Twistor spinor
= Twistor spinor
{title2=$\nabla_a\epsilon=\frac1n\gamma_a\gamma^b\nabla_b\epsilon$}
= Conformal Killing spinor
{synonym}
A <twistor spinor> has vanishing gamma-trace-free part of its <spinor covariant derivative>. In $n$ dimensions the displayed equation uses <gamma matrices> satisfying $\{\gamma_a,\gamma_b\}=2g_{ab}$. It is weaker than being a <parallel spinor>. In four dimensions it implies $[\gamma_a\nabla_b+\gamma_b\nabla_a-g_{ab}\gamma^c\nabla_c/2]\epsilon=0$.