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

Extended supersymmetry is also called ${\displaystyle {\mathcal {N}}=2}$, ${\displaystyle {\mathcal {N}}=4}$ 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."

See also※

• Supersymmetry algebra
• Harmonic superspace
• Projective superspace

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