  We study theories generated by orbifolding the {\cal N}=4 super conformal
U(N) Yang Mills theory with finite N, focusing on the r\^ole of the remnant
U(1) gauge symmetries of the orbifold process. It is well known that the one
loop beta functions of the non abelian SU(N) gauge couplings vanish in these
theories. It is also known that in the large N limit the beta functions vanish
to all order in perturbation theory. We show that the beta functions of the non
abelian SU(N) gauge couplings vanish to two and three loop order even for
finite N. This is the result of taking the abelian U(1) of U(N)=SU(N)xU(1) into
account. However, the abelian U(1) gauge couplings have a non vanishing beta
function. Hence, those theories are not conformal for finite N. We analyze the
renormalization group flow of the orbifold theories, discuss the suppression of
the cosmological constant and tackle the hierarchy problem in the non
supersymmetric models.
