Resolutions of Cones over Einstein-Sasaki Spaces

TL;DR

This paper explores non-singular resolutions of Calabi-Yau cones over Einstein-Sasaki spaces, generalizing previous specific examples and identifying new classes of higher-dimensional resolutions with particular topologies.

Contribution

It extends the understanding of Calabi-Yau cone resolutions by finding new classes of non-singular higher-dimensional Einstein-Sasaki space resolutions with specific bundle topologies.

Findings

No new six-dimensional resolutions over L^{pqr} spaces.

Identifies classes of non-singular cohomogeneity-2 resolutions.

Resolved spaces are R^2 bundles over S^2 bundles over Einstein-Kahler manifolds.

Abstract

Recently an explicit resolution of the Calabi-Yau cone over the inhomogeneous five-dimensional Einstein-Sasaki space Y^{2,1} was obtained. It was constructed by specialising the parameters in the BPS limit of recently-discovered Kerr-NUT-AdS metrics in higher dimensions. We study the occurrence of such non-singular resolutions of Calabi-Yau cones in a more general context. Although no further six-dimensional examples arise as resolutions of cones over the L^{pqr} Einstein-Sasaki spaces, we find general classes of non-singular cohomogeneity-2 resolutions of higher-dimensional Einstein-Sasaki spaces. The topologies of the resolved spaces are of the form of an R^2 bundle over a base manifold that is itself an $S^2$ bundle over an Einstein-Kahler manifold.