[s1dev]

That's not quite true. The dimension of the ambient space is constrained to be exactly 10 (in strings, 11 in M-theory) by consistency considerations.

The important question is what is the geometry of the extra dimensions, if they exist. You need a large amount of energy to probe the extra dimensions, so it would appear just like some extra particles in the theory to a low energy observer. (Of course, the observer has to have enough energy to find even those particles).

The standard model also has seemingly arbitrary particle content and interactions without much to constrain it. A majority of the particle content was put in the theory by hand after seeing a failure of the theory. In strings, this choice has been moved from the theory to the initial data (choice of geometry of the extra dimensions).

[eddieh]

I'm not a theoretical physicist and only took a few math courses beyond which were required by my major, but it was my understanding that mainstream string theories have 10, 11, and 26 dimensions, but I recall, and could be wrong, that there can be infinitely many string theories with 4 dimensions being the lower bound and some unspecified upper bound.

But I'm not an expert and I was mostly being hyperbolic with my original reply. Corrections are always welcome.

[evanb]

26 is for theories with bosons only. If you want fermions you need 10; 11 in M-theory as GP suggested.