Can we make sense out of "Tensor Field Theory"?

TL;DR

This paper advances the understanding of tensor field theories by analyzing a rank five model with quartic interactions, demonstrating its renormalizability and non-perturbative asymptotic freedom.

Contribution

It establishes the power counting, divergence structure, and RG flow of a new rank five tensor field theory, providing evidence of its non-perturbative asymptotic freedom.

Findings

Identified divergent graphs in the model

Established the power counting scheme

Provided evidence of non-perturbative asymptotic freedom

Abstract

We continue the constructive program about tensor field theory through the next natural model, namely the rank five tensor theory with quartic melonic interactions and propagator inverse of the Laplacian on $U(1)^5$. We make a first step towards its construction by establishing its power counting, identifiying the divergent graphs and performing a careful study of (a slight modification of) its RG flow. Thus we give strong evidence that this just renormalizable tensor field theory is non perturbatively asymptotically free.