Understand
Possible short and semi-short positive energy, unitary representations of the Osp(2N|4) superconformal group in three dimensions are discussed.
- Corresponding character formulae are obtained, consistent with character formulae for the SO(3,2) conformal group, revealing long multiplet decomposition at unitarity bounds in a simple way.
- Limits, corresponding to reduction to various Osp(2N|4) subalgebras, are taken in the characters that isolate contributions from fewer states, at a given unitarity threshold, leading to considerably simpler formulae.
- Via these limits, applied to partition functions, closed formulae for the generating functions for numbers of BPS operators in the free field limit of superconformal U(n)\times U(n) \N=6 Chern Simons theory and its supergravity dual are obtained in the large n limit.