Extended supersymmetry

In theoretical physics, extended supersymmetry is supersymmetry^[1] 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.^[2] 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

References

1. West, Peter (1990-05-01). Introduction To Supersymmetry And Supergravity (Revised And Extended 2nd ed.). World Scientific Publishing Company. p. 3. ISBN 978-981-310-371-9. Retrieved 2025-07-25.
2. Weinberg, Steven (2005-05-09). The Quantum Theory of Fields: Volume 3, Supersymmetry. Cambridge University Press. ISBN 978-1-139-64343-6. Retrieved 2025-07-25.