Superfield Realizations of $N=2$ Super-$W_3$

TL;DR

This paper develops a manifestly N=2 supersymmetric framework for the classical super-W_3 algebra, introducing new representations and connecting it to super Boussinesq equations with a specific Hamiltonian structure.

Contribution

It presents a novel N=2 supersymmetric formulation of super-W_3 algebra using supercurrents and introduces two new Feigin-Fuchs representations.

Findings

Two types of Feigin-Fuchs representations are identified.

A one-parameter family of N=2 super Boussinesq equations is constructed.

Super-W_3 algebra is linked to the Hamiltonian structure of these equations.

Abstract

We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3$ algebra (its classical version) in terms of the spin 1 and spin 2 supercurrents. Two closely related types of the Feigin-Fuchs representation for these supercurrents are found: via two chiral spin $\frac{1}{2}$ superfields generating $N=2$ extended $U(1)$ Kac-Moody algebras and via two free chiral spin 0 superfields. We also construct a one-parameter family of $N=2$ super Boussinesq equations for which $N=2$ super-$W_3$ provides the second hamiltonian structure.