Some remarks on (super)-conformal Killing-Yano tensors

TL;DR

This paper explores generalizations of conformal Killing-Yano tensors, which are antisymmetric tensors satisfying specific differential constraints, and discusses their relevance in supersymmetry and higher symmetries of Dirac operators.

Contribution

It introduces a new class of conformal Killing-Yano tensors of mixed symmetry type and analyzes their role in supersymmetric particle models and Dirac operator symmetries.

Findings

Identifies the mathematical structure of generalized conformal Killing-Yano tensors.

Connects these tensors to supersymmetry in spinning particles.

Discusses potential extensions to spacetime supersymmetry.

Abstract

A Killing-Yano tensor is an antisymmetric tensor obeying a first-order differential constraint similar to that obeyed by a Killing vector. In this article we consider generalisations of such objects, focusing on the conformal case. These generalised conformal Killing-Yano tensors are of mixed symmetry type and obey the constraint that the largest irreducible representation of $o(n)$ contained in the tensor constructed from the first-derivative applied to such an object should vanish. Such tensors appear naturally in the context of spinning particles having $N_0=1$ worldline supersymmetry and in the related problem of higher symmetries of Dirac operators. Generalisations corresponding to extended worldline supersymmetries and to spacetime supersymmetry are discussed.