Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1991-12-05
Commun.Math.Phys. 152 (1993) 41-72
Physics
High Energy Physics
High Energy Physics - Theory
50 p. (with a4.sty: 40 p.)
Scientific paper
We discuss gauge theory with a topological N=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space $\cal M$ and the partition function equals the Euler number of $\cal M$. We explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions. To motivate our constructions we explain the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of connections. As a consequence of these considerations we propose the Euler number of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. We also comment on the possibility of constructing a topological version of the Penner matrix model.
gauge theory N=2 topological
invariant the Casson
moduli spaces the Euler characteristic of
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