3D Tensor Field Theory: Renormalization and One-loop $\beta$-functions

TL;DR

This paper proves the renormalizability of a rank 3 tensor field theory in momentum space and computes its one-loop beta functions, revealing asymptotic freedom in the ultraviolet regime.

Contribution

It establishes the all-order renormalizability of a specific rank 3 tensor model and calculates its one-loop beta functions, demonstrating asymptotic freedom.

Findings

Model is renormalizable at all orders in perturbation theory.

One-loop beta functions show the model is asymptotically free.

The theory has a single coupling constant and wave function renormalization.

Abstract

We prove that the rank 3 analogue of the tensor model defined in [arXiv:1111.4997 [hep-th]] is renormalizable at all orders of perturbation. The proof is given in the momentum space. The one-loop $\gamma$- and $\beta$-functions of the model are also determined. We find that the model with a unique coupling constant for all interactions and a unique wave function renormalization is asymptotically free in the UV.