N=1 super Yang-Mills theory

The $\mathcal{N}=1\,$ supersymmetric Yang-Mills theory in $4\,$ dimensions is described by the action

$S = \int\!d^4x\,\left( -\frac{1}{4}\operatorname{tr} F^{\mu\nu} F_{\mu\nu} -\frac{1}{2} \operatorname{tr} \bar\Psi D\!\!\!\!/\,\Psi \right)\,$ ,

where $\bar\Psi = \Psi^{T}C\,$ and $\Psi = \Psi^a T^a\,$ is in the adjoint representation of the group.

References

↑ Jose Figueroa-O'Farrill (2001). "BUSSTEPP Lectures on Supersymmetry". e-print. arXiv:hep-th/0109172.