Nonrenormalization Theorems in Nonrenormalizable Theories

A perturbative nonrenormalization theorem is presented that applies to general supersymmetric theories, including nonrenormalizable theories in which the $\int d^2\theta$ integrand of the action is an arbitrary gauge-invariant function $F(\Phi ,W)$ of the chiral superfields $\Phi$ and gauge field-strength superfields $W$, and the $\int d^4\theta$ integrand is restricted only by gauge invariance. In the Wilsonian Lagrangian, $F(\Phi ,W)$ is nonrenormalized except for the one-loop renormalization of the gauge coupling parameter, and Fayet-Iliopoulos terms can be renormalized only by one-loop graphs. One consequence of this theorem is that in nonrenormalizable as well as renormalizable theories, in the absence of Fayet-Iliopoulos terms supersymmetry will be unbroken to all orders, if the bare superpotential has a stationary point.