Dimensional Deception from Noncommutative Tori: An alternative to Horava-Lifschitz

TL;DR

This paper investigates the geometry of quantum spaces, specifically fuzzy tori, revealing a non-trivial flow of scaling dimension from 2 in the IR to 1 in the UV without preferred directions, contrasting with Horava-Lifshitz models.

Contribution

It introduces a new model based on fuzzy tori with a natural deformed Laplace operator, demonstrating a dimension flow achieved through degrees of freedom rearrangement, not directional bias.

Findings

Scaling dimension flows from 2 to 1 across scales.

The model lacks preferred directions unlike Horava-Lifshitz.

Physical implications of dimension flow are discussed.

Abstract

We study the dimensional aspect of the geometry of quantum spaces. Introducing a physically motivated notion of the scaling dimension, we study in detail the model based on a fuzzy torus. We show that for a natural choice of a deformed Laplace operator, this model demonstrates quite non-trivial behaviour: the scaling dimension flows from 2 in IR to 1 in UV. Unlike another model with the similar property, the so-called Horava-Lifshitz model, our construction does not have any preferred direction. The dimension flow is rather achieved by a rearrangement of the degrees of freedom. In this respect the number of dimensions is deceptive. Some physical consequences are discussed.