$N=2$ Super-$W_3^{(2)}$ Algebra in Superfields

TL;DR

This paper develops a manifestly N=2 supersymmetric formulation of the classical super-$W_3^{(2)}$ algebra using superfields, and explores its reduction to super-$W_3$ along with associated evolution equations.

Contribution

It introduces a new superfield-based formulation of the N=2 super-$W_3^{(2)}$ algebra and constructs evolution equations with this algebra as the second Hamiltonian structure.

Findings

Superfield formulation of N=2 super-$W_3^{(2)}$ algebra.

Reduction to N=2 super-$W_3$ algebra.

Family of evolution equations related to the algebra.

Abstract

We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3^{(2)}$ algebra (its classical version) in terms of the spin 1 unconstrained supercurrent generating a $N=2$ superconformal subalgebra and the spins 1/2, 2 bosonic and spins 1/2, 2 fermionic constrained supercurrents. We consider a superfield reduction of $N=2$ super-$W_3^{(2)}$ to $N=2$ super-$W_3$ and construct a family of evolution equations for which $N=2$ super-$W_3^{(2)}$ provides the second hamiltonian structure.