Superconformal Interpretation of BPS States in AdS Geometries

We carry out a general analysis of the representations of the superconformal algebras SU(2, 2/N), OSp(8/4, ∝), and OSp(8*/2N) and give their realization in superspace. We present a construction of their UIRs by multiplication of the different types of massless superfields (“supersingletons”). Particular attention is paid to the so-called “short multiplets.” Representations undergoing shortening have “protected dimension” and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.