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

Understand

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.