N=2 Affine Superalgebras and Hamiltonian Reduction in N=2 Superspace

Abstract

We construct N=2 affine current algebras for the superalgebras sl(n|n-1)^{(1)} in terms of N=2 supercurrents subjected to nonlinear constraints and discuss the general procedure of the hamiltonian reduction in N=2 superspace at the classical level. We consider in detail the simplest case of N=2 sl(2|1)^{(1)} and show how N=2 superconformal algebra in N=2 superspace follows via the hamiltonian reduction. Applying the hamiltonian reduction to the case of N=2 sl(3|2)^{(1)}, we find two new extended N=2 superconformal algebras in a manifestly supersymmetric N=2 superfield form. Decoupling of four component currents of dimension 1/2 in them yields, respectively, u(2|1) and u(3) Knizhnik-Bershadsky superconformal algebras. We also discuss how the N=2 superfield formulations of N=2 W_{3} and N=2 W_{3}^{(2)} superconformal algebras come out in this framework, as well as some unusual extended N=2 superconformal algebras containing constrained N=2 stress tensor and/or spin 0 supercurrents.

47 pages, LaTeX, name of the first author extended

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Cited by in corpus (12)

• On the Super-NLS Equation and its Relation with N=2 Super-KdV within Coset Approach
• Higher Spin Currents in Wolf Space: Part I
• Dualities from higher-spin supergravity
• N=4 Super NLS-mKdV Hierarchies
• The Hamiltonian structure of the N=2 supersymmetric GNLS hierarchy
• Higher Spin Currents in Orthogonal Wolf Space
• Coset approach to the N=2 supersymmetric matrix GNLS hierarchies
• N=4 Sugawara construction on affine sl(2|1), sl(3) and mKdV-type superhierarchies
• Generalized N=2 Supersymmetric Toda Field Theories
• Worldsheet Free Fields, Higher Spin Symmetry and Free $\mathcal{N}=4$ Super Yang-Mills
• Super-Affine Hierarchies and their Poisson Embeddings
• Hamiltonian structure and coset construction of the supersymmetric extensions of N=2 KdV hierarchy