Many theories of quantum gravity features the so called "dimensional reduction" (e.g. Asymptotic Safety, Causal Dynamical Triangulations, Euclidean Dynamical Triangulations, Loop Quantum Gravity, Group Field Theories, Causal Sets ... etc), which means, that the theory manages to capture the dimensionality of space time as four in large scales, however on short scales (UV range) the dimensionality of space time decreases to a smaller number (2 or 1.5, depending on the model).
Now, I was wondering whether there is any theory that captures this phenomena in a different way. For example, where the action or the Lagrangian measure is not four dimensional, but depends on the scale dependent dimensionality of the underlying manifold based on some observables. Or another way: there is a bare action of the model, but an effective action emerges from it, that "doesn't really care about" the bare action. This can be observed in lattice models, as the bare action drives the dynamics of the system but an effective description fits to the observed quantities. I wonder whether there are such analytical models (where numerical simulations are not involved).
