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.
extractive_keyphrases: background solution compactified space dimensional reductions effective spacetime dimension einstein–hilbert action false vacuum low energy effective theory low energy regime minkowski space physical spacetime dimension prediction of the theory propagators for the dynamical fields select this configuration standard theories
abstractive_keyphrases: d>4 eleven-dimensional theory four-dimensional effective theory (super)symmetric state