In theoretical physics a nonrenormalization theorem is a limitation on how a certain quantity in the classical description of a quantum field theory may be modified by renormalization in the full quantum theory. Renormalization theorems are common in theories with a sufficient amount of supersymmetry, usually at least 4 supercharges. Perhaps the first nonrenormalization theorem was introduced by Marcus T. Grisaru, Martin Rocek and Warren Siegel in their 1979 paper Improved methods for supergraphs. Nonrenormalization in supersymmetric theories and holomorphy Nonrenormalization theorems in supersymmetric theories are often consequences of the fact that certain objects must have a holomorphic dependence on the quantum fields and coupling constants. In this case the nonrenormalization theory is said to be a consequence of holomorphy. The more supersymmetry a theory has, the more renormalization theorems apply. Therefore a renormalization theorem that is valid for a theory with supersymmetries will also apply to any theory with more than supersymmetries. Examples in 4-dimensional theories In 4 dimensions the number counts the number of 4-component Majorana spinors of supercharges. Some examples of nonrenormalization theorems in 4-dimensional supersymmetric theories are: In an 4D SUSY theory involving only chiral superfields, the superpotential is immune from renormalization. With an arbitrary field content it is immune from renormalization in perturbation theory but may be renormalized by nonperturbative effects such as instantons. In an 4D SUSY theory the moduli space of the hypermultiplets, called the Higgs branch, has a hyper-Kähler metric and is not renormalized. In the article Lagrangians of N=2 Supergravity - Matter Systems it was further shown that this metric is independent of the scalars in the vector multiplets. They also proved that the metric of the Coulomb branch, which is a rigid special Kähler manifold parametrized by the scalars in vector multiplets, is independent of the scalars in the hypermultiplets. Therefore the vacuum manifold is locally a product of a Coulomb and Higgs branch. The derivations of these statements appear in The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD. In an 4D SUSY theory the superpotential is entirely determined by the matter content of the theory. Also there are no perturbative corrections to the β-function beyond one-loop, as was shown in 1983 in the article Superspace Or One Thousand and One Lessons in Supersymmetry by Sylvester James Gates, Marcus Grisaru, Martin Rocek and Warren Siegel. In super Yang–Mills the β-function is zero for all couplings,