Nonrenormalization theorems

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 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 ${\displaystyle {\mathcal {N}}}$ supersymmetries will also apply to any theory with more than ${\displaystyle {\mathcal {N}}}$ supersymmetries.

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