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Tensor models were introduced in the early 1990s as a generalization of matrix models, generating Feynman diagrams in one-to-one correspondence with higher-dimensional dynamical triangulations. However, there was initially no way to fix the topology of the diagrams, and no way to construct a large-N limit. The latter was only discovered in 2010, leading to a number of analytical results. In particular, the large-N limit of tensor model was shown to be dominated by so-called melonic diagrams, a small subclass of planar diagrams.

Unfortunately, from the quantum gravity point of view, so far this has not led to a concrete progress, as the melonic diagrams describe the universality class of branched polymers, already found numerically in the 1990s.

Nevertheless, the melonic limit has been revived more recently in the context of the Sachdev-Ye-Kitaev model, and of quantum field theories with the tensor model type of global symmetries.

In this talk I will fill in some details of this story, and briefly review some results obtained in the quantum field theory applications of the melonic large-N limit, where such limit provides a useful theoretical tool for constructing and studying a new class of interacting fixed points of the renormalization group.