  Random tensor models are generalizations of random matrix models which admit
$1/N$ expansions. In this article we show that the topological recursion, a
modern approach to matrix models which solves the loop equations at all orders,
is also satisfied in some tensor models. While it is obvious in some tensor
models which are matrix models in disguise, it is far from clear that it can be
applied to others. Here we focus on melonic interactions for which the models
are best understood, and further restrict to the quartic case. Then
Hubbard-Stratonovich transformation maps the tensor model to a multi-matrix
model with multi-trace interactions. We study this matrix model and show that
after substracting the leading order, it satisfies the blobbed topological
recursion. It is a new extension of the topological recursion, recently
introduced by Borot and further studied by Borot and Shadrin. Here it applies
straightforwardly, yet with a novelty as our model displays a disconnected
spectral curve, which is the union of several spectral curves of the Gaussian
Unitary Ensemble. Finally, we propose a way to evaluate expectations of
tensorial observables using the correlation functions computed from the blobbed
topological recursion.
