Nonrenormalization Theorems in Nonrenormalizable Theories

A perturbative nonrenormalization theorem is presented that applies to general supersymmetric theories, including nonrenormalizable theories in which the ∫d²θ integrand of the action is an arbitrary gauge-invariant function F(Φ,W) of the chiral superfields Φ and gauge field-strength superfields W, and the ∫d⁴θ integrand is restricted only by gauge invariance. In the Wilsonian Lagrangian, F(Φ,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.