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. Extended supersymmetry is very important for analysis of mathematical properties of quantum field theory and superstring theory. The more extended supersymmetry is, the more it constrains physical observables and parameters.