EQUIVARIANCE IN TOPOLOGICAL GRAVITY

We present models of topological gravity for a variety of moduli space conditions. In four dimensions, we construct a model for self-dual gravity characterized by the moduli condition R(muupsilon)+ = 0, and in two dimensions we treat the case of constant scalar curvature. Details are also given for both flat and Yang-Mills type moduli conditions in arbitrary dimensions. All models are based on the same fundamental multiplet which conveniently affords the construction of a complete hierarchy of observables. This approach is founded on a symmetry algebra which includes a local vector supersymmetry, in addition to a global BRST-like symmetry which is equivariant with respect to Lorentz transformations. Different moduli spaces are accommodated through the choice of additional multiplets, and we explicitly construct these together with associated invariant actions.