= Killing-spinor integrability with rescaled gamma matrices
{c}
{title2=$[D_a,D_b]=R_{abcd}\gamma^{cd}/(4s)+2c^2\gamma_{ab}$}
For $\{\gamma_a,\gamma_b\}=2s g_{ab}$, the compatible <spinor covariant derivative> has curvature $R_{abcd}\gamma^{cd}/(4s)$. The torsion-free connection preserves <Clifford multiplication>, so the mixed derivative terms cancel for $D_a=\nabla_a+c\gamma_a$. Its integrability is therefore $(R_{abcd}\gamma^{cd}+8s c^2\gamma_{ab})\epsilon=0$. Changing antisymmetrization weight cannot change the relative coefficient. The common normalization uses $s=1$; $s=2$ gives the coefficient $16c^2$.
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