It depends on what type of string theory. I'm no expert, but if I remember correctly there were, at some point, 5 or 6 formulations of string theory. They required 10, 11, even 26 dimensions. It was proved that some formulations were equivalent (you could treat one with perturbation theory and you would end up with another), and the number decreased. Right now I think 10 or 11 is the preferred number of dimensions. Mathematicians and physicists deal with abstract spaces of any number of dimensions, such as the phase space (the plot of every possible degree of freedom of a system).