COHOMOLOGICAL GRAVITY

We construct a theory of cohomological gravity in arbitrary dimensions based upon a local vector supersymmetry algebra. The observables in t his theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization app roach, different moduli spaces are obtained by introducing curvature s ingularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occurring diffe rential form of co-degree two in the theory, and we are led to specula te on connections between this continuum quantum field theory, and the discrete Regge calculus.