Tensor models from the viewpoint of matrix models: the case of loop models on random surfaces

Understand

We study a connection between random tensors and random matrices through $U(\tau)$ matrix models which generate fully packed, oriented loops on random surfaces.

• The latter are found to be in bijection with a set of regular edge-colored graphs typically found in tensor models.
• It is shown that the expansion in the number of loops is organized like the 1/N expansion of rank-three tensor models.
• Recent results on tensor models are reviewed and applied in this context.