## Conformal superalgebras, massless representations, and hidden symmetries

In this paper we study the massless representations of the conformal superalgebras u(2,2/N-italic), su(2,2/N-italic), pu(2,2/4), and psu(2,2/4). It is argued that they are the only unitary representations of conformal supersymmetry that have a realistic (i.e., finite) particle spectrum. We show that the massless unitary irreducible representations (UIR's) of an N-italic-extended conformal supersymmetry symmetry restrict to irreducible representations of the N-italic-extended super-Poincare-acute-accent algebra and prove that the massless UIR's of the N-italic-extended super-Poincare-acute-accent algebra have unique extensions to massless UIR's of su(2,2/N-italic) if N-italicnot =4, or to massless UIR's of pu(2,2/4) if N-italic = 4. These facts suggest that the hiddenmore »