New 1/N expansions in random tensor models

TL;DR

This paper introduces multiple 1/N expansions in random tensor models, enabling the study of rectangular tensors and revealing new large N limit behaviors, including Gaussian and non-Gaussian regimes.

Contribution

It demonstrates the existence of multiple 1/N expansions depending on dimension, extending tensor model analysis to rectangular tensors and identifying conditions for non-Gaussian large N limits.

Findings

Multiple 1/N expansions depend on tensor dimension.

Large N limits are mostly Gaussian, extending universality.

A non-Gaussian large N limit is identified in even dimensions.

Abstract

Although random tensor models were introduced twenty years ago, it is only in 2011 that Gurau proved the existence of a 1/N expansion. Here we show that there actually is more than a single 1/N expansion, depending on the dimension. These new expansions can be used to define tensor models for `rectangular' tensors (whose indices have different sizes). In the large N limit, they retain more than the melonic graphs. Still, in most cases, the large N limit is found to be Gaussian, and therefore extends the scope of the universality theorem for large random tensors. Nevertheless, a scaling which leads to non-Gaussian large N limits, in even dimensions, is identified for the first time.