Linearizing $W_{2,4}$ and $WB_2$ Algebras

TL;DR

This paper demonstrates how certain nonlinear $W$-algebras, including $W_{2,4}$, $WB_2$, and Zamolodchikov's superalgebra, can be embedded into linear conformal algebras, enabling new realizations useful for $W$-string theories.

Contribution

It introduces a method to embed nonlinear $W$-algebras into linear conformal algebras with finite currents, expanding tools for $W$-string theory construction.

Findings

Nonlinear $W_{2,4}$ and $WB_2$ algebras can be embedded into linear conformal algebras.

New realizations of nonlinear algebras are obtained through this embedding.

Potential applications in constructing $W$-string theories.

Abstract

It has recently been shown that the $W_3$ and $W_3^{(2)}$ algebras can be considered as subalgebras in some linear conformal algebras. In this paper we show that the nonlinear algebras $W_{2,4}$ and $WB_2$ as well as Zamolodchikov's spin $5/2$ superalgebra also can be embedded as subalgebras into some linear conformal algebras with a finite set of currents. These linear algebras give rise to new realizations of the nonlinear algebras which could be suitable in the construction of $W$-string theories.