Two-derivative global supersymmetric gauge action ($\int d^4\theta K+\int d^2\theta [W+\frac{1}{4}{f}_{ab}{W}^{a\alpha }{W}_{\alpha }^b]+h.c.$)

A two-derivative four-dimensional $\mathcal{N}=1$ gauge action is specified by a real gauge-invariant Kähler potential, a gauge-invariant holomorphic superpotential, and a holomorphic symmetric gauge kinetic function. A constant Fayet–Iliopoulos term is additionally allowed for an Abelian gauge factor. Renormalizability restricts the matter kinetic function to a quadratic form, the superpotential to degree at most three, and the gauge kinetic function to a constant invariant tensor.