On the supersymmetric limit of Kerr-NUT-AdS metrics

Generalizing the scaling limit of Martelli and Sparks [D. Martelli, J. Sparks, Phys. Lett. B 621 (2005) 208, hep-th/0505027] into an arbitrary number of spacetime dimensions we re-obtain the (most general explicitly known) Einstein–Sasaki spaces constructed by Chen et al. [W. Chen, H. Lü, C.N. Pope, Class. Quantum Grav. 23 (2006) 5323, hep-th/0604125]. We demonstrate that this limit has a well-defined geometrical meaning which links together the principal conformal Killing–Yano tensor of the original Kerr-NUT-(A)dS spacetime, the Kähler 2-form of the resulting Einstein–Kähler base, and the Sasakian 1-form of the final Einstein–Sasaki space. The obtained Einstein–Sasaki space possesses the tower of Killing–Yano tensors of increasing rank—underlined by the existence of Killing spinors. A similar tower of hidden symmetries is observed in the original (odd-dimensional) Kerr-NUT-(A)dS spacetime. This rises an interesting question whether also these symmetries can be related to the existence of some ‘generalized’ Killing spinor.