= Spinor calibration form
{title2=$\varphi_{ab}=\epsilon^\dagger\Gamma_0\Gamma_{ab}\epsilon$}
In a flux-free static supergravity background with a parallel unit <Killing spinor>, this two-form satisfies the membrane tangent-plane bound because $\Gamma_0\gamma(u)\gamma(v)$ is a Hermitian involution. Its eigenvalues are $\pm1$, so $\varphi(u,v)\leq1$, with equality precisely at the <kappa symmetry projector> condition. Parallel transport gives $\nabla\varphi=0$ and hence $d\varphi=0$. This constructs an ordinary <calibration>; flux backgrounds instead call for a <generalized calibration>.
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