document: In these frameworks, however, the physical spacetime dimension is an input rather than a prediction of the theory. In fact, in standard theories whose gravitational sector is described by the Einstein–Hilbert action, there is no obstruction to perform dimensional reductions to spacetimes of dimensions d≠4. Then the question arises, since eleven-dimensional Minkowski space is a maximally (super)symmetric state, and the theory is well-behaved around it, why the theory does not select this configuration as the vacuum, but instead, it chooses a particular compactified space with less symmetry. An ideal situation, instead, would be that the eleven-dimensional theory dynamically predicted a low energy regime which could only be a four-dimensional effective theory. In such a scenario, a background solution with an effective spacetime dimension d>4 should be expected to be a false vacuum where the propagators for the dynamical fields are ill-defined, lest a low energy effective theory could exist in dimensions higher than four.
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