Generalized symmetry superalgebras

Abstract

We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by Killing spinors in all dimensions. We show that bilinears of geometric Killing spinors produce special Killing-Yano and special conformal Killing-Yano forms. After defining the Lie algebra structure of hidden symmetries generated by Killing spinors, we construct the symmetry operators as the generalizations of the Lie derivative on spinor fields. All these constructions together constitute the structure of generalized symmetry superalgebras. We exemplify the construction on weak $G_2$ and nearly Kähler manifolds.

arXiv comment25 pages, published version

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Cited by in corpus (4)

• Twistor spinors and extended conformal superalgebras
• Choices of spinor inner products on M-theory backgrounds
• Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion
• Symmetries of modified Dirac operators in supergravity flux backgrounds