Non-Trivial Non-Canonical W-Algebras from Kac-Moody Reductions

TL;DR

This paper introduces a new class of W-algebras derived from Kac-Moody reductions that feature non-canonical properties, such as negative conformal spin fields, expanding the understanding of algebraic structures in theoretical physics.

Contribution

It presents a novel reduction method producing non-trivial W-algebras with unique features not seen in canonical versions.

Findings

W-algebras contain fields of negative conformal spin

The constructed W-algebras are not trivial extensions of canonical ones

New algebraic structures from Kac-Moody reductions

Abstract

By reducing a split $G_2$ Kac-Moody algebra by a non-maximal set of first-class constraints we produce W-algebras which (i) contain fields of negative conformal spin and (ii) are not trivial extensions of canonical W-algebras.