Conformal superfields and BPS states in AdS_4/7 geometries

TL;DR

This paper analyzes superconformal algebra representations in AdS_4/7 geometries using harmonic superspace, focusing on BPS states and short multiplets relevant for dual supergravity theories and boundary conformal field theories.

Contribution

It constructs highest-weight unitary irreducible representations of superconformal algebras using harmonic superspace and classifies BPS states and short multiplets.

Findings

Identification of protected dimension multiplets as BPS states

Construction of superconformal representations via harmonic superspace

Classification of multitrace operators and supersymmetric AdS black holes

Abstract

We carry out a general analysis of the representations of the superconformal algebras OSp(8/4,R) and OSp(8*/2N) in terms of harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal 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.