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

Abstract

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 $$ \mathfrak{o} $$ 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.