On the unitary representations of a class of N = 4 superconformal algebras

Abstract

We derive properties of unitary highest weight representations of the N = 4 superconformal algebras in 2 dimensions, characterized by two SU(2) Kač-Moody subalgebras. For the range 3 ⩽ c < 6 we can prove that we have constructed all unitary highest weight representations. These reduce in N = 2 to the discrete series. For other values of the parameters we derive bounds on the values of h, and we conjecture that these are complete. This is motivated by explicit constructions of representations for various values of the parameters. For the so-called massless representations we do indeed prove that our treatment is complete.