My question is: Is there a max number of types of elementary particles predicted in advanced physics theories such as string theory? What are the reasons for this?Are the arguments purely mathematical?
DefinitelyThere is no finite limit, at least in String theory, there is no such finite number. In string theory, where the closed string mass spectrum is given (in unnatural units, although it would work in natural units, too) by:
$$m=\frac{2\pi T\ell_s}{c_0^2}\sqrt{N+\tilde N-a-\tilde a}$$$$m=2\pi\sqrt{N+\tilde N-a-\tilde a}$$
Where $a,\tilde a$ are the left- and right- moving normal ordering constant. Hereconstants, and the number operators $N,\tilde N$ can be ANYany integer or half-integer. So, they vary from 0 to $\infty$ and thus, so does the mass $m$without limit. In other words,So the mass spectrum is infintely large.
Andinfinite, and since each mass correpondscorresponds to a different particle, there is an infinite "particle spectrum"..particle spectrum.