= Chirality constraint on extended supersymmetry
In a four-dimensional theory with unbroken $\mathcal N\ge2$ <supersymmetry>, a full charged <hypermultiplet> contains $\mathcal N=1$ <chiral superfields> in $R$ and $\overline R$. Their net complex <chiral gauge spectrum> vanishes. The <vector multiplet> is in the real adjoint <gauge group representation>. Half-<hypermultiplets> in <pseudoreal representations> do not supply genuinely complex gauge chirality. Thus the chiral matter of the <Standard Model> can have at most unbroken $\mathcal N=1$ <supersymmetry> in four dimensions.
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