Beta functions of $U(1)^d$ gauge invariant just renormalizable tensor models

TL;DR

This paper computes the first order beta functions of certain gauge-invariant tensor models, demonstrating their asymptotic freedom in the ultraviolet regime, which advances understanding of their renormalization properties.

Contribution

It provides the first calculation of beta functions for $U(1)^d$ gauge-invariant tensor models, revealing their asymptotic freedom and contributing to tensor model renormalization theory.

Findings

Both models are asymptotically free in the UV.

First order beta functions are explicitly computed.

Models considered are polynomial Abelian $ ext{ϕ}^4_6$ and $ ext{ϕ}^6_5$.

Abstract

This manuscript reports the first order $\beta$-functions of recently proved just renormalizable random tensor models endowed with a $U(1)^d$ gauge invariance [arXiv:1211. 2618]. The models that we consider are polynomial Abelian $\vp^4_6$ and $\vp^6_5$ models. We show in this work that both models are asymptotically free in the UV.