A Killing spinor is a specific type of spinor field that arises in the context of differential geometry and theoretical physics, particularly in the study of Riemannian and Lorentzian manifolds. Killing spinors generalize the notion of Killing vectors, which are associated with symmetries of a manifold.
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A Killing spinor is a nonzero supersymmetry parameter that makes the fermionic transformations vanish on a bosonic background. In undeformed minimal four-dimensional supergravity it is parallel, ; in its cosmological deformation the equation uses . Its commuting Dirac current is a Killing vector, since the spinor equation makes the symmetric covariant derivative of the current vanish. General supergravity theories also impose the vanishing of matter-fermion transformations.