New Realisations of W Algebras and W Strings

TL;DR

This paper introduces new realizations of W algebras involving two energy-momentum tensors and free scalars, leading to novel W-string theories described as two independent Virasoro-like strings.

Contribution

It presents a novel class of W algebra realizations with two energy-momentum tensors, expanding the known structures and enabling new W-string constructions.

Findings

New realizations of W algebras with two energy-momentum tensors

Construction of W-string theories as two independent Virasoro-like strings

Intrinsic interest due to the rarity of non-linear algebra realizations

Abstract

We discuss new realisations of $W$ algebras in which the currents are expressed in terms of two arbitrary commuting energy-momentum tensors together with a set of free scalar fields. This contrasts with the previously-known realisations, which involve only one energy-momentum tensor. Since realisations of non-linear algebras are not easy to come by, the fact that this new class exists is of intrinsic interest. We use these new realisations to build the corresponding $W$-string theories and show that they are effectively described by two independent ordinary Virasoro-like strings.