= One-loop exactness of the holomorphic gauge kinetic function
{title2=$f_{\rm pert}=f_{\rm tree}+f_{\rm one\ loop}$}
In a supersymmetry-preserving local <Wilsonian effective action>, the <gauge kinetic function> receives only a one-loop perturbative correction. For one simple gauge factor, $\mu\,df/d\mu=b_0/(8\pi^2)$ with $b_0=3C_2(G)-\sum_iT(R_i)$. A perturbative shift of the topological angle leaves the running coefficient invariant; the <Cauchy-Riemann equations> then make its holomorphic beta function independent of the gauge coupling. Holomorphic regularity and spurionic <R-charges> exclude higher-loop Yukawa combinations, which would require antichiral couplings. The constant is fixed by one-loop matching. This does not assert one-loop exactness of a canonically normalized physical coupling, or forbid nonperturbative terms.
// Target: quantum-field-theory.bigb
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