For example, in our universe, gravity and electromagnetism obey an inverse-square law due to the dimensionality of space; in higher dimensions, they would drop off faster (with the consequence that there would be no non-circular stable orbits). The nuclear force, on the other hand, is effectively one-dimensional, being restricted to flux tubes between quarks, despite living in 3D space. But, it's also a strictly short-range force.
So, is there any sensible model or set of models for how a hypothetical force could behave which is both long-range, and constrained to a lower dimension than the space it lives in? E.g., a 1D version of gravity in 3-space, or a 3D analog for electromagnetism in 4-space that would permit something like atoms to exist in a 4D universe, etc.?