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We construct explicit Einstein-Kähler metrics in all even dimensions D = 2 n + 4 ≥ 6 , in terms of a 2 n -dimensional Einstein-Kähler base metric. These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter, or gravomagnetic charge, in addition to.." in addition to mass and rotation parameters. Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D = 2 n + 5 ≥ 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 nonsingular manifolds, even though the underlying Einstein-Kähler 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 rôle in the AdS 4 / CFT 3 correspondence.
Physical Review D – American Physical Society (APS)
Published: Jan 15, 2007
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