New Einstein-Sasaki and Einstein spaces from kerr-de Sitter

Abstract

In this paper, which is an elaboration of our results in Phys. Rev. Lett. 95:071101, 2005 (hep-th/0504225), we construct new Einstein-Sasaki spaces Lp,q,r 1,r n-1 in all odd dimensions D = 2n+1 ≥ 5. They arise by taking certain BPS limits of the Euclideanised Kerr-de Sitter metrics. This yields local Einstein-Sasaki metrics of cohomogeneity n, with toric U(1) n+1 principal orbits, and n real non-trivial parameters. By studying the structure of the degenerate orbits we show that for appropriate choices of the parameters, characterised by the (n+1) coprime integers (p,q,r 1,r n-1), the local metrics extend smoothly onto complete and non-singular compact Einstein-Sasaki manifolds Lp,q,r 1,r n-1. We also construct new complete and non-singular compact Einstein spaces Λp,q,r 1,r n in D = 2n+1 that are not Sasakian, by choosing parameters appropriately in the Euclideanised Kerr-de Sitter metrics when no BPS limit is taken. © SISSA 2009.