A New Large N Expansion for General Matrix-Tensor Models

TL;DR

This paper introduces a novel large N expansion for tensor models with enhanced scaling, organizing Feynman graphs by a new index, and extends the framework to matrix models with additional symmetry, revealing leading order structures for prime R.

Contribution

It proposes a new large N limit based on an enhanced coupling scaling, providing a natural organization of tensor model graphs and extending to large D expansions in matrix models.

Findings

New large N expansion based on an index for tensor models.

Optimal scaling for a broad class of non-melonic interactions.

Identification of leading order graphs for prime R in complete interactions.

Abstract

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.