Supersymmetry nonrenormalization theorems

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In supersymmetry, there are a couple of versions of nonrenormalization theorems. One of them states that in an \mathcal{N}=1 4D SUSY theory involving only chiral superfields, the superpotential is immune from renormalization. This can be proved using holomorphy.

Another version states that the β-function in \mathcal{N}=4 superYang-Mills is zero for all couplings.

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