A New Large $N$ Expansion for General Matrix–Tensor Models
Résumé
We define a new large N limit for general $\text {O}(N)^{R}$ or $\text {U}(N)^{R}$ invariant tensor models, based on an enhanced large N scaling of the coupling constants. The resulting large N expansion is organized in terms of a half-integer associated with Feynman graphs that we call the index. This index has a natural interpretation in terms of the many matrix models embedded in the tensor model. Our new scaling can be shown to be optimal for a wide class of non-melonic interactions, which includes all the maximally single-trace terms. Our construction allows to define a new large D expansion of the sum over diagrams of fixed genus in matrix models with an additional $\text {O}(D)^{r}$ global symmetry. When the interaction is the complete vertex of order $R+1$ , we identify in detail the leading order graphs for R a prime number. This slightly surprising condition is equivalent to the complete interaction being maximally single-trace.