Shadow multiplets in AdS(4)/CFT(3) and the super-Higgs mechanism

We discuss a general pairing that occurs in compactifications of M-theory on AdS_4 x X^7 backgrounds between massless ultra short multiplets and their massive shadows, namely certain universal long multiplets with fixed protected dimensions. In particular we consider the shadow of the short graviton multiplet in N=3 compactifications. It turns out to be a massive spin 3/2 multiplet with scale dimension E_0=3 and with the quantum numbers of a super-Higgs multiplet. Hence each N=3 AdS_4 x X^7 vacuum is actually to be interpreted as a spontaneously broken phase of an N=4 theory. Comparison with standard gauged N=4 supergravity in 4 dimensions reveals the unexpected bound E_0<3 on the dimension of the broken gravitino multiplet. This hints to the existence of new versions of extended supergravities, in particular N=4 where such upper bounds are evaded and where all possible vacua have a reduced supersymmetry N_0