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

TL;DR

This paper explores deformations of the minimal unitary supermultiplet of OSp(8*|2N), showing they correspond to massless 6D conformal supermultiplets and relate to known supermultiplets in M-theory.

Contribution

It introduces a new framework for understanding deformations of minimal unitary supermultiplets of OSp(8*|2N) using quasiconformal methods, linking them to massless 6D conformal supermultiplets.

Findings

Deformations are labeled by the SU(2) spin t of the little group SO(4).

Constructed deformed minimal unitary representations correspond to massless 6D conformal supermultiplets.

Deformations of the supermultiplet of OSp(8*|4) are isomorphic to doubleton supermultiplets.

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 arXiv:1005.3580. In this paper we study the minimal unitary supermultiplet of OSp(8*|2N) with the even subgroup SO*(8) x 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 6D 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 x S^4. We study its deformations in further detail and show that they are isomorphic to the doubleton supermultiplets constructed by using twistorial oscillators.