Dual formulation of classical W-algebras

TL;DR

This paper introduces a dual formulation of classical nonlinear W-algebras, connecting them to three-dimensional actions similar to Chern-Simons theories, with an explicit superfield construction for N=2 super W4.

Contribution

It presents a novel dual formulation of classical W-algebras and links them to three-dimensional Chern-Simons-like actions, including explicit superfield constructions.

Findings

Dual formulation of classical W-algebras introduced

Connection to three-dimensional Chern-Simons-like actions established

Explicit superfield construction for N=2 super W4 provided

Abstract

By extending the concept of \mc, I introduce a dual formulation of (classical) nonlinear extensions of the \vir\ algebra. This dual formulation is closely related to three dimensional actions which are analogous to a \cs\ action. I present an explicit construction in terms of superfields of the $N=2$ super \wfour.