COVARIANT FORMULATION OF CLASSICAL W-GRAVITY

A covariant formulation of the recently discovered gauge theory for W3-type algebras is presented. It is obtained by a systematic construction, which starts from the classical (Poisson) W3-algebra. Having associated to each annihilation generator a gauge field and local parameter, and to each creation generator a field in the coadjoint representation, we require that all curvatures vanish and we adopt gauge choices which are such that only a finite number of gauge fields remain: the vielbeins e-mu +/- and W-vielbeins B-mu++, B-mu--, corresponding to the gauge parameters k +/- (diffeomorphisms) and lambda+/-+/- (W-gravity). Apart from these the gauge sector has manifest local Weyl,Lorentz and "W-Weyl" and "W-Lorentz" symmetries. Matter is coupled by introducing an infinite set of scalar fields subject to a constraint which leaves only one physical field. This constraint is in turn identified with a field equation and yields upon integration, using an integrating factor, an invariant action. Various gauge choices are discussed.