spectrum.
  • When you go to energies above the "string scale," the theory is strongly coupled. Then a perturbative description of the string spectrum in terms of particle states may not be appropriate. I don't think anyone knows what fully non-perturbative string theory "really is" though, so I don't think anyone can tell you what the spectrum does look like.
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  • $\begingroup$ And how exactly does the compactification method affect the spectrum? For one Calabi-Yau manifold the spectrum is infinite, for another is finite? $\endgroup$ Jan 25, 2021 at 4:16
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    $\begingroup$ Essentially you will always have an infinite tower of massive states. However, various "moduli" fields (these are fields describing things like the size of the extra dimensions) will take on different values in different compactifications. This will change the spacing of masses in the tower, and the couplings between fields. For example, in a simple "Kaluza-Klein" compactification where you simply identify $x$ with $x+L$, you will get a tower of massive particles evenly spaced, with the spacing scaling like $1/L$. $\endgroup$
    – Andrew
    Jan 25, 2021 at 4:33
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    $\begingroup$ Being more general than that is well beyond the scope of this answer, but if you are really interested you can google some of the key words: "compactification," "spectrum," "Calabi-Yau." There are some TASI lecture notes by Uranga I found doing a quick google search that looks like it goes into some details: cds.cern.ch/record/933469/files/cer-002601054.pdf $\endgroup$
    – Andrew
    Jan 25, 2021 at 4:35
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    $\begingroup$ To be honest I am not an expert on the swampland conjecture, but to me "infinite distance" sounds like an infrared/long-distance effect, which is also backed up by the fact that one is finding exponentially massless states. The ultraviolet/small-distance physics should actually be relatively insensitive to the compactification, and the states should become increasingly massive. (However this is also the regime where the theory is likely strongly coupled). $\endgroup$
    – Andrew
    Jan 25, 2021 at 5:38
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    $\begingroup$ Actually, getting a consistent theory with a finite tower of massive states would be an accomplishment... There are cosmologists working on alternative theories of gravity who would be very interested to find a consistent compactification with only a finite number of graviton states. However no one knows how to do this as far as I know; having infinite tower of states seems to be crucial for the consistency of extra dimensional theories, truncating the tower at a finite point tends to lead to inconsistencies. $\endgroup$
    – Andrew
    Jan 25, 2021 at 5:47

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