Hidden symmetries and Killing tensors on curved spaces

TL;DR

This paper explores higher order symmetries in curved spaces through Killing tensors and their relation to supersymmetries, revealing complex algebraic structures like superalgebras in specific geometries such as the Taub-NUT space.

Contribution

It uncovers the connection between Killing-Yano tensors and non-standard supersymmetries, and constructs an infinite dimensional superalgebra of Dirac operators on the Taub-NUT space.

Findings

Killing-Yano tensors generate Dirac type operators with rich algebraic structures.

An infinite dimensional superalgebra of Dirac operators is constructed for the Taub-NUT space.

Existence of conformal Killing-Yano tensors is analyzed in spaces with mixed Sasakian structures.

Abstract

Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.