Abstract
We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. We show that the background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Moreover, we prove that any such metric defines a supersymmetric background. Finally, we construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.
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