Conformal superalgebras, massless representations, and hidden symmetries.

Abstract

In this paper we study the massless representations of the conformal superalgebras u(2,2/N), su(2,2/N), 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-extended conformal supersymmetry symmetry restrict to irreducible representations of the N-extended super-Poincar\'e algebra and prove that the massless UIR's of the N-extended super-Poincar\'e algebra have unique extensions to massless UIR's of su(2,2/N) if N\ensuremath{\ne}4, or to massless UIR's of pu(2,2/4) if N=4. These facts suggest that the hidden U(N) symmetries found in N-extended supersymmetric gauge theories may be, in fact, only a subalgebra of an overall N-extended conformal superalgebra. An explicit construction of all the massless representations of su(2,2/N\ensuremath{\ne}4) and pu(2,2/4) is given. It is seen that the adjoint representation of the internal su(N) subalgebra never appears in a massless representation of N-extended conformal supersymmetry.