Polchinski's exact renormalisation group for tensorial theories: Gaussian universality and power counting

TL;DR

This paper applies the exact renormalisation group to tensor models and tensorial group field theories, rederiving Gaussian universality and establishing a power counting framework that identifies five renormalizable theories.

Contribution

It introduces a new power counting method for Abelian tensorial field theories and clarifies the renormalization properties of tensor models.

Findings

Rederived Gaussian universality for random tensors

Developed a general power counting scheme for Abelian tensorial theories

Identified five renormalizable tensorial theories

Abstract

In this paper, we use the exact renormalisation in the context of tensor models and tensorial group field theories. As a byproduct, we rederive Gaussian universality for random tensors and provide a general power counting for Abelian tensorial field theories with a closure constraint, leading us to a only five renormalizable theories.