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

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.

28 pages, Latex, Reference added, minor corrections

References in corpus (5)

• Killing-Yano equations and G-structures
• Notes on Super Killing Tensors
• First-quantized N=4 Yang-Mills
• Super-Laplacians and their symmetries
• Hidden Symmetries of the Dirac equation in curved spacetime

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• Symmetries of supergravity backgrounds and supersymmetric field theory
• Superconformal geometries and local twistors
• New currents with Killing-Yano tensors
• On higher-spin $\mathcal{N}=2$ supercurrent multiplets
• Killing-Yano Cotton Currents
• Tensionless Strings and Killing(-Yano) Tensors
• Uses of Killing and Killing-Yano Tensors
• Twisted form hierarchies, Killing-Yano equations and supersymmetric backgrounds
• Symmetries of $\mathcal{N}=(1,0)$ supergravity backgrounds in six dimensions
• Geometry, conformal Killing-Yano tensors and conserved "currents"
• TCFHs, hidden symmetries and type II theories
• TCFHs, hidden symmetries and M-theory backgrounds
• The TCFHs of D=11 AdS backgrounds and hidden symmetries
• TCFHs, IIB warped AdS backgrounds and hidden symmetries
• TCFHs and hidden symmetries of type IIA AdS backgrounds