Chern-Simons $p$-Branes and $p$-Dimensional Classical $W$-Algebras

TL;DR

This paper demonstrates that certain generalized Chern-Simons p-branes in D-dimensional space possess an infinite set of constraints forming a closed algebra that includes p-dimensional classical W-algebras, revealing their topological nature in finite dimensions.

Contribution

It introduces a novel connection between generalized Chern-Simons p-branes and p-dimensional classical W-algebras, expanding understanding of their algebraic structure and topological properties.

Findings

Constraints form a closed algebra containing p-dimensional classical W-algebras.

In finite-dimensional target spaces, the theory is topological.

The algebraic structure is consistent with the presence of secondary constraints.

Abstract

It is shown that the generalized (with nonpolynomial Lagrangian) Chern-Simons membranes and in general $p$-branes moving in $D$-dimensional target space admit an infinite set of secondary constraints. With respect to the Poisson bracket these constraints satisfy closed algebra containing $p$-dimensional classical $W$ algebra as a subalgebra. In the case when the target space dimension $D$ is finite the theory is topological.