Representations of superconformal algebras in the AdS_7/4/CFT_6/3 correspondence

TL;DR

This paper analyzes superconformal algebra representations in harmonic superspace, classifies short multiplets, and discusses their relevance to BPS states, boundary operators, and AdS black holes in the AdS/CFT correspondence.

Contribution

It provides a systematic construction and classification of superconformal representations, including short multiplets, in harmonic superspace for AdS_7/4/CFT_6/3.

Findings

Classified all short multiplets with protected dimensions.

Constructed representations via multiplication of massless superfields.

Linked representations to BPS states and boundary operator classification.

Abstract

We perform a general analysis of representations of the superconformal algebras OSp(8/4,R) and OSp(8*/2N) in harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). In particular, all "short multiplets" are classified. 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.