Doing a Google search i found a paper called The maximum number of elementary particles in a super symmetric extension of the standard model.
It claims in the abstract that the upper bound is 84 (i don't have access to the article)
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?
The paper you cite employs Mohammed El Naschie's "E-infinity theory" of physics, which is one big exercise in what physicists call "numerology". Numerology is where you match up numbers - e.g. the three generations of particles in the standard model, and the three dimensions of space - and then you state or insinuate that there is a connection; but you cannot justify the connection logically (deductively). Another common example is where people find formulae for particle masses and other unexplained quantities, using combinations of transcendental numbers, other particle masses, and so on.
This "numerology" sometimes does work in physics and mathematics. That is, the search for quantitative coincidences sometimes does stumble upon relationships which have a deeper origin. Balmer's formula for the emissions of the hydrogen atom was explained by quantum mechanics; the coincidence in mathematics known as "monstrous moonshine" was proven to be true by Richard Borcherds; there are many other examples. But it is also possible to make extremely contrived relationships - e.g. you can approximate any real number arbitrarily closely, using combinations of e and $\pi$, if you use enough of them. You can also pile up lots of deductively unjustified "connections", and claim to have a theory of everything. "E-infinity theory" is in the latter category. These papers don't contain even the moderately difficult sorts of calculation that you see in real particle physics papers - I mean scattering amplitudes, particle lifetimes, and all the other detailed quantities which come from employing a theory with a proper equation of motion. Instead, these papers are full of basic algebra equations in which various known quantities are "explained" in a meaningless way. But these papers don't actually explain anything, nor do they predict anything, and the journal which publishes most of them is considered low-quality for this reason.
There is no finite limit, at least in string theory, where the closed string mass spectrum is:
$$m=2\pi\sqrt{N+\tilde N-a-\tilde a}$$
Where $a,\tilde a$ are the normal ordering constants, and the number operators $N,\tilde N$ can be any integer or half-integer, without limit. So the spectrum is infinite, and since each mass corresponds to a different particle, there is an infinite particle spectrum.
The number of particles depends on the theory assumed. Symmetries, such as super symmetry impose limits, but who knows what the theory of everything is?
Yes, the arguments are purely mathematical, until some experiment at a future date will chose among the multiplicity of theoretical models.
