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The Geometry of Supersymmetric Partition Functions

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Three-dimensional N=2
theories with a U(1)_R symmetry, can be placed on a compact three manifold M
preserving some supersymmetry if and only if M admits a transversely
holomorphic foliation (THF). I will show that the partition function of the
resulting theory is independent of the metric and depends holomorphically on
the moduli of the THF. When applied to supersymmetric field theories on
manifolds diffeomorphic to S^3 and S^2 x S^1, this result explains many of the
properties observed in explicit determinations of their partition functions.