A New Large N Expansion for General Matrix–Tensor Models

Abstract

We define a new large N limit for general O (N) R or 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 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. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.