Topological gauge theories from supersymmetric quantum mechanics on spaces of connections

Details Topological gauge theories from supersymmetric quantum mechanics on spaces of connections Topological gauge theories from supersymmetric quantum mechanics on spaces of connections

1991-12-20

arxiv.org/abs/hep-th/9112064v1

Int. J. Mod. Phys. A8 (1993) 573-586

Physics

High Energy Physics

High Energy Physics - Theory

~15 pp

Scientific paper

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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