Some classes of renormalizable tensor models

TL;DR

This paper introduces new classes of renormalizable tensor models by transforming existing models through a rank-changing mapping, revealing connections between tensor, matrix, and vector models with implications for their renormalizability.

Contribution

It presents a novel mapping technique that relates tensor models of different ranks, demonstrating renormalizability transfer and uncovering super-renormalizable vector models from tensor models.

Findings

Identified new families of renormalizable tensor models.

Established a rank-changing mapping preserving renormalizability.

Reduced rank 3 tensor model to a super-renormalizable vector model.

Abstract

We identify new families of renormalizable of tensor models from anterior renormalizable tensor models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property. Mainly, a version of the rank 3 tensor model as defined in [arXiv:1201.0176 [hep-th]], the Grosse-Wulkenhaar model in 4D and 2D generate three different classes of renormalizable models. The proof of the renormalizability is fully performed for the first reduced model. The same procedure can be applied for the remaining cases. Interestingly, we find that, due to the peculiar behavior of anisotropic wave function renormalizations, the rank 3 tensor model reduced to a matrix model generates a simple super-renormalizable vector model.