Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps

Understand

Ordinary tensor models of rank $D\geq 3$ are dominated at large $N$ by tree-like graphs, known as melonic triangulations.

• We here show that non-melonic contributions can be enhanced consistently, leading to different types of large $N$ limits.
• We first study the most generic quartic model at $D=4$, with maximally enhanced non-melonic interactions.
• The existence of the $1/N$ expansion is proved and we further characterize the dominant triangulations.