DOUBLE SCALING LIMIT IN O(N) VECTOR MODELS

Using the standard 1/N expansion, we study O(N) vector models with an arbitrary potential in zero dimensions and we show that a double scaling limit exists as in the case of matrix models. We find in general a hierarchy of critical theories labelled by an integer k. The universal partition function of the kth theory obtained in the double scaling limit is constructed both from the effective action in the double scaling limit and as a solution of a kth order differential equation that follows from the Schwinger-Dyson equations of the theory in the same limit. We also show that the theory possesses the Virasoro symmetry acting on the partition function.