= Supermembrane closed four-form
{title2=$G_4\ \propto\ i\Pi^m\wedge\Pi^n\wedge d\bar\theta\gamma_{mn}d\theta$}
The four-dimensional membrane <Fierz rearrangement> identity $(C\gamma_{mn})_{(\alpha\beta}(C\gamma^n)_{\gamma\delta)}=0$ makes the displayed supertranslation-invariant four-form closed. It is locally the <exterior derivative> of a three-form potential, which can change by an exact form under target <supersymmetry>. Pulling the potential back to a closed <worldvolume> gives an invariant <Wess-Zumino brane coupling>. The charge magnitude and normalization of this form are fixed together by cancellation of the area variation under <kappa symmetry>.
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