Conformal primaries of OSp(8/4,R) and BPS states in AdS4

TL;DR

This work analyzes short unitary irreducible representations of the three-dimensional $N=8$ superconformal algebra $OSp(8/4,\mathbb{R})$ by imposing shortening conditions on the highest-weight states. The authors develop a harmonic superspace framework and identify two basic ultrashort supersingleton multiplets, whose composites realize all short multiplets corresponding to AdS$_4$ BPS states, including 1/2, 3/8, 1/4, and 1/8 BPS classes. They show that 3/8 BPS states arise only when mixing the two supersingletons, while single-type composites yield the 1/2, 1/4, and 1/8 sectors; this yields a complete, unitary classification of short representations relevant to M-theory on $AdS_4\times S^7$. The results provide a concrete AdS/CFT4-like map for M-theory excitations and clarify how BPS shortening translates between boundary conformal operators and bulk AdS states using harmonic analyticity. Overall, the paper establishes a robust framework for organizing perturbative and non-perturbative AdS$_4$ excitations via supersingleton composites.

Abstract

We derive short UIR's of the OSp(8/4,R) superalgebra of 3d N=8 superconformal field theories by the requirement that the highest weight states are annihilated by a subset of the super-Poincare odd generators. We then find a superfield realization of these BPS saturated UIR's as "composite operators" of the two basic ultrashort "supersingleton" multiplets. These representations are the AdS4 analogue of BPS states preserving different fractions of supersymmetry and are therefore suitable to classify perturbative and non-perturbative excitations of M-theory compactifications.