Gauge kinetic function ($\frac{1}{4}\int d^2\theta f_{ab}(\Phi ){\mathcal{W}}^{a\alpha }{\mathcal{W}}_{\alpha }^b+h.c.$)

The gauge kinetic function is a symmetric holomorphic function of chiral superfields multiplying the gauge field-strength F-term. Its real part controls gauge kinetic coefficients and its imaginary part controls topological-angle terms. Its Wilsonian perturbative correction is constrained by one-loop exactness of the holomorphic gauge kinetic function; canonical and one-particle-irreducible gauge couplings require separate normalization and infrared analysis.

// Target: supersymmetry.bigb

A holomorphic gauge coupling is the coefficient of the gauge kinetic F-term in a local Wilsonian effective action written in holomorphic variables. In a common normalization its real part is $1/g_h^2$. The continuous perturbative shift of its topological angle, together with holomorphy, restricts its beta function to one-loop order. Wave-function renormalization and anomalous canonical field rescalings distinguish it from the physical gauge coupling.

// Target: supersymmetry.bigb