Continuous spin representations of the Poincaré and super-Poincaré groups

We construct Wigner’s continuous spin representations of the Poincaré algebra for massless particles in higher dimensions. The states are labeled both by the length of a spacelike translation vector and the Dynkin indices of the short little group SO(d−3), where d is the space–time dimension. Continuous spin representations are in one-to-one correspondence with representations of the short little group. We also demonstrate how combinations of the bosonic and fermionic representations form supermultiplets of the super-Poincaré algebra. If the light-cone translations are nilpotent, these representations become finite dimensional, but contain zero or negative norm states, and their supersymmetry algebra contains a central charge in four and ten dimensions.