Hidden symmetries and Lie algebra structures from geometric and supergravity Killing spinors

Abstract

We consider geometric and supergravity Killing spinors and the spinor bilinears constructed out of them. The spinor bilinears of geometric Killing spinors correspond to the antisymmetric generalizations of Killing vector fields which are called Killing-Yano forms. They constitute a Lie superalgebra structure in constant curvature spacetimes. We show that the Dirac currents of geometric Killing spinors satisfy a Lie algebra structure up to a condition on 2-form spinor bilinears. We propose that the spinor bilinears of supergravity Killing spinors give way to different generalizations of Killing vector fields to higher degree forms. It is also shown that those supergravity Killing forms constitute a Lie algebra structure in six and ten dimensional cases. For five and eleven dimensional cases, the Lie algebra structure depends on an extra condition on supergravity Killing forms.

17 pages, published version

References in corpus (5)

• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Do Killing-Yano tensors form a Lie Algebra?
• Geometry of Lax pairs: particle motion and Killing-Yano tensors
• Symmetry operators of Killing spinors and superalgebras in AdS_5
• The homogeneity theorem for supergravity backgrounds II: the six-dimensional theories

Cited by in corpus (6)

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• Generalized symmetry superalgebras
• Decomposable $(4,7)$ solutions in eleven-dimensional supergravity
• Choices of spinor inner products on M-theory backgrounds