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A New Construction of Einstein-Sasaki Metrics in D >= 7

H. Lu·C. N. Pope·J. F. Vazquez-Poritz
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Abstract

We construct explicit Einstein-Kahler metrics in all even dimensions D=2n+4 \ge 6, in terms of a $2n$-dimensional Einstein-Kahler base metric. These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter, in addition to mass and rotation parameters. Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D=2n+5 \ge 7. As is commonly the case in this type of construction, for suitable choices of the free parameters the Einstein-Sasaki metrics can extend smoothly onto complete and non-singular manifolds, even though the underlying Einstein-Kahler metric has conical singularities. We discuss some explicit examples in the case of seven-dimensional Einstein-Sasaki spaces. These new spaces can provide supersymmetric backgrounds in M-theory, which play a role in the AdS_4/CFT_3 correspondence.

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H. Lu, C. N. Pope, J. F. Vazquez-Poritz. 2006-02-03. A New Construction of Einstein-Sasaki Metrics in D >= 7. https://doi.org/10.1103/physrevd.75.026005

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