Shadow multiplets in AdS(4)/CFT3 and the super-Higgs mechanism

We discuss a general pairing that occurs in compactifications of M-theory o n AdS(4) x X-7 backgrounds between massless ultra short multiplets and thei r massive shadows, namely certain universal long multiplets with fixed prot ected dimensions. In particular we consider the shadow of the short gravito n 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. Compari son with standard gauged N = 4 supergravity in 4 dimensions reveals the une xpected bound E-0 < 3 on the dimension of the broken gravitino multiplet. T his hints to the existence of new versions of extended supergravities, in p articular N = 4 where such upper bounds are evaded and where all possible v acua have a reduced supersymmetry N-0 < N. We name them shadow supergraviti es. In particular, using arguments based on the solvable Lie algebra parame trization of the scalar manifold, we discuss the possible structure of shad ow N = 4 supergravity. Using our previous results on the SCFT dual of the A dS(4) x N-0.1.0 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. (C) 2000 Elsevier Science B.V. All rights reserved.