On the supersymmetric limit of Kerr-NUT-AdS metrics

TL;DR

This paper explores the geometric and symmetry properties of Einstein-Sasaki spaces derived from Kerr-NUT-(A)dS metrics, revealing connections between Killing-Yano tensors, spinors, and the supersymmetric limit in various dimensions.

Contribution

It generalizes the scaling limit to arbitrary dimensions, linking Kerr-NUT-(A)dS spacetimes to Einstein-Sasaki spaces and their hidden symmetries, including Killing-Yano tensors and spinors.

Findings

Re-derivation of Einstein-Sasaki spaces from Kerr-NUT-(A)dS metrics.

Identification of a geometric link between Killing-Yano tensors and Sasakian structures.

Observation of a tower of hidden symmetries related to Killing spinors.

Abstract

Generalizing the scaling limit of Martelli and Sparks [hep-th/0505027] into an arbitrary number of spacetime dimensions we re-obtain the (most general explicitly known) Einstein-Sasaki spaces constructed by Chen, Lu, and Pope [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 Kahler 2-form of the resulting Einstein-Kahler 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.