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We study the double scaling limit of the $O(N)^3$-invariant tensor model,initially introduced in Carrozza and Tanasa, Lett. Math. Phys. (2016). Thismodel has an interacting part containing two types of quartic invariants, thetetrahedric and the pillow one. For the 2-point function, we rewrite the sumover Feynman graphs at each order in the $1/N$ expansion as a \emph{finite}sum, where the summand is a function of the generating series of melons andchains (a.k.a. ladders). The graphs which are the most singular in thecontinuum limit are characterized at each order in the $1/N$ expansion. Thisleads to a double scaling limit which picks up contributions from all orders inthe $1/N$ expansion. In contrast with matrix models, but similarly to previousdouble scaling limits in tensor models, this double scaling limit is summable.The tools used in order to prove our results are combinatorial, namely athorough diagrammatic analysis of Feynman graphs, as well as an analysis of thesingularities of the relevant generating series.

Double scaling limit for the $O(N)^3$-invariant tensor model