Massless supermultiplet

A massless supermultiplet is a positive-energy unitary irreducible representation of the Super-Poincaré algebra with null four-momentum. For finite helicity states in four dimensions, half the supercharges act trivially and the others form a fermionic Fock space.

For a four-dimensional massless supermultiplet with $\mathcal{N}$ independent supercharges and highest helicity $\lambda$, level $k$ has helicity $\lambda -k/2$ and multiplicity $\left(\genfrac{}{}{0ex}{}{\mathcal{N}}{k}\right)$. The total is $2^{\mathcal{N}}$ states and the helicity range has width $\mathcal{N}/2$, before any necessary CPT completion of a supermultiplet.