Toric Sasaki–Einstein metrics on [formula omitted

Dario Martelli,James Sparks

doi:10.1016/j.physletb.2005.06.059

Dario Martelli, James Sparks

Open Access

https://doi.org/10.1016/j.physletb.2005.06.059

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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 Kähler–Einstein metrics. These can be used to construct local Sasaki–Einstein metrics in five dimensions which are generalisations of the Yp,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 S2×S3. We conclude by setting up the equations describing the warped version of the Calabi–Yau cones, supporting (2,1) three-form flux.

Highlights

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
Preprint submitted to Elsevier Science of this work was to investigate if there exist other local Kahler–Einstein metrics in dimension four from which one can construct complete Sasaki–Einstein manifolds in one dimension higher
One can obtain a family of local toric Kahler–Einstein metrics by taking a certain scaling limit of a Euclideanised form of the Plebanski– Demianski metrics [8]

Summary

Introduction

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. Preprint submitted to Elsevier Science of this work was to investigate if there exist other local Kahler–Einstein metrics in dimension four from which one can construct complete Sasaki–Einstein manifolds in one dimension higher. One can obtain a family of local toric Kahler–Einstein metrics by taking a certain scaling limit of a Euclideanised form of the Plebanski– Demianski metrics [8]. Toric refers to the fact that the metric has two commuting holomorphic Killing vector fields.

Results

Conclusion