The double scaling limit of random tensor models

Abstract

Tensor models generalize matrix models and generate colored triangulations of pseudo-manifolds in dimensions $D\geq 3$. The free energies of some models have been recently shown to admit a double scaling limit, i.e. large tensor size $N$ while tuning to criticality, which turns out to be summable in dimension less than six. This double scaling limit is here extended to arbitrary models. This is done by means of the Schwinger--Dyson equations, which generalize the loop equations of random matrix models, coupled to a double scale analysis of the cumulants.Comment: 37 pages, 13 figures; several references were added. A new subsection was added to first present all the results (before the technical proofs which will follow). A misprint was correcte