
arXiv: hep-th/0505027
handle: 2318/1739881
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} manifolds. In fact, we find that these metrics are diffeomorphic to those recently found by Cvetic, Lu, Page and Pope. We argue that the corresponding 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.
9 pages; v2: complex coordinates given
High Energy Physics - Theory, Mathematics - Differential Geometry, High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), FOS: Mathematics, FOS: Physical sciences
High Energy Physics - Theory, Mathematics - Differential Geometry, High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), FOS: Mathematics, FOS: Physical sciences
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