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

TL;DR

This paper constructs N=2 affine superalgebras and explores Hamiltonian reduction in N=2 superspace, revealing new superconformal algebras and their superfield formulations, advancing understanding of supersymmetric conformal structures.

Contribution

It introduces a method to derive N=2 superconformal algebras via Hamiltonian reduction, including new extended algebras and superfield formulations for known structures.

Findings

Derived N=2 superconformal algebra from sl(2|1)^{(1)}

Found two new extended N=2 superconformal algebras

Presented superfield formulations of N=2 W_{3} and W_{3}^{(2)}

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.