Abstract
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 ⁎ | 2 N ) with the even subgroup SO ⁎ ( 8 ) × USp ( 2 N ) and its deformations using quasiconformal methods. We show that the minimal unitary supermultiplet of OSp ( 8 ⁎ | 2 N ) 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 AdS 7 × S 4 . We study its deformations in further detail and show that they are isomorphic to the doubleton supermultiplets constructed by using twistorial oscillators.
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