beta functions of orbifold theories and the hierarchy problem - art. no. 025019

We examine a class of gauge theories obtained by projecting out certain fie lds from an N=4 supersymmetric SU(N) gauge theory. These theories are non-s upersymmetric and in the large N limit are known to be conformal. Recently it was proposed that the hierarchy problem could be solved by embedding the standard model in a theory of this kind with finite N. In order to check t his claim one must find the conformal points of the theory. To do this we c alculate the one-loop beta functions for the Yukawa and quartic scalar coup lings. We find that with the beta functions set to zero the one-loop quadra tic divergences are not canceled at sub-leading order in N; thus the hierar chy between the weak scale and the Planck scale is not stabilized unless N is of the order 10(28) or larger. We also find that at sub-leading orders i n N renormalization induces new interactions, which were not present in the original Lagrangian.