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

Research output: Contribution to journalJournal articlepeer-review

Published
Article number165002
<mark>Journal publication date</mark>14/07/2016
<mark>Journal</mark>Classical and Quantum Gravity
Issue number16
Volume33
Number of pages22
Publication StatusPublished
<mark>Original language</mark>English

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