arXiv:hep-th/9112064v1 20 Dec 1991 MZ-TH/91-42 December 1991 Topological Gauge Theories from Supersymmetric Quantum Mechanics on Spaces of Connections Matthias Blau 1 NIKHEF-H P.O. Box 41882, 1009 DB Amsterdam The Netherlands George Thompson 2 Institut f¨ ur Physik Johannes-Gutenberg-Universit¨at Mainz Staudinger Weg 7, D-6500 Mainz, FRG Abstract We rederive the recently introduced N = 2 topological gauge the- ories, representing the Euler characteristic of moduli spaces M of connections, from supersymmetric quantum mechanics on the infi- nite dimensional spaces A/G of gauge orbits. To that end we dis- cuss 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 ex- plain 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. 1 e-mail: t75@nikhefh.nikhef.nl, 22747::t75 2 e-mail: thompson@vipmzt.physik.uni-mainz.de