Appears in collection : 2023 - T1A - Quantum gravity, random geometry and holography

Random tensors exhibit a $1/N$ expansion dominated by melonic graphs. The large $N$ limit of these models is thus richer than the large $N$ limit of vector models, but more amenable to computations than the one of matrix models. This series of lectures is divided into two parts. In the first part I will review the melonic large $N$ limit in combinatorial tensor and vector/tensor models. In the second part I will discuss the $O(N)^3$ field theory in the large N limit.