Gauging of Chern-Simons $p$-branes

TL;DR

This paper explores the algebraic structure of Chern-Simons p-branes, revealing a connection to W-infinity algebra and constructing a gauged phase-space theory analogous to W-gravity.

Contribution

It demonstrates that the secondary constraints of Chern-Simons p-branes form a closed algebra containing W_{1+infinity} as a subalgebra and constructs a corresponding gauged Hamiltonian theory.

Findings

Constraints form a closed algebra including W_{1+infinity}

A gauged phase-space theory analogous to W-gravity is constructed

The algebraic structure provides insights into the symmetries of Chern-Simons p-branes

Abstract

The Chern-Simons membranes and in general the Chern-Simons p-branes moving in $D$-dimensional target space admit an infinite set of secondary constraints. With respect to the Poisson bracket these constraints form a closed algebra which contains classical \ $W_{1+\infty }$ \ algebra in $p$-dimensions as a subalgebra. Corresponding gauged theory in the phase-space is constructed in a Hamilton gauge as an analog of the ordinary $W$-gravity.