Resolutions of cones over Einstein-Sasaki spaces. (English) Zbl 1188.53044
Summary: Recently [W. Chen and the authors, Nucl. Phys., B 762, No. 1-2, 38–54 (2007; Zbl 1116.83015)] 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 \(\mathbb R^2\) bundle over a base manifold that is itself an \(S^2\) bundle over an Einstein-Kähler manifold.
MSC:
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
| 53C80 | Applications of global differential geometry to the sciences |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83E30 | String and superstring theories in gravitational theory |
Citations:
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