Quantum Hamiltonian Reduction in Superspace Formalism

Abstract

Recently the quantum hamiltonian reduction was done in the case of general $s\ell (2)$ 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 $\hf$); thus we construct explicitly all generators in the superconformal, quasi-superconformal and ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ superconformal algebras.

13 pages latex, ENSLAPP-A-459

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Cited by in corpus (10)

• N=2 Affine Superalgebras and Hamiltonian Reduction in N=2 Superspace
• Supersymmetric W-algebras
• Strings from $N=2$ Gauged Wess-Zumino-Witten Models
• Free Field Realization of $WB{C}_n$ and $W{G}_2$ algebras
• Dirac reductions and Classical W-algebras
• Generators of Supersymmetric Classical $W$-algebras
• Spinor Field Realizations of the half-integer $W_{2,s}$ Strings
• $W$-algebras associated with centralizers in type $A$
• Physical States and BRST Operators for Higher-spin $W$ Strings
• Explicit field realizations of W algebras