Is there an infinite variety of particles in string theory?

Question

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?

Answer 1

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.