On the Double Scaling Limit of O(N) Vector Models in d=2

Recent interest in large N matrix models in the double scaling limit raised new interest also in O(N) vector models. The limit $N \rightarrow \infty$, correlated with the limit $g \rightarrow g_c$, results in an expansion in terms of filamentary surfaces and explicit calculations can be carried out also in dimensions $d\geq 2$. It is shown here that the absence of physical massless bound states in two dimensions sets strong constraints on this limit.