Topological Gauge Theories from Supersymmetric Quantum Mechanics on Spaces of Connections

We rederive the recently introduced N = 2 topological gauge theories, representing the Euler characteristic of moduli spaces M of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces A/G of gauge orbits. To that end we discuss variants of ordinary supersymmetric quantum mechanics which have meaningful extensions to infinite-dimensional target spaces and introduce supersymmetric quantum mechanics actions modelling the Riemannian geometry of submersions and embeddings, relevant to the projections A → A/G and inclusions M ⊂ A/G respectively. We explain the relation between Donaldson theory and the gauge theory of flat connections in 3d and illustrate the general construction by other 2d and 4d examples. e-mail: [email protected], 22747::t75 e-mail: [email protected]