= Generalized calibration
A generalized calibration bounds the full energy of a supersymmetric brane, including its potential or gauge couplings. For a membrane, compatible spinor bilinears obey $d\Omega=\iota_KF$. In a stationary gauge $\mathcal L_KA=0$, <Cartan's magic formula> proves $d(\Omega+\iota_KA)=0$. The closed charge form then supplies the energy bound. This extends ordinary <calibration> from volume alone to charged branes, as developed in https://arxiv.org/abs/hep-th/0306267[Topological charges for branes in M-theory].
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