Equivalence of effective superpotentials

We show that the low-energy effective superpotential of an N=1 U(N) gauge theory with matter in the adjoint and arbitrary even tree-level superpotential has, in the classically unbroken case, the same functional form as the effective superpotential of a U(N) gauge theory with matter in the fundamental and the same tree-level interactions, up to some rescalings of the couplings. We also argue that the same kind of reasoning can be applied to other cases as well.