Explicit field realizations of W algebras

TL;DR

This paper constructs explicit field realizations of linear W_{1,2,s} algebras using double-scalar and double-spinor fields, enabling the realization of non-linear W_{2,s} algebras through basis transformations.

Contribution

It provides explicit constructions of linear W_{1,2,s} algebra realizations, facilitating the realization of W_{2,s} algebras from linear ones, which was not explicitly demonstrated before.

Findings

Realizations using double-scalar fields

Realizations using double-spinor fields

All realizations are Romans-type

Abstract

The fact that certain non-linear $W_{2,s}$ algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize $W_{2,s}$ algebras from linear $W_{1,2,s}$ algebras. In this paper, we first construct the explicit field realizations of linear $W_{1,2,s}$ algebras with double-scalar and double-spinor, respectively. Then, after a change of basis, the realizations of $W_{2,s}$ algebras are presented. The results show that all these realizations are Romans-type realizations.