Do string theory’s compactified dimensions have a predicted physical interpretation? Do they for example represent the space/planes/domains in which a string ‘lives’? That is, the local permissible evolution space of a given string?
One dimension open or closed strings vibrate in 10 dimensions, at least mathematically. The later M Theory had 11 dimensions. Outside of our visual 3 space dimensions and one time dimensions may lie the other 6 or 7 compact dimensions that if they exist, they maybe so small , Planck length order of magnitude, that nothing, nor even light and gamma rays, can penetrate them. Nothing, that is , except possible high frequency gravity waves with wave lengths so small that makes them possible to enter them and beyond to the postulated multiverse (other Branes) by way of black holes. This is all postulated, the Theory may not be falsifiable, but much attention will be focused on M theory and quantum gravity in the decades ahead, as the search continues for a Theory of Everything to unlock the universes darkest secrets. Maybe. And that's about all I know from the readings.