Extended supersymmetry

In theoretical physics, extended supersymmetry is supersymmetry whose infinitesimal generators $Q_i^\alpha$ carry not only a spinor index $\alpha$ , but also an additional index $i=1,2 \dots \mathcal{N}$ where $\mathcal{N}$ is integer (such as 2 or 4).

Extended supersymmetry is also called $\mathcal{N}=2$ , $\mathcal{N}=4$ supersymmetry, for example. The more extended supersymmetry is, the more it constrains physical observables and parameters. Only the minimal (un-extended) supersymmetry is a realistic conjecture for particle physics, but extended supersymmetry is very important for analysis of mathematical properties of quantum field theory and superstring theory.