6533b871fe1ef96bd12d19fe

RESEARCH PRODUCT

TOPOLOGICAL GAUGE THEORIES FROM SUPERSYMMETRIC QUANTUM MECHANICS ON SPACES OF CONNECTIONS

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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.