Killing-Yano tensors and some applications

TL;DR

This paper reviews the significance of Killing and Killing-Yano tensors in analyzing particle motion in curved spaces, extends existing classifications of these tensors in G structures, and discusses potential applications in supersymmetry and AdS/CFT.

Contribution

It extends the Papadopoulos list of Killing-Yano tensors to include additional G structures beyond the Berger classification.

Findings

Extended the classification of Killing-Yano tensors in G structures.

Reproduced and enlarged the Papadopoulos list for non-Berger G structures.

Outlined applications in supersymmetric particle actions and AdS/CFT correspondence.

Abstract

The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally the Papadopoulos list [74] for Killing-Yano tensors in G structures is reproduced by studying the torsion types these structures admit. The Papadopoulos list deals with groups G appearing in the Berger classification, and we enlarge the list by considering additional G structures which are not of the Berger type. Possible applications of these results in the study of supersymmetric particle actions and in the AdS/CFT correspondence are outlined.