= Killing spinor
{c}
{title2=$\mathcal D_\mu\epsilon=0$}
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, $\nabla_\mu\epsilon=0$; in its cosmological deformation the equation uses $\mathcal D_\mu=\nabla_\mu+(m/2)\gamma_\mu$. 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.
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