  We discuss a general feature of Freund Rubin compactifications that was
previously overlooked. It consist in a curious pairing, which we call a shadow
relation, of completely different (in terms of spin and mass) fields of the
dimensionally reduced theory. Particularly interesting is the case where the
compactification preserves a certain amount of supersymmetry, giving rise to a
shadowing phenomenon between whole supermultiplets of fields. In particular,
there are strong suggestions about the consistency of a massive truncation of
11D supergravity to the massless modes of the graviton supermultiplet plus the
massive modes of its shadow partner. This fact has important consequences in
the ${\cal N}=2$ and ${\cal N}=3$ cases, which seem to realize respectively a
Higgs or a superHiggs phenomenon. In other words, we are led to reinterpret the
dimensionally reduced theory as a spontaneously broken phase of some higher
(super)symmetric theory.
