  In an approach towards naturalness without supersymmetry, renormalization
properties of nonsupersymmetric abelian quiver gauge theories are studied. In
the construction based on cyclic groups Z_p the gauge group is U(N)^p, the
fermions are all in bifundamentals and the construction allows scalars in
adjoints and bifundamentals. Only models without adjoint scalars, however,
exhibit both chiral fermions and the absence of one-loop quadratic divergences
in the scalar propagator.
