Free Field Representations of Extended Superconformal Algebras

Abstract

We study the classical and quantum $G$ extended superconformal algebras from the hamiltonian reduction of affine Lie superalgebras, with even subalgebras $G\oplus sl(2)$. At the classical level we obtain generic formulas for the Poisson bracket structure of the algebra. At the quantum level we get free field (Feigin-Fuchs) representations of the algebra by using the BRST formalism and the free field realization of the affine Lie superalgebra. In particular we get the free field representation of the $sl(2)\oplus sp(2N)$ extended superconformal algebra from the Lie superalgebra $osp(4|2N)$. We also discuss the screening operators of the algebra and the structure of singular vectors in the free field representation.

37 pages, Latex

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• Exceptional Superconformal Algebras
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• Supergroup - extended super Liouville correspondence
• Comments on N=4 Superconformal Algebras
• Extended Superconformal Algebras and Free Field Realizations from Hamiltonian Reduction
• Constructing Classical and Quantum Superconformal Algebras on the Boundary of AdS_3
• Classical Hamiltonian Reduction On $D(2|1;\alpha )$ Chern-Simons Gauge Theory and Large N=4 Superconformal Symmetry
• Seven Sphere and the Exceptional Nonlinear Superconformal Algebras