O(N)-symmetric Wess-Zumino-type models

Some peculiar features of an O(N)-symmetric Wess-Zumino model in four dimensions have recently been pointed out and traced to the lack of asymptotic freedom of the theory. Our first remark is that in the large-N limit supersymmetric nonasymptotically free field theories are, however, perfectly consistent as low-energy effective theories, i.e., well below the Landau-ghost region. Moreover, we comment on the nonexistence of ultraviolet-stable fixed points of the renormalization group in such theories