Shadow Multiplet

A general feature of Kaluza Klein spectra for compactifications of type AdS₄ × X ₇, which a consequence of the mass formulae [1], when the supermultiplets are paired by some relations that to each multiplet associate another shadow multiplet of different spin and of different type, but with masses exactly predicted by those of the parent multiplet [2] (so to say, by the second roots of the quadratic relations). The shadows of short multiplets are generically long ones, but with rational conformal dimensions and explain why the appearance of protected multiplets is so common as AdS-compactifications on Einstein manifolds. The long shadow multiplet of the massless graviton is universal since it has the volume of the internal manifold as one of its scalar component and, moreover, it has a universal structure that is independent from the detailed geometry of X ₇. In N = 2compactifications, the massless graviton shadow is a long, massive,...