= Closed three-form on four-dimensional superspace
{title2=$H_3=\Pi^m\wedge d\bar\theta\gamma_m d\theta$}
The contraction of invariant vector and spinor frames makes $H_3$ invariant under the <Super-Poincaré group>. Odd-coordinate differentials commute in the graded exterior algebra. The four-dimensional <Fierz rearrangement> identity $(C\gamma^m)_{(\alpha\beta}(C\gamma_m)_{\gamma\delta)}=0$ consequently gives $dH_3=i(d\bar\theta\gamma^m d\theta)(d\bar\theta\gamma_m d\theta)=0$. Its three-form degree is distinct from the four-form needed in the <four-dimensional supermembrane> Wess-Zumino coupling.
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