Superconformal current algebras and their unitary representations

Abstract

A natural supersymmetric extension $$(\widehat{dG})_\kappa$$ is defined of the current (= affine Kac-Moody Lie) algebra $$\widehat{dG}$$ ; it corresponds to a superconformal and chiral invariant 2-dimensional quantum field theory (QFT), and hence appears as an ingredient in superstring models. All unitary irreducible positive energy representations of $$(\widehat{dG})_\kappa$$ are constructed. They extend to unitary representations of the semidirect sumS κ(G) of $$(\widehat{dG})_\kappa$$ with the superconformal algebra of Neveu-Schwarz, for $$\kappa = \frac{1}{2}$$ , or of Ramond, for κ=0.