O(N) vector field theories in the double scaling limit

With the hope of getting some new insight into the problem arising in matrix models of 2D gravity when the dimension of matter is larger than 1, and inspired by several articles showing that O(N) invariant vector models have, at least in zero dimensions, nontrivial scaling limits, we study the large N behaviour of field theory vector models in d dimensions and discuss the nature and form of the critical behaviour. We show that there exists a double scaling limit where a bound state of the vector φ itself remains massive. The model can be described by an effective local interaction for the corresponding O(N) invariant field. (orig.)