Chiral field-strength superfield ($W_{\alpha }$)

For a non-Abelian vector superfield, the chiral field-strength superfield isIt obeys ${\bar{D}}_{\dot{\alpha }}{W}_{\alpha }=0$ and transforms covariantly under a supergauge transformation.

The four-dimensional supersymmetric Yang-Mills action is the chiral superspace integral of $\mathrm{Tr}(W^{\alpha }{W}_{\alpha })$ plus its Hermitian conjugate. Its component fields are a Yang-Mills gauge field, a gaugino and an auxiliary field.