Diffeomorphisms from higher dimensional W-algebras

TL;DR

This paper constructs a finitely generated subalgebra within higher-dimensional classical W-algebras that is isomorphic to the algebra of local diffeomorphisms, revealing a higher-dimensional generalization of w_infinity.

Contribution

It introduces a finitely generated subalgebra isomorphic to local diffeomorphisms and uncovers a higher-dimensional generalization of the w_infinity algebra.

Findings

Identification of a finitely generated subalgebra isomorphic to local diffeomorphisms in D dimensions

Discovery of a tower of fields transforming as symmetric tensorial densities

Unveiling a structure isomorphic to the Schouten symmetric bracket

Abstract

Classical W-algebras in higher dimensions have been recently constructed. In this letter we show that there is a finitely generated subalgebra which is isomorphic to the algebra of local diffeomorphisms in D dimensions. Moreover, there is a tower of infinitely many fields transforming under this subalgebra as symmetric tensorial one-densities. We also unravel a structure isomorphic to the Schouten symmetric bracket, providing a natural generalization of w_\infty in higher dimensions.