Supercoherent states of OSp(8*/2N), conformal superfields and the AdS₇/CFT₆ duality

We study the positive energy unitary representations of 2N extended superconformal algebras OSp(8*2N) in six dimensions. These representations can be formulated in a particle basis or a supercoherent state basis, which are labeled by the superspace coordinates in d = 6. We show that the supercoherent states that form the bases of positive energy representations of OSp(8*2N) can be identified with conformal superfields in six dimensions. The massless conformal superfields correspond precisely to the ultra short doubleton supermultiplets of OSp (8*2N). The other positive energy unitary representations correspond to massive conformal superfields in six dimensions and they can be obtained by tensoring an arbitrary number of doubleton supermultiplets with each other. The supermultiplets obtained by tensoring two copies of the doubletons correspond to massless anti-de-Sitter supermultiplets in d = 7.