I read that it might be related to the phenomenon of spontaneous symmetry breaking. After Big Bang, universe underwent spontaneous symmetry breaking, in which ten dimensions randomly divided into four dimensional and six dimensional parts. Four of them underwent inflation to macroscopic scale, while the other six had been compactified. This theory makes sense to me but I'm not sure if it is appropriate.
First I should say, as you probably already know, we have absolutely no concrete evidence for the existence of any more than the 3 spatial dimensions that are obviously in existence. It may be that we will never be able to detect them directly, but indirectly we might.
This would involve a change of the currently accepted inverse square law, for example. So if at some distance close enough to the possible dimensionless electron, we found a sharp (or subtle) discontinuation in the expected smoothness of the electromagnetic force, then that would lend support to the idea that the force was being diluted by "leaking into" into a compactified dimension(s).
A similar phenomenon involving gravity would also indicate that another dimension(s) exist.
Spontanantous symmetry breaking (SSB) is invoked to try to explain how the forces we now see as separate might have existed at high enough energy levels, and the Running Constants phenomenon supports that, but how SSB is proposed to have divided dimensions is a question that someone else may be able to answer, as frankly I don't know.
In this case I think you might be confusing dimensions and forces in relation to the effects of SSB, but hopefully we can both learn from a more informed source than myself.