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

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

2005-05-03

arxiv.org/abs/hep-th/0505027v2

Phys.Lett. B621 (2005) 208-212

Physics

High Energy Physics

High Energy Physics - Theory

9 pages; v2: complex coordinates given

Scientific paper

10.1016/j.physletb.2005.06.059

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.

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