SU(2) deformations of the minimal unitary representation of OSp(8^*|2N) as massless 6D conformal supermultiplets

Minimal unitary representation of SO^*(8)~SO(6,2) realized over the Hilbert space of functions of five variables and its deformations labeled by the spin t of an SU(2) subgroup correspond to massless conformal fields in six dimensions as was shown in [S. Fernando, M. Gunaydin, arXiv:1005.3580]. In this paper we study the minimal unitary supermultiplet of OSp(8^*|2N) with the even subgroup SO^*(8)×USp(2N) and its deformations using quasiconformal methods. We show that the minimal unitary supermultiplet of OSp(8^*|2N) admits deformations labeled uniquely by the spin t of an SU(2) subgroup of the little group SO(4) of lightlike vectors in six dimensions. We construct the deformed minimal unitary representations and show that they correspond to massless 6. D conformal supermultiplets. The minimal unitary supermultiplet of OSp(8^*|4) is the massless supermultiplet of (2,0) conformal field theory that is believed to be dual to M-theory on AdS₇×S⁴. We study its deformations in further detail and show that they are isomorphic to the doubleton supermultiplets constructed by using twistorial oscillators.