Abstract
We present a vector supersymmetry for Witten-type topological gauge theories, and examine its algebra in terms of a superconnection formalism. When covariant constraints on the supercurvature are chosen, a correspondence is established with the universal bundle construction of Atiyah and Singer. The vector supersymmetry represents a certain shift operator in the curvature of the universal bundle, and can be used to generate the hierarchy of observables in these theories. This formalism should lead to the construction of vector supergravity theories, and perhaps to the gravitational analogue of the universal bundle.
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