Toric Sasaki-Einstein metrics on S^2 x S^3

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Abstract
We show that by taking a certain scaling limit of a Euclideanised form of the Plebanski-Demianski metrics one obtains a family of local toric Kahler-Einstein metrics. These can be used to construct local Sasaki-Einstein metrics in five dimensions, which are generalisations of the Y^{p,q} metrics. In fact, we find that the local metrics are diffeomorphic to those recently found by Cvetic, Lu, Page and Pope. We argue that the resulting family of smooth Sasaki-Einstein manifolds all have topology S^2 x S^3. We conclude by setting up the equations describing the warped version of the Calabi-Yau cones, supporting (2,1) three-form flux.

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