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

TL;DR

This paper constructs new five-dimensional Sasaki-Einstein metrics on S^2 x S^3 by scaling limits of Plebanski-Demianski metrics, generalizing known manifolds and exploring their geometric and flux properties.

Contribution

It introduces a novel family of local toric Kähler-Einstein metrics leading to new Sasaki-Einstein structures on S^2 x S^3, extending previous classifications.

Findings

Metrics are diffeomorphic to known Y^{p,q} manifolds.

All smooth Sasaki-Einstein manifolds in the family have topology S^2 x S^3.

Set up equations for warped Calabi-Yau cones with fluxes.

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} 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.