N=2 affine superalgebras and Hamiltonian reduction inN=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 (2) 3 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. *

Generalized N = 2 supersymmetric Toda field theories

“…A hamiltonian reduction in N = 2 superspace based on the N = 2 current algebra has been developed in ref. [22]. In this reference the cases of sl(2|1) and sl(3|2) and their associated W algebras were discussed.…”

QUANTUM N = 2${\rm SUPER}-W_3^{\left( 2 \right)} $ ALGEBRA IN SUPERSPACE

“…As a final result we arrive at the following SOPEs which obey all the Jacobi identities except for (T, T, T ) 4 for the generic value of the central charge algebra, (3), (6), (8), in N = 2 superspace.…”

“…In [7], N = 2 W (2) 3 algebra has been reformulated in terms of the spins (1/2, 2) bosonic supercurrents and spins (1/2, 2) fermionic ones satisfying the first class nonlinear chiral constraints, and a modified N = 2 spin 1 stress tensor J(Z) (see the next section for notation). In [8] this N = 2 superfield formulation of classical N = 2 W (2) 3 algebra has been reproduced in the framework of N = 2 superfield Hamiltonian reduction, starting from N = 2 super affine extension of the superalgebra sl(3|2).…”

Coset approach to the N = 2 supersymmetric matrix GNLS hierarchies

“…Thus, the classification problem reduces to the classification of admissible (see below) cosets of N=2 sl(n|n − 1) superalgebra.The letter is organized as follows. In section 2 we briefly recall the structure of N=2 sl(n|n − 1) superalgebra [19]. The N=2 supercurrents J which span the sl(n|n − 1) superalgebra, satisfy nonlinear chirality constraints.…”

“…Here, we give a short account of the N=2 superalgebra sl(n|n − 1) [19], which will be needed in the construction of the N=2 super (k|l, m)-MGNLS hierarchies and their second Hamiltonian structures. The N=2 superalgebra sl(n|n − 1) contains an equal number, precisely 2n(n − 1), of fermionic and bosonic N=2 supercurrents obeying the proper covariant nonlinear chirality conditions.…”