Just Renormalizable TGFT's on U(1)^d with Gauge Invariance

TL;DR

This paper proves the all-order renormalizability of certain tensorial group field theories with gauge invariance on U(1)^d, including models that are super-renormalizable, advancing the understanding of their quantum properties.

Contribution

It establishes the just renormalizability of specific Abelian tensorial group field theories with gauge invariance in arbitrary dimensions, including super-renormalizable cases.

Findings

Proves all-order perturbative renormalizability of phi^4_6 and phi^6_5 models.

Shows phi^4_5 tensor model is super-renormalizable.

Analyzes tensorial group field theories with gauge invariance on U(1)^d.

Abstract

We study the polynomial Abelian or U(1)^d Tensorial Group Field Theories equipped with a gauge invariance condition in any dimension d. From our analysis, we prove the just renormalizability at all orders of perturbation of the phi^4_6 and phi^6_5 random tensor models. We also deduce that the phi^4_5 tensor model is super-renormalizable.