In recent years a new large-N limit has been discovered: the melonic limit
of tensor models. It is a generalization of the planar limit of matrix
models to higher-rank tensors, but it is simpler than the planar limit
because it retains only a special subclass of planar diagrams, which have
been named “melonic diagrams”, or just “melons”. At the same time it is
richer than the large-N limit of vector models, which retains simple chain
diagrams. For these reasons it is a promising theoretical tool for
discovering new interesting phenomena in quantum field theory.
In this talk I will first review the origin of the melonic limit in
quantum gravity models, then I will describe its surprising recent
rediscovery in the context of AdS/CFT, namely in the SYK model and its
generalizations. To conclude, I will discuss its application to a
generalization of the Gross-Neveu model in two spacetime dimensions.