Solution (source code)

= Solution

Specify the <gauge group>, its <gauge group representations> and gaugings, a real <Kähler potential> $K$, a <holomorphic superpotential> $W$, and a symmetric <holomorphic> <gauge kinetic function> $f_{ab}$, with positive kinetic matrices. The latter includes the <gauge couplings> and theta angles; allowed Abelian <Fayet–Iliopoulos terms> require constants $\xi_a$. For local <supersymmetry>, also specify the <Planck mass>; <constant Fayet–Iliopoulos terms in conventional N=1 supergravity> require a compatible gauged <R-symmetry> and transformation of $W$. \b[$W$ and $f$ are holomorphic; $K$ generally is not.] <Radiative corrections> generally change $K$. The <Wilsonian effective action> obeys <superpotential non-renormalization> perturbatively, although physical couplings run through field normalization and nonperturbative corrections can change $W$. The <gauge kinetic function> does receive corrections while remaining <holomorphic>; its perturbative Wilsonian running has <one-loop exactness of the holomorphic gauge kinetic function>, not all-order constancy of the physical <gauge coupling>.