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arXiv · hep-th/9112064

Topological gauge theories from supersymmetric quantum mechanics on spaces of connections

M Blau·G Thompson
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Abstract

We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\cal A}/{\cal G}$ 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 ${\cal A}\rightarrow {\cal A}/{\cal G}$ and inclusions ${\cal M}\subset{\cal A}/{\cal G}$ 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.

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M Blau, G Thompson. 1991-12-20. Topological gauge theories from supersymmetric quantum mechanics on spaces of connections. https://doi.org/10.1142/s0217751x93000229

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