Quantum Hamiltonian Reduction in Superspace Formalism

Recently the quantum hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. In this paper we extend the results to the quantum hamiltonian reduction of N = 1 affine Lie superalgebras in the superspace formalism. We show that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum hamiltonian reduction reduces to quantum hamiltonian reduction of non-supersymmetric Lie superalgebras. We construct explicitly the super energy-momentum tensor, as well as all generators of spin 1 (and 1 2 ); thus we construct explicitly all generators in the superconformal, quasi-superconformal and ZZ2 × ZZ2 superconformal algebras. ENSLAPP-A-459/94 February 1994 email : [email protected] Address after March 1, 1994 : Niels Bohr Inst., Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark. email : [email protected]