Minimal unitary representation of SO∗(8)=SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions

We study the minimal unitary representation (minrep) of SO(6,2) over an Hilbert space of functions of five variables, obtained by quantizing its quasiconformal realization. The minrep of SO(6,2), which coincides with the minrep of SO∗(8) similarly constructed, corresponds to a massless conformal scalar field in six spacetime dimensions. There exists a family of “deformations” of the minrep of SO∗(8) labeled by the spin t of an SU(2)T subgroup of the little group SO(4) of lightlike vectors. These deformations labeled by t are positive energy unitary irreducible representations of SO∗(8) that describe massless conformal fields in six dimensions. The SU(2)T spin t is the six-dimensional counterpart of U(1) deformations of the minrep of 4D conformal group SU(2,2) labeled by helicity. We also construct the supersymmetric extensions of the minimal unitary representation of SO∗(8) to minimal unitary representations of OSp(8∗|2N) that describe massless six-dimensional 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.