Toric Sasaki-Einstein metrics on S2 × S3
Toric Sasaki-Einstein metrics on S2 × S3
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DOI：
10.1016/j.physletb.2005.06.059
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发表时间：
2004-03
影响因子：
4.4
通讯作者：
J. Gauntlett;D. Martelli;J. Sparks;D. Waldram
中科院分区：
文献类型：
--
作者：
J. Gauntlett;D. Martelli;J. Sparks;D. Waldram
我们表明，通过采取一定的标度限制的欧几里德形式的Plebanski-Demianski度量得到一个家庭的本地环面Kahler-Einstein度量。这些可以用来构建当地的Sasaki-Einstein度量在五个维度，这是概括的Y{supp，q}流形。事实上，我们发现，这些指标是同构的Cvetic，Lu，Page和教皇最近发现的。我们证明了相应的光滑Sasaki-Einstein流形族都具有拓扑S{sup 2}xS{sup 3}.最后，我们建立了描述翘曲形式的卡-丘锥的方程，支持（2，1）三形式通量。
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{sup 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{sup 2}xS{sup 3}. We conclude by setting up the equations describing the warped version of the Calabi-Yau cones, supporting (2,1) three-form flux.