Does the cancellation of quadratic divergences imply supersymmetry?

Abstract

We consider a large class of renormalizable field theories containing scalar particles and look for relations among the various coupling constants such that the one-loop contributions to the quadratic divergence for each scalar cancel. With the severe restriction that any such relation be invariant under the renormalization group, we show in all cases considered that whenever such relations exist, they are those of a supersymmetric theory. Non-Abelian and Abelian gauge theories as well as Yukawa theories are treated.