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 AdS4×X 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 32 multiplet with scale dimension E0 = 3 and with the quantum numbers of a superHiggs multiplet. Hence each N = 3 AdS4 ×X7 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 E0 < 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 N0 < N . We name them shadow supergravities. In particular, using arguments based on the solvable Lie algebra parametrization of the scalar manifold, we discuss the possible structure of shadow N = 4 supergravity. Using our previous results on the SCFT dual of the AdS4×N vacuum we discuss the SCFT realization of the universal N = 3 shadow multiplet. RG flows from an N = 4 to an N = 3 phase are ruled out by the fact that the N = 4 vacuum is at infinite distance in moduli space, denoting the presence of a topology change. † Supported by EEC under TMR contract ERBFMRX-CT96-0045