Representations of (1,0) and (2,0) superconformal algebras in six dimensions: massless and short superfields

TL;DR

This paper constructs unitary representations of the six-dimensional (1,0) and (2,0) superconformal algebras via harmonic superspace, defining massless multiplets (supersingletons) and their analytic realizations. By tensoring these short multiplets, the authors systematically build all short representations corresponding to $1/2$ and $1/4$ BPS AdS bulk states, including the massless bulk states as special cases. The harmonic-superspace framework, with cosets $USp(2n)/[U(1)]^n$, renders constraints as Grassmann analyticity and enables a transparent construction of analytic, ultrashort, and composite multiplets, thereby organizing the KK towers of M-theory on $AdS_7 imes S^4$ into $OSp(8^*/2n)$ representations. The results provide a concrete, field-theoretic realization of BPS spectra and deepen the AdS$_7$/CFT$_6$ dictionary by connecting supersingleton tensor products to KK states and their masses. Overall, the work clarifies how to generate complete short representation hierarchies from basic massless multiplets in six dimensions, with explicit implications for holography and higher-dimensional conformal field theories.

Abstract

We construct unitary representations of (1,0) and (2,0) superconformal algebras in six dimensions by using superfields defined on harmonic superspaces with coset manifolds USp(2n)/[U(1)]^n, n=1,2. In the spirit of the AdS_7/CFT_6 correspondence massless conformal fields correspond to "supersingletons" in AdS_7. By tensoring them we produce all short representations corresponding to 1/2 and 1/4 BPS anti-de Sitter bulk states of which "massless bulk" representations are particular cases.