Extended supersymmetry ($\mathcal{N}>1$)

In four-dimensional Minkowski spacetime, extended supersymmetry has more than one independent Weyl spinor supercharge, together with their adjoints. The index $A=1,\dots ,\mathcal{N}$ distinguishes these supercharges.

A full four-dimensional $\mathcal{N}=2$ hypermultiplet is a matter supermultiplet equivalent to two $\mathcal{N}=1$ chiral superfields in conjugate gauge group representations. Pseudoreal representations can admit half-hypermultiplets; these do not provide genuinely complex chiral gauge spectra.