Higher-degree Dirac Currents of Twistor and Killing Spinors in Supergravity Theories

Abstract

We show that higher degree Dirac currents of twistor and Killing spinors correspond to the hidden symmetries of the background spacetime which are generalizations of conformal Killing and Killing vector fields respectively. They are the generalizations of 1-form Dirac currents to higher degrees which are used in constructing the bosonic supercharges in supergravity theories. In the case of Killing spinors, we find that the equations satisfied by the higher degree Dirac currents are related to Maxwell-like and Duffin-Kemmer-Petiau equations. Correspondence between the Dirac currents and harmonic forms for parallel and pure spinor cases is determined. We also analyze the supergravity twistor and Killing spinor cases in 10 and 11-dimensional supergravity theories and find that although different inner product classes induce different involutions on spinors, the higher degree Dirac currents still correspond to the hidden symmetries of the spacetime.

18 pages, published version

References in corpus (4)

• Spinor Fields Classification in Arbitrary Dimensions and New Classes of Spinor Fields on 7-Manifolds
• The homogeneity theorem for supergravity backgrounds
• Couplings of gravitational currents with Chern-Simons gravities
• On pseudo-Riemannian manifolds with many Killing spinors

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• Generalized symmetry superalgebras
• Field equations from Killing spinors
• Harmonic spinors from twistors and potential forms
• Twistors from Killing Spinors alias Radiation from Pair Annihilation I: Theoretical Considerations
• Choices of spinor inner products on M-theory backgrounds
• Spin Geometry and Some Applications
• Motion of membranes in space-times with torsion
• Bilinear forms of Kählerian twistor spinors
• Rigidity of Killing-Yano and conformal Killing-Yano superalgebras