New supersymetries for spinning particles and black holes

TL;DR

This paper introduces new supersymmetries for spinning particles and black holes by relaxing algebra constraints, leveraging Killing-Yano tensors on manifolds like Kerr-Newman space-times, expanding the theoretical framework beyond traditional Kähler structures.

Contribution

It demonstrates that supersymmetries can be extended to manifolds with Killing-Yano tensors, broadening the class of geometries compatible with supersymmetric theories.

Findings

New supersymmetries exist on manifolds with Killing-Yano tensors.

Kerr-Newman black hole space-times admit these extended supersymmetries.

Relaxing algebra constraints enables supersymmetry in non-Kähler geometries.

Abstract

The usual extensions of supersymmetry require the existence of a complex structure and the formulation of the theory on K\"{a}hler manifolds. It is shown, that by relaxing the constraints on the algebra of supercharges we can get new supersymmetries whenever a manifold possesses a structure admitting the existence of a Killing-Yano tensor field. Examples of such manifolds are the Kerr-Newman space-times describing spinning black holes in four dimensions.